Changes

====Excerpt 1. Leibniz====

====Excerpt 1. Leibniz====

<p>Now that I have proved sufficiently that everything comes to pass according to determinate reasons, there cannot be any more difficulty over these principles of God's foreknowledge.  Although these determinations do not compel, they cannot but be certain, and they foreshadow what shall happen.</p>

<p>Now that I have proved sufficiently that everything comes to pass according to determinate reasons, there cannot be any more difficulty over these principles of God's foreknowledge.  Although these determinations do not compel, they cannot but be certain, and they foreshadow what shall happen.</p>

<p>What is more, I have proved conclusively that God sees in each portion of the universe the whole universe, owing to the perfect connexion of things.  He is infinitely more discerning than Pythagoras, who judged the height of Hercules by the size of his footprint.  There must therefore be no doubt that effects follow their causes determinately, in spite of contingency and even of freedom, which nevertheless exist together with certainty or determination.</p>

<p>What is more, I have proved conclusively that God sees in each portion of the universe the whole universe, owing to the perfect connexion of things.  He is infinitely more discerning than Pythagoras, who judged the height of Hercules by the size of his footprint.  There must therefore be no doubt that effects follow their causes determinately, in spite of contingency and even of freedom, which nevertheless exist together with certainty or determination.</p>

<p>Gottfried Wilhelm (Freiherr von) Leibniz, ''Theodicy : Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil'', Edited with an Introduction by Austin Farrer, Translated by E.M. Huggard from C.J. Gerhardt's Edition of the ''Collected Philosophical Works'', 1875&ndash;1890.  Routledge 1951.  Open Court 1985.  Paragraph 360, page 341.</p>

<p>Gottfried Wilhelm (Freiherr von) Leibniz, ''Theodicy : Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil'', Edited with an Introduction by Austin Farrer, Translated by E.M. Huggard from C.J. Gerhardt's Edition of the ''Collected Philosophical Works'', 1875&ndash;1890.  Routledge 1951.  Open Court 1985.  Paragraph 360, page 341.</p>

====Excerpt 2. Prigogine====

====Excerpt 2. Prigogine====

<p>Earlier this century in ''The Open Universe : An Argument for Indeterminism'', Karl Popper wrote, "Common sense inclines, on the one hand, to assert that every event is caused by some preceding events, so that every event can be explained or predicted. &hellip; On the other hand, &hellip; common sense attributes to mature and sane human persons &hellip; the ability to choose freely between alternative possibilities of acting." This "dilemma of determinism", as William James called it, is closely related to the meaning of time.  Is the future given, or is it under perpetual construction?  A profound dilemma for all of mankind, as time is the fundamental dimension of our existence.</p>

<p>Earlier this century in ''The Open Universe : An Argument for Indeterminism'', Karl Popper wrote, &ldquo;Common sense inclines, on the one hand, to assert that every event is caused by some preceding events, so that every event can be explained or predicted. &hellip; On the other hand, &hellip; common sense attributes to mature and sane human persons &hellip; the ability to choose freely between alternative possibilities of acting.&rdquo; This &ldquo;dilemma of determinism&rdquo;, as William James called it, is closely related to the meaning of time.  Is the future given, or is it under perpetual construction?  A profound dilemma for all of mankind, as time is the fundamental dimension of our existence.</p>

<p>Ilya Prigogine (with Isabelle Stengers), ''The End of Certainty : Time, Chaos, and the New Laws of Nature'', The Free Press, New York, NY, 1997, p. 1.  Originally published as ''La Fin des Certitudes'', Éditions Odile Jacob, 1996.</p>

<p>Ilya Prigogine (with Isabelle Stengers), ''The End of Certainty : Time, Chaos, and the New Laws of Nature'', The Free Press, New York, NY, 1997, p. 1.  Originally published as ''La Fin des Certitudes'', Éditions Odile Jacob, 1996.</p>

====Excerpt 3. Peirce (CP 6.347)====

====Excerpt 3. Peirce (CP 6.347)====

<p>Of triadic Being the multitude of forms is so terrific that I have usually shrunk from the task of enumerating them;  and for the present purpose such an enumeration would be worse than superfluous:  it would be a great inconvenience.  In another paper, I intend to give the formal definition of a sign, which I have worked out by arduous and long labour.  I will omit the explanation of it here.</p>

<p>Of triadic Being the multitude of forms is so terrific that I have usually shrunk from the task of enumerating them;  and for the present purpose such an enumeration would be worse than superfluous:  it would be a great inconvenience.  In another paper, I intend to give the formal definition of a sign, which I have worked out by arduous and long labour.  I will omit the explanation of it here.</p>

<p>Suffice it to say that a sign endeavors to represent, in part at least, an Object, which is therefore in a sense the cause, or determinant, of the sign even if the sign represents its object falsely.  But to say that it represents its Object implies that it affects a mind, and so affects it as, in some respect, to determine in that mind something that is mediately due to the Object.  That determination of which the immediate cause, or determinant, is the Sign, and of which the mediate cause is the Object may be termed the ''Interpretant''.</p>

<p>Suffice it to say that a sign endeavors to represent, in part at least, an Object, which is therefore in a sense the cause, or determinant, of the sign even if the sign represents its object falsely.  But to say that it represents its Object implies that it affects a mind, and so affects it as, in some respect, to determine in that mind something that is mediately due to the Object.  That determination of which the immediate cause, or determinant, is the Sign, and of which the mediate cause is the Object may be termed the ''Interpretant''.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 6.347</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 6.347</p>

====Excerpt 4. Peirce (CP 6.332)====

====Excerpt 4. Peirce (CP 6.332)====

<p>That whatever action is brute, unintelligent, and unconcerned with the result of it is purely dyadic is either demonstrable or is too evident to be demonstrable.  But in case that dyadic action is merely a member of a triadic action, then so far from its furnishing the least shade of presumption that all the action in the physical universe is dyadic, on the contrary, the entire and triadic action justifies a guess that there may be other and more marked examples in the universe of the triadic pattern.  No sooner is the guess made than instances swarm upon us amply verifying it, and refuting the agnostic position;  while others present new problems for our study.  With the refutation of agnosticism, the agnostic is shown to be a superficial neophyte in philosophy, entitled at most to an occasional audience on special points, yet infinitely more respectable than those who seek to bolster up what is really true by sophistical arguments &mdash; the traitors to truth that they are.</p>

<p>That whatever action is brute, unintelligent, and unconcerned with the result of it is purely dyadic is either demonstrable or is too evident to be demonstrable.  But in case that dyadic action is merely a member of a triadic action, then so far from its furnishing the least shade of presumption that all the action in the physical universe is dyadic, on the contrary, the entire and triadic action justifies a guess that there may be other and more marked examples in the universe of the triadic pattern.  No sooner is the guess made than instances swarm upon us amply verifying it, and refuting the agnostic position;  while others present new problems for our study.  With the refutation of agnosticism, the agnostic is shown to be a superficial neophyte in philosophy, entitled at most to an occasional audience on special points, yet infinitely more respectable than those who seek to bolster up what is really true by sophistical arguments &mdash; the traitors to truth that they are.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 6.332</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 6.332</p>

====Excerpt 5. Peirce (CP 5.447)====

====Excerpt 5. Peirce (CP 5.447)====

<p>Accurate writers have apparently made a distinction between the ''definite'' and the ''determinate''.  A subject is ''determinate'' in respect to any character which inheres in it or is (universally and affirmatively) predicated of it, as well as in respect to the negative of such character, these being the very same respect.  In all other respects it is ''indeterminate''.  The ''definite'' shall be defined presently.</p>

<p>Accurate writers have apparently made a distinction between the ''definite'' and the ''determinate''.  A subject is ''determinate'' in respect to any character which inheres in it or is (universally and affirmatively) predicated of it, as well as in respect to the negative of such character, these being the very same respect.  In all other respects it is ''indeterminate''.  The ''definite'' shall be defined presently.</p>

<p>A sign (under which designation I place every kind of thought, and not alone external signs), that is in any respect objectively indeterminate (i.e., whose object is undetermined by the sign itself) is objectively 'general' in so far as it extends to the interpreter the privilege of carrying its determination further.</p>

<p>A sign (under which designation I place every kind of thought, and not alone external signs), that is in any respect objectively indeterminate (i.e., whose object is undetermined by the sign itself) is objectively 'general' in so far as it extends to the interpreter the privilege of carrying its determination further.</p>

<p>''Example:''  "Man is mortal." To the question, What man? the reply is that the proposition explicitly leaves it to you to apply its assertion to what man or men you will.</p>

<p>''Example:''  &ldquo;Man is mortal.&rdquo; To the question, What man? the reply is that the proposition explicitly leaves it to you to apply its assertion to what man or men you will.</p>

<p>A sign that is objectively indeterminate in any respect is objectively ''vague'' in so far as it reserves further determination to be made in some other conceivable sign, or at least does not appoint the interpreter as its deputy in this office.</p>

<p>A sign that is objectively indeterminate in any respect is objectively ''vague'' in so far as it reserves further determination to be made in some other conceivable sign, or at least does not appoint the interpreter as its deputy in this office.</p>

<p>''Example:''  "A man whom I could mention seems to be a little conceited." The ''suggestion'' here is that the man in view is the person addressed;  but the utterer does not authorize such an interpretation or ''any'' other application of what she says.  She can still say, if she likes, that she does ''not'' mean the person addressed.</p>

<p>''Example:''  &ldquo;A man whom I could mention seems to be a little conceited.&rdquo; The ''suggestion'' here is that the man in view is the person addressed;  but the utterer does not authorize such an interpretation or ''any'' other application of what she says.  She can still say, if she likes, that she does ''not'' mean the person addressed.</p>

<p>Every utterance naturally leaves the right of further exposition in the utterer;  and therefore, in so far as a sign is indeterminate, it is vague, unless it is expressly or by a well-understood convention rendered general.</p>

<p>Every utterance naturally leaves the right of further exposition in the utterer;  and therefore, in so far as a sign is indeterminate, it is vague, unless it is expressly or by a well-understood convention rendered general.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 5.447</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 5.447</p>

====Excerpt 6. Peirce (CP 5.448)====

====Excerpt 6. Peirce (CP 5.448)====

<p>Perhaps a more scientific pair of definitions would be that anything is ''general'' in so far as the principle of the excluded middle does not apply to it and is ''vague'' in so far as the principle of contradiction does not apply to it.</p>

<p>Perhaps a more scientific pair of definitions would be that anything is ''general'' in so far as the principle of the excluded middle does not apply to it and is ''vague'' in so far as the principle of contradiction does not apply to it.</p>

<p>Thus, although it is true that "Any proposition you please, ''once you have determined its identity'', is either true or false";  yet ''so long as it remains indeterminate and so without identity'', it need neither be true that any proposition you please is true, nor that any proposition you please is false.</p>

<p>Thus, although it is true that &ldquo;Any proposition you please, ''once you have determined its identity'', is either true or false&rdquo;;  yet ''so long as it remains indeterminate and so without identity'', it need neither be true that any proposition you please is true, nor that any proposition you please is false.</p>

<p>So likewise, while it is false that "A proposition ''whose identity I have determined'' is both true and false", yet until it is determinate, it may be true that a proposition is true and that a proposition is false.</p>

<p>So likewise, while it is false that &ldquo;A proposition ''whose identity I have determined'' is both true and false&rdquo;, yet until it is determinate, it may be true that a proposition is true and that a proposition is false.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 5.448</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 5.448</p>

====Excerpt 7. Peirce (CP 5.448, n. 1)====

====Excerpt 7. Peirce (CP 5.448, n. 1)====

<p>These remarks require supplementation.  Determination, in general, is not defined at all;  and the attempt at defining the determination of a subject with respect to a character only covers (or seems only to cover) explicit propositional determination.</p>

<p>These remarks require supplementation.  Determination, in general, is not defined at all;  and the attempt at defining the determination of a subject with respect to a character only covers (or seems only to cover) explicit propositional determination.</p>

<p>The incidental remark [5.447] to the effect that words whose meaning should be determinate would leave "no latitude of interpretation" is more satisfactory, since the context makes it plain that there must be no such latitude either for the interpreter or for the utterer.  The explicitness of the words would leave the utterer no room for explanation of his meaning.  This definition has the advantage of being applicable to a command, to a purpose, to a medieval substantial form;  in short to anything capable of indeterminacy.</p>

<p>The incidental remark [5.447] to the effect that words whose meaning should be determinate would leave &ldquo;no latitude of interpretation&rdquo; is more satisfactory, since the context makes it plain that there must be no such latitude either for the interpreter or for the utterer.  The explicitness of the words would leave the utterer no room for explanation of his meaning.  This definition has the advantage of being applicable to a command, to a purpose, to a medieval substantial form;  in short to anything capable of indeterminacy.</p>

<p>(That everything indeterminate is of the nature of a sign can be proved inductively by imagining and analyzing instances of the surdest description.  Thus, the indetermination of an event which should happen by pure chance without cause, ''sua sponte'', as the Romans mythologically said, ''spontanément'' in French (as if what was done of one's own motion were sure to be irrational), does not belong to the event &mdash; say, an explosion &mdash; ''per se'', or as an explosion.  Neither is it by virtue of any real relation:  it is by virtue of a relation of reason.  Now what is true by virtue of a relation of reason is representative, that is, is of the nature of a sign.  A similar consideration applies to the indiscriminate shots and blows of a Kentucky free fight.)</p>

<p>(That everything indeterminate is of the nature of a sign can be proved inductively by imagining and analyzing instances of the surdest description.  Thus, the indetermination of an event which should happen by pure chance without cause, ''sua sponte'', as the Romans mythologically said, ''spontanément'' in French (as if what was done of one's own motion were sure to be irrational), does not belong to the event &mdash; say, an explosion &mdash; ''per se'', or as an explosion.  Neither is it by virtue of any real relation:  it is by virtue of a relation of reason.  Now what is true by virtue of a relation of reason is representative, that is, is of the nature of a sign.  A similar consideration applies to the indiscriminate shots and blows of a Kentucky free fight.)</p>

<p>Even a future event can only be determinate in so far as it is a consequent.  Now the concept of a consequent is a logical concept.  It is derived from the concept of the conclusion of an argument.  But an argument is a sign of the truth of its conclusion;  its conclusion is the rational ''interpretation'' of the sign.  This is in the spirit of the Kantian doctrine that metaphysical concepts are logical concepts applied somewhat differently from their logical application.  The difference, however, is not really as great as Kant represents it to be, and as he was obliged to represent it to be, owing to his mistaking the logical and metaphysical correspondents in almost every case.</p>

<p>Even a future event can only be determinate in so far as it is a consequent.  Now the concept of a consequent is a logical concept.  It is derived from the concept of the conclusion of an argument.  But an argument is a sign of the truth of its conclusion;  its conclusion is the rational ''interpretation'' of the sign.  This is in the spirit of the Kantian doctrine that metaphysical concepts are logical concepts applied somewhat differently from their logical application.  The difference, however, is not really as great as Kant represents it to be, and as he was obliged to represent it to be, owing to his mistaking the logical and metaphysical correspondents in almost every case.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 5.448, n. 1</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 5.448, n. 1</p>

====Excerpt 8. Peirce (CP 5.448, n. 1)====

====Excerpt 8. Peirce (CP 5.448, n. 1)====

<p>Another advantage of this definition is that it saves us from the blunder of thinking that a sign is indeterminate simply because there is much to which it makes no reference;  that, for example, to say, "C.S. Peirce wrote this article", is indeterminate because it does not say what the color of the ink used was, who made the ink, how old the father of the ink-maker when his son was born, nor what the aspect of the planets was when that father was born.  By making the definition turn upon the interpretation, all that is cut off.</p>

<p>Another advantage of this definition is that it saves us from the blunder of thinking that a sign is indeterminate simply because there is much to which it makes no reference;  that, for example, to say, &ldquo;C.S. Peirce wrote this article&rdquo;, is indeterminate because it does not say what the color of the ink used was, who made the ink, how old the father of the ink-maker when his son was born, nor what the aspect of the planets was when that father was born.  By making the definition turn upon the interpretation, all that is cut off.</p>

<p>C.S. Peirce, ''Collected Papers;'', CP 5.448, n. 1</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 5.448, n. 1</p>

====Excerpt 9. Peirce (CP 5.448, n. 1)====

====Excerpt 9. Peirce (CP 5.448, n. 1)====

<p>At the same time, it is tolerably evident that the definition, as it stands, is not sufficiently explicit, and further, that at the present stage of our inquiry cannot be made altogether satisfactory.  For what is the interpretation alluded to?  To answer that convincingly would be either to establish or to refute the doctrine of pragmaticism.</p>

<p>At the same time, it is tolerably evident that the definition, as it stands, is not sufficiently explicit, and further, that at the present stage of our inquiry cannot be made altogether satisfactory.  For what is the interpretation alluded to?  To answer that convincingly would be either to establish or to refute the doctrine of pragmaticism.</p>

<p>[And so] the latitude of interpretation which constitutes the indeterminacy of a sign must be understood as a latitude which might affect the achievement of a purpose.  For two signs whose meanings are for all possible purposes equivalent are absolutely equivalent.  This, to be sure, is rank pragmaticism;  for a purpose is an affection of action.</p>

<p>[And so] the latitude of interpretation which constitutes the indeterminacy of a sign must be understood as a latitude which might affect the achievement of a purpose.  For two signs whose meanings are for all possible purposes equivalent are absolutely equivalent.  This, to be sure, is rank pragmaticism;  for a purpose is an affection of action.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 5.448, n. 1</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 5.448, n. 1</p>

====Excerpt 10. Peirce (CP 5.448, n. 1)====

====Excerpt 10. Peirce (CP 5.448, n. 1)====

<p>The October remarks [i.e. those in the above paper] made the proper distinction between the two kinds of indeterminacy, viz.:  indefiniteness and generality, of which the former consists in the sign's not sufficiently expressing itself to allow of an indubitable determinate interpretation, while the [latter] turns over to the interpreter the right to complete the determination as he please.</p>

<p>The October remarks [i.e. those in the above paper] made the proper distinction between the two kinds of indeterminacy, viz.:  indefiniteness and generality, of which the former consists in the sign's not sufficiently expressing itself to allow of an indubitable determinate interpretation, while the [latter] turns over to the interpreter the right to complete the determination as he please.</p>

<p>It seems a strange thing, when one comes to ponder over it, that a sign should leave its interpreter to supply a part of its meaning;  but the explanation of the phenomenon lies in the fact that the entire universe &mdash; not merely the universe of existents, but all that wider universe, embracing the universe of existents as a part, the universe which we are all accustomed to refer to as "the truth" &mdash; that all this universe is perfused with signs, if it is not composed exclusively of signs.  Let us note this in passing as having a bearing upon the question of pragmaticism.</p>

<p>It seems a strange thing, when one comes to ponder over it, that a sign should leave its interpreter to supply a part of its meaning;  but the explanation of the phenomenon lies in the fact that the entire universe &mdash; not merely the universe of existents, but all that wider universe, embracing the universe of existents as a part, the universe which we are all accustomed to refer to as &ldquo;the truth&rdquo; &mdash; that all this universe is perfused with signs, if it is not composed exclusively of signs.  Let us note this in passing as having a bearing upon the question of pragmaticism.</p>

<p>The October remarks, with a view to brevity, omitted to mention that both indefiniteness and generality might primarily affect either the logical breadth or the logical depth of the sign to which it belongs.  It now becomes pertinent to notice this.  When we speak of the depth, or signification, of a sign we are resorting to hypostatic abstraction, that process whereby we regard a thought as a thing, make an interpretant sign the object of a sign.</p>

<p>The October remarks, with a view to brevity, omitted to mention that both indefiniteness and generality might primarily affect either the logical breadth or the logical depth of the sign to which it belongs.  It now becomes pertinent to notice this.  When we speak of the depth, or signification, of a sign we are resorting to hypostatic abstraction, that process whereby we regard a thought as a thing, make an interpretant sign the object of a sign.</p>

<p>At any rate, whenever we speak of a predicate we are representing a thought as a thing, as a ''substantia'', since the concepts of ''substance'' and ''subject'' are one, its concomitants only being different in the two cases.  It is needful to remark this in the present connexion, because, were it not for hypostatic abstraction, there could be no generality of a predicate, since a sign which should make its interpreter its deputy to determine its signification at his pleasure would not signify anything, unless ''nothing'' be its significate.</p>

<p>At any rate, whenever we speak of a predicate we are representing a thought as a thing, as a ''substantia'', since the concepts of ''substance'' and ''subject'' are one, its concomitants only being different in the two cases.  It is needful to remark this in the present connexion, because, were it not for hypostatic abstraction, there could be no generality of a predicate, since a sign which should make its interpreter its deputy to determine its signification at his pleasure would not signify anything, unless ''nothing'' be its significate.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 5.448, n. 1</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 5.448, n. 1</p>

====Excerpt 11. Peirce (CP 2.364)====

====Excerpt 11. Peirce (CP 2.364)====

<p>Concepts, or terms, are, in logic, conceived to have ''subjective parts'', being the narrower terms into which they are divisible, and ''definitive parts'', which are the higher terms of which their definitions or descriptions are composed:  these relationships constitute "quantity".</p>

<p>Concepts, or terms, are, in logic, conceived to have ''subjective parts'', being the narrower terms into which they are divisible, and ''definitive parts'', which are the higher terms of which their definitions or descriptions are composed:  these relationships constitute &ldquo;quantity&rdquo;.</p>

<p>This double way of regarding a class-term as a whole of parts is remarked by Aristotle in several places (e.g., ''Metaphysics'', D. xxv. 1023 b22).  It was familiar to logicians of every age. &hellip; and it really seems to have been Kant who made these ideas pervade logic and who first expressly called them quantities.  But the idea was old.</p>

<p>This double way of regarding a class-term as a whole of parts is remarked by Aristotle in several places (e.g., ''Metaphysics'', D. xxv. 1023 b22).  It was familiar to logicians of every age. &hellip; and it really seems to have been Kant who made these ideas pervade logic and who first expressly called them quantities.  But the idea was old.</p>

<p>Archbishop Thomson, W.D. Wilson, and C.S. Peirce endeavor to make out a third quantity of terms.  The last calls his third quantity "information", and defines it as the "sum of synthetical propositions in which the symbol is subject or predicate", antecedent or consequent.  The word "symbol" is here employed because this logician regards the quantities as belonging to propositions and to arguments, as well as to terms.</p>

<p>Archbishop Thomson, W.D. Wilson, and C.S. Peirce endeavor to make out a third quantity of terms.  The last calls his third quantity &ldquo;information&rdquo;, and defines it as the &ldquo;sum of synthetical propositions in which the symbol is subject or predicate&rdquo;, antecedent or consequent.  The word &ldquo;symbol&rdquo; is here employed because this logician regards the quantities as belonging to propositions and to arguments, as well as to terms.</p>

<p>A distinction of ''extensive'' and ''comprehensive distinctness'' is due to Scotus (''Opus Oxon.'', I. ii. 3):  namely, the usual effect upon a term of an increase of information will be either to increase its breadth without without diminishing its depth, or to increase its depth without diminishing its breadth.  But the effect may be to show that the subjects to which the term was already known to be applicable include the entire breadth of another another term which had not been known to be so included.  In that case, the first term has gained in ''extensive distinctness''.  Or the effect may be to teach that the marks already known to be predicable of the term include the entire depth of another term not previously known to be so included, thus increasing the ''comprehensive distinctness'' of the former term.</p>

<p>A distinction of ''extensive'' and ''comprehensive distinctness'' is due to Scotus (''Opus Oxon.'', I. ii. 3):  namely, the usual effect upon a term of an increase of information will be either to increase its breadth without without diminishing its depth, or to increase its depth without diminishing its breadth.  But the effect may be to show that the subjects to which the term was already known to be applicable include the entire breadth of another another term which had not been known to be so included.  In that case, the first term has gained in ''extensive distinctness''.  Or the effect may be to teach that the marks already known to be predicable of the term include the entire depth of another term not previously known to be so included, thus increasing the ''comprehensive distinctness'' of the former term.</p>

<p>When an increase of real information has the effect of increasing the depth of a term without diminishing the breadth, the proper word for the process is ''amplification''.  In ordinary language, we are inaccurately said to ''specify'', instead of to ''amplify'', when we add to information in this way.  The logical operation of forming a hypothesis often has this effect, which may, in such case, be called ''supposition''.  Almost any increase of depth may be called ''determination''.</p>

<p>When an increase of real information has the effect of increasing the depth of a term without diminishing the breadth, the proper word for the process is ''amplification''.  In ordinary language, we are inaccurately said to ''specify'', instead of to ''amplify'', when we add to information in this way.  The logical operation of forming a hypothesis often has this effect, which may, in such case, be called ''supposition''.  Almost any increase of depth may be called ''determination''.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 2.364</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 2.364</p>

====Excerpt 12. Shipley====

====Excerpt 12. Shipley====

<p>'''Determine.'''</p>

<p>'''Determine.'''</p>

<p>To ''determine'' is to set down limits or bounds to something, as when you ''determine'' to perform a task, or as ''determinism'' pictures limits set to man's freedom.  ''Predetermined'' follows this sense;  but ''extermination'' comes later.  Otherwise, existence would be ''interminable''.</p>

<p>To ''determine'' is to set down limits or bounds to something, as when you ''determine'' to perform a task, or as ''determinism'' pictures limits set to man's freedom.  ''Predetermined'' follows this sense;  but ''extermination'' comes later.  Otherwise, existence would be ''interminable''.</p>

<p>Joseph T. Shipley, ''Dictionary of Word Origins'', Rowman and Allanheld, Totowa, NJ, 1967, 1985.</p>

<p>Joseph T. Shipley, ''Dictionary of Word Origins'', Rowman and Allanheld, Totowa, NJ, 1967, 1985.</p>

====Excerpt 13. Peirce (CE 1, 245&ndash;246)====

====Excerpt 13. Peirce (CE 1, 245&ndash;246)====

<p>To determine means to make a circumstance different from what it might have been otherwise.  For example, a drop of rain falling on a stone determines it to be wet, provided the stone may have been dry before.  But if the fact of a whole shower half an hour previous is given, then one drop does not determine the stone to be wet;  for it would be wet, at any rate.</p>

<p>To determine means to make a circumstance different from what it might have been otherwise.  For example, a drop of rain falling on a stone determines it to be wet, provided the stone may have been dry before.  But if the fact of a whole shower half an hour previous is given, then one drop does not determine the stone to be wet;  for it would be wet, at any rate.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 245&ndash;246</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 245&ndash;246</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 14. Peirce (CE 1, 168&ndash;169)====

====Excerpt 14. Peirce (CE 1, 168&ndash;169)====

<p>Taking it for granted, then, that the inner and outer worlds are superposed throughout, without possibility of separation, let us now proceed to another point.  There is a third world, besides the inner and the outer;  and all three are coëxtensive and contain every experience.  Suppose that we have an experience.  That experience has three determinations &mdash; three different references to a substratum or substrata, lying behind it and determining it.</p>

<p>Taking it for granted, then, that the inner and outer worlds are superposed throughout, without possibility of separation, let us now proceed to another point.  There is a third world, besides the inner and the outer;  and all three are coëxtensive and contain every experience.  Suppose that we have an experience.  That experience has three determinations &mdash; three different references to a substratum or substrata, lying behind it and determining it.</p>

<p>In the second place, it is a determination of our own soul, it is ''our'' experience;  we feel that it is so because it lasts in time.  Were it a flash of sensation, there for less than an instant, and then utterly gone from memory, we should not have time to think it ours.  But while it lasts, and we reflect upon it, it enters into the internal world.</p>

<p>In the second place, it is a determination of our own soul, it is ''our'' experience;  we feel that it is so because it lasts in time.  Were it a flash of sensation, there for less than an instant, and then utterly gone from memory, we should not have time to think it ours.  But while it lasts, and we reflect upon it, it enters into the internal world.</p>

<p>We have now considered that experience as a determination of the modifying object and of the modified soul;  now, I say, it may be and is naturally regarded as also a determination of an idea of the Universal mind;  a preëxistent, archetypal Idea.  Arithmetic, the law of number, ''was'' before anything to be numbered or any mind to number had been created.  It ''was'' though it did not ''exist''.  It was not ''a fact'' nor a thought, but it was an unuttered word.   Ἐν ἀρχῇ ἦν ὁ λόγος.  We feel an experience to be a determination of such an archetypal <font size="2">L</font><font size="1">OGOS</font>, by virtue of its //&nbsp;''depth of tone'' / logical intension&nbsp;//, and thereby it is in the ''logical world''.</p>

<p>We have now considered that experience as a determination of the modifying object and of the modified soul;  now, I say, it may be and is naturally regarded as also a determination of an idea of the Universal mind;  a preëxistent, archetypal Idea.  Arithmetic, the law of number, ''was'' before anything to be numbered or any mind to number had been created.  It ''was'' though it did not ''exist''.  It was not ''a fact'' nor a thought, but it was an unuttered word. Ἐν ἀρχῇ ἦν ὁ λόγος.  We feel an experience to be a determination of such an archetypal <font size="2">L</font><font size="1">OGOS</font>, by virtue of its //&nbsp;''depth of tone'' / logical intension&nbsp;//, and thereby it is in the ''logical world''.</p>

<p>Note the great difference between this view and Hegel's.  Hegel says, logic is the science of the pure idea.  I should describe it as the science of the laws of experience in virtue of its being a determination of the idea, or in other words as the formal science of the logical world.</p>

<p>Note the great difference between this view and Hegel's.  Hegel says, logic is the science of the pure idea.  I should describe it as the science of the laws of experience in virtue of its being a determination of the idea, or in other words as the formal science of the logical world.</p>

<p>In this point of view, efforts to ascertain precisely how the intellect works in thinking, &mdash; that is to say investigation of internal characterictics &mdash; is no more to the purpose which logical writers as such, however vaguely have in view, than would be the investigation of external characteristics.</p>

<p>In this point of view, efforts to ascertain precisely how the intellect works in thinking, &mdash; that is to say investigation of internal characteristics &mdash; is no more to the purpose which logical writers as such, however vaguely have in view, than would be the investigation of external characteristics.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 168&ndash;169</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 168&ndash;169</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 15. Peirce (CE 1, 174&ndash;175)====

====Excerpt 15. Peirce (CE 1, 174&ndash;175)====

<p>But not to follow this subject too far, we have now established three species of representations:  ''copies'', ''signs'', and ''symbols'';  of the last of which only logic treats.  A second approximation to a definition of it then will be, the science of symbols in general and as such.  But this definition is still too broad;  this might, indeed, form the definition of a certain science which would be a branch of Semiotic or the general science of representations which might be called Symbolistic, and of this logic would be a species.  But logic only considers symbols from a particular point of view.</p>

<p>But not to follow this subject too far, we have now established three species of representations:  ''copies'', ''signs'', and ''symbols'';  of the last of which only logic treats.  A second approximation to a definition of it then will be, the science of symbols in general and as such.  But this definition is still too broad;  this might, indeed, form the definition of a certain science which would be a branch of Semiotic or the general science of representations which might be called Symbolistic, and of this logic would be a species.  But logic only considers symbols from a particular point of view.</p>

<p>At the same time ''symbolistic'' in general gives a trivium consisting of Universal Grammar, Logic, and Universal Rhetoric, using this last term to signify the science of the formal conditions of intelligibility of symbols.</p>

<p>At the same time ''symbolistic'' in general gives a trivium consisting of Universal Grammar, Logic, and Universal Rhetoric, using this last term to signify the science of the formal conditions of intelligibility of symbols.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 174&ndash;175</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 174&ndash;175</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 16. Peirce (CE 1, 179)====

====Excerpt 16. Peirce (CE 1, 179)====

<p>The consideration of this imperfect datum leads us to make a fundamental observation;  namely, that the problem how we can make an induction is one and the same with the problem how we can make any general statement, with reason;  for there is no way left in which such a statement can originate except from induction or pure fiction.  Hereby, we strike down at once all attempts at solving the problem as involve the supposition of a major premiss as a datum.  Such explanations merely show that we can arrive at one general statement by deduction from another, while they leave the real question, untouched.  The peculiar merit of Aristotle's theory is that after the objectionable portion of it is swept away and after it has thereby been left utterly powerless to account for any certainty or even probability in the inference from induction, we still retain these ''forms'' which show what the ''actual process'' is.</p>

<p>The consideration of this imperfect datum leads us to make a fundamental observation;  namely, that the problem how we can make an induction is one and the same with the problem how we can make any general statement, with reason;  for there is no way left in which such a statement can originate except from induction or pure fiction.  Hereby, we strike down at once all attempts at solving the problem as involve the supposition of a major premiss as a datum.  Such explanations merely show that we can arrive at one general statement by deduction from another, while they leave the real question, untouched.  The peculiar merit of Aristotle's theory is that after the objectionable portion of it is swept away and after it has thereby been left utterly powerless to account for any certainty or even probability in the inference from induction, we still retain these ''forms'' which show what the ''actual process'' is.</p>

<p>And what is this process?  We have in the apodictic conclusion, some most extraordinary observation, as for example that a great number of animals &mdash; namely neat and deer, feed only upon vegetables.  This proposition, be it remarked, need not have had any generality;  if the animals observed instead of being all ''neat'' had been so very various that we knew not what to say of them except that they were ''herbivora'' and ''cloven-footed'', the effect would have been to render the argument simply irresistable.  In addition to this datum, we have another;  namely that these same animals are all cloven-footed.  Now it would not be so very strange that all cloven-footed animals should be herbivora;  animals of a particular structure very likely may use a particular food.  But if this be indeed so, then all the marvel of the conclusion is explained away.  So in order to avoid a marvel which must in some form be accepted, we are led to believe what is easy to believe though it is entirely uncertain.</p>

<p>And what is this process?  We have in the apodictic conclusion, some most extraordinary observation, as for example that a great number of animals &mdash; namely neat and deer, feed only upon vegetables.  This proposition, be it remarked, need not have had any generality;  if the animals observed instead of being all ''neat'' had been so very various that we knew not what to say of them except that they were ''herbivora'' and ''cloven-footed'', the effect would have been to render the argument simply irresistible.  In addition to this datum, we have another;  namely that these same animals are all cloven-footed.  Now it would not be so very strange that all cloven-footed animals should be herbivora;  animals of a particular structure very likely may use a particular food.  But if this be indeed so, then all the marvel of the conclusion is explained away.  So in order to avoid a marvel which must in some form be accepted, we are led to believe what is easy to believe though it is entirely uncertain.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 179</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 179</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 17. Peirce (CE 1, 180)====

====Excerpt 17. Peirce (CE 1, 180)====

<p>There is a large class of reasonings which are neither deductive nor inductive.  I mean the inference of a cause from its effect or reasoning to a physical hypothesis.  I call this reasoning ''à posteriori''.  If I reason that certain conduct is wise because it has a character which belongs ''only'' to wise things, I reason ''à priori''.  If I think it is wise because it once turned out to be wise, that is if I infer that it is wise on this occasion because it was wise on that occasion, I reason inductively.  But if I think it is wise because a wise man does it, I then make the pure hypothesis that he does it because he is wise, and I reason ''à posteriori''.  The form this reasoning assumes, is that of an inference of a minor premiss in any of the figures.  The following is an example.</p>

<p>There is a large class of reasonings which are neither deductive nor inductive.  I mean the inference of a cause from its effect or reasoning to a physical hypothesis.  I call this reasoning ''à posteriori''.  If I reason that certain conduct is wise because it has a character which belongs ''only'' to wise things, I reason ''à priori''.  If I think it is wise because it once turned out to be wise, that is if I infer that it is wise on this occasion because it was wise on that occasion, I reason inductively.  But if I think it is wise because a wise man does it, I then make the pure hypothesis that he does it because he is wise, and I reason ''à posteriori''.  The form this reasoning assumes, is that of an inference of a minor premiss in any of the figures.  The following is an example.</p>

|}

|}

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 180</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 180</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 18. Peirce (CE 1, 183)====

====Excerpt 18. Peirce (CE 1, 183)====

<p>We come now to the question, what is the ''rationale'' of these three kinds of reasoning.  And first let us understand precisely what we intend by this.  It is clear then that it is none of our business to inquire in what manner we think when we reason, for we have already seen that logic is wholly separate from psychology.  What we seek is an explicit statement of the logical ground of these different kinds of inference.  This logical ground will have two parts, 1st the ground of possibility and 2nd the ground of proceedure.  The ground of possibility is the special property of symbols upon which every inference of a certain kind rests.  The ground of proceedure is the property of symbols which makes a certain inference possible from certain premisses.  The ground of possibility must be both discovered and demonstrated, fully.  The ground of proceedure must be exhibited in outline, but it is not requisite to fill up all the details of this subject, especially as that would lead us too far into the technicalities of logic.</p>

<p>We come now to the question, what is the ''rationale'' of these three kinds of reasoning.  And first let us understand precisely what we intend by this.  It is clear then that it is none of our business to inquire in what manner we think when we reason, for we have already seen that logic is wholly separate from psychology.  What we seek is an explicit statement of the logical ground of these different kinds of inference.  This logical ground will have two parts, 1st the ground of possibility and 2nd the ground of proceedure.  The ground of possibility is the special property of symbols upon which every inference of a certain kind rests.  The ground of proceedure is the property of symbols which makes a certain inference possible from certain premisses.  The ground of possibility must be both discovered and demonstrated, fully.  The ground of proceedure must be exhibited in outline, but it is not requisite to fill up all the details of this subject, especially as that would lead us too far into the technicalities of logic.</p>

<p>As the three kinds of reasoning are entirely distinct, each must have a different ground of possibility;  and the principle of each kind must be proved by that same kind of inference for it would be absurd to attempt to rest it on a weaker kind of inference and to rest it on one as strong as itself would be simply to reduce it to that other kind of reasoning.  Moreover, these principles must be logical principles because we do not seek any other ground now, than a logical ground.  As logical principles, they will not relate to the symbol in itself or in its relation to equivalent symbols but wholly in its relation to what it symbolizes.  In other words it will relate to the symbolization of objects.</p>

<p>As the three kinds of reasoning are entirely distinct, each must have a different ground of possibility;  and the principle of each kind must be proved by that same kind of inference for it would be absurd to attempt to rest it on a weaker kind of inference and to rest it on one as strong as itself would be simply to reduce it to that other kind of reasoning.  Moreover, these principles must be logical principles because we do not seek any other ground now, than a logical ground.  As logical principles, they will not relate to the symbol in itself or in its relation to equivalent symbols but wholly in its relation to what it symbolizes.  In other words it will relate to the symbolization of objects.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 183</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 183</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 19. Peirce (CE 1, 183&ndash;184)====

====Excerpt 19. Peirce (CE 1, 183&ndash;184)====

<p>Now all symbolization is of three objects, at once;  the first is a possible thing, the second is a possible form, the third is a possible symbol.  It will be objected that the two latter are not properly objects.  We have hitherto regarded the symbol as ''standing for'' the thing, as a concrete determination of its form, and addressing a symbol;  and it is true that it is only by referring to a possible thing that a symbol has an objective relation, it is only by bearing in it a form that it has any subjective relation, and it is only by equaling another symbol that it has any tuistical relation.  But this objective relation once given to a symbol is at once applicable to all to which it necessarily refers;  and this is shown by the fact of our regarding every symbol as ''connotative'' as well as ''denotative'', and by our regarding one word as standing for another whenever we endeavor to clear up a little obscurity of meaning.  And the reason that this is so is that the possible symbol and the possible form to which a symbol is related each relate also to that thing which is its immediate object.  Things, forms, and symbols, therefore, are symbolized in every symbolization.  And this being so, it is natural to suppose that our three principles of inference which we know already refer to some three objects of symbolization, refer to these.</p>

<p>Now all symbolization is of three objects, at once;  the first is a possible thing, the second is a possible form, the third is a possible symbol.  It will be objected that the two latter are not properly objects.  We have hitherto regarded the symbol as ''standing for'' the thing, as a concrete determination of its form, and addressing a symbol;  and it is true that it is only by referring to a possible thing that a symbol has an objective relation, it is only by bearing in it a form that it has any subjective relation, and it is only by equaling another symbol that it has any tuistical relation.  But this objective relation once given to a symbol is at once applicable to all to which it necessarily refers;  and this is shown by the fact of our regarding every symbol as ''connotative'' as well as ''denotative'', and by our regarding one word as standing for another whenever we endeavor to clear up a little obscurity of meaning.  And the reason that this is so is that the possible symbol and the possible form to which a symbol is related each relate also to that thing which is its immediate object.  Things, forms, and symbols, therefore, are symbolized in every symbolization.  And this being so, it is natural to suppose that our three principles of inference which we know already refer to some three objects of symbolization, refer to these.</p>

<p>That such really is the case admits of proof.  For the principle of inference ''à priori'' must be established ''à priori'';  that is by reasoning analytically from determinant to determinate, in other words from definition.  But this can only be applied to an object whose characteristics depend upon its definition.  Now of most things the definition depends upon the character, the definition of a symbol alone determines its character.  Hence the principle of inference ''à priori'' must relate to symbols.  The principle of inference ''à posteriori'' must be established ''à posteriori'', that is by reasoning from determinate to determinant.  This is only applicable to that which is determined by what it determines;  in other words, to that which is only subject to the truth and falsehood which affects its determinant and which in itself is mere ''zero''.  But this is only true of pure forms.  Hence the principle of inference ''à posteriori'' must relate to pure form.  The principle of inductive inference must be established inductively;  that is by reasoning from parts to whole.  This is only applicable to that whose whole is given in the sum of the parts;  and this is only the case with things.  Hence the principle of inductive inference must relate to things.</p>

<p>That such really is the case admits of proof.  For the principle of inference ''à priori'' must be established ''à priori'';  that is by reasoning analytically from determinant to determinate, in other words from definition.  But this can only be applied to an object whose characteristics depend upon its definition.  Now of most things the definition depends upon the character, the definition of a symbol alone determines its character.  Hence the principle of inference ''à priori'' must relate to symbols.  The principle of inference ''à posteriori'' must be established ''à posteriori'', that is by reasoning from determinate to determinant.  This is only applicable to that which is determined by what it determines;  in other words, to that which is only subject to the truth and falsehood which affects its determinant and which in itself is mere ''zero''.  But this is only true of pure forms.  Hence the principle of inference ''à posteriori'' must relate to pure form.  The principle of inductive inference must be established inductively;  that is by reasoning from parts to whole.  This is only applicable to that whose whole is given in the sum of the parts;  and this is only the case with things.  Hence the principle of inductive inference must relate to things.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 183&ndash;184</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 183&ndash;184</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 20. Peirce (CE 1, 245&ndash;246)====

====Excerpt 20. Peirce (CE 1, 245&ndash;246)====

<p>The terms ''à priori'' and ''à posteriori'' in their ancient sense denote respectively reasoning from an antecedent to a consequent and from a consequent to an antecedent.  Thus suppose we know that every incompetent general will meet with defeat.  Then if we reason that because a given general is incompetent that he must meet with a defeat, we reason ''à priori'';  but if we reason that because a general is defeated he was a bad one, we reason ''à posteriori''.</p>

<p>The terms ''à priori'' and ''à posteriori'' in their ancient sense denote respectively reasoning from an antecedent to a consequent and from a consequent to an antecedent.  Thus suppose we know that every incompetent general will meet with defeat.  Then if we reason that because a given general is incompetent that he must meet with a defeat, we reason ''à priori'';  but if we reason that because a general is defeated he was a bad one, we reason ''à posteriori''.</p>

<p>Kant however uses these terms in another and derived sense.  He did not entirely originate their modern use, for his contemporaries were already beginning to apply them in the same way, but he fixed their ''meaning'' in the new application and made them household words in subsequent philosophy.</p>

<p>Kant however uses these terms in another and derived sense.  He did not entirely originate their modern use, for his contemporaries were already beginning to apply them in the same way, but he fixed their ''meaning'' in the new application and made them household words in subsequent philosophy.</p>

<p>If one judges that a house falls down on the testimony of his eyesight then it is clear that he reasons ''à posteriori'' because he infers the fact from an effect of it on his eyes.  If he judges that a house falls because he knows that the props have been removed he reasons ''à priori'';  yet not purely ''à priori'' for his premisses were obtained from experience.  But if he infers it from axioms innate in the constitution of the mind, he may be said to reason purely 'à priori'. All this had been said previously to Kant.  I will now state how he modified the meaning of the terms while preserving this application of them.  What is known from experience must be known ''à posteriori'', because the thought is determined from without. To determine means to make a circumstance different from what it might have been otherwise.  For example, a drop of rain falling on a stone determines it to be wet, provided the stone may have been dry before.  But if the fact of a whole shower half an hour previous is given, then one drop does not determine the stone to be wet;  for it would be wet, at any rate. Now, it is said that the results of experience are inferred ''à posteriori'', for this reason that they are determined from without the mind by something not previously present to it;  being so determined their determinants or //&nbsp;causes / reasons&nbsp;// are not present to the mind and of course could not be reasoned from.  Hence, a thought determined from without by something not in consciousness even implicitly is inferred ''à posteriori''.</p>

<p>If one judges that a house falls down on the testimony of his eyesight then it is clear that he reasons ''à posteriori'' because he infers the fact from an effect of it on his eyes.  If he judges that a house falls because he knows that the props have been removed he reasons ''à priori'';  yet not purely ''à priori'' for his premisses were obtained from experience.  But if he infers it from axioms innate in the constitution of the mind, he may be said to reason purely 'à priori'.</p>

 

<p>All this had been said previously to Kant.  I will now state how he modified the meaning of the terms while preserving this application of them.  What is known from experience must be known ''à posteriori'', because the thought is determined from without.</p>

 

<p>To determine means to make a circumstance different from what it might have been otherwise.  For example, a drop of rain falling on a stone determines it to be wet, provided the stone may have been dry before.  But if the fact of a whole shower half an hour previous is given, then one drop does not determine the stone to be wet;  for it would be wet, at any rate.</p>

 

<p>Now, it is said that the results of experience are inferred ''à posteriori'', for this reason that they are determined from without the mind by something not previously present to it;  being so determined their determinants or //&nbsp;causes / reasons&nbsp;// are not present to the mind and of course could not be reasoned from.  Hence, a thought determined from without by something not in consciousness even implicitly is inferred ''à posteriori''.</p>

<p>Kant, accordingly, uses the term ''à posteriori'' as meaning what is determined from without.  The term ''à priori'' he uses to mean determined from within or involved implicitly in the whole of what is present to consciousness (or in a conception which is the logical condition of what is in consciousness).  The twist given to the words is so slight that their application remains almost exactly the same.  If there is any change it is this.  A primary belief is ''à priori'' according to Kant;  for it is determined from within.  But it is not ''inferred'' at all and therefore neither of the terms is applicable in their ancient sense.  And yet as an explicit judgment it is inferred and inferred ''à priori''.</p>

<p>Kant, accordingly, uses the term ''à posteriori'' as meaning what is determined from without.  The term ''à priori'' he uses to mean determined from within or involved implicitly in the whole of what is present to consciousness (or in a conception which is the logical condition of what is in consciousness).  The twist given to the words is so slight that their application remains almost exactly the same.  If there is any change it is this.  A primary belief is ''à priori'' according to Kant;  for it is determined from within.  But it is not ''inferred'' at all and therefore neither of the terms is applicable in their ancient sense.  And yet as an explicit judgment it is inferred and inferred ''à priori''.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 245&ndash;246</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 245&ndash;246</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 21. Peirce (CE 1, 246&ndash;247)====

====Excerpt 21. Peirce (CE 1, 246&ndash;247)====

<p>Is there any knowledge ''à priori''?  All our thought begins with experience, the mind furnishes no material for thought whatever.  This is acknowledged by all the philosophers with whom we need concern ourselves at all.  The mind only works over the materials furnished by sense;  no dream is so strange but that all its elementary parts are reminiscences of appearance, the collocation of these alone are we capable of originating. In one sense, therefore, everything may be said to be inferred from experience;  everything that we know, or think or guess or make up may be said to be inferred by some process valid or fallacious from the impressions of sense.  But though everything in this loose sense is inferred from experience, yet everything does not require experience to be as it is in order to afford data for the inference.  Give me the relations of ''any'' geometrical intuition you please and you give me the data for proving all the propositions of geometry.  In other words, everything is not determined by experience. And this admits of proof.  For suppose there may be universal and necessary judgements;  as for example the moon must be made of green cheese.  But there is no element of necessity in an impression of sense for necessity implies that things would be the same as they are were certain accidental circumstances different from what they are.  I may here note that it is very common to misstate this point, as though the necessity here intended were a necessity of thinking.  But it is not meant to say that what we feel compelled to think we are absolutely compelled to think, as this would imply;  but that if we think a fact ''must be'' we cannot have observed that it ''must be''.  The principle is thus reduced to an analytical one.  In the same way universality implies that the event would be the same were the things within certain limits different from what they are. Hence universal and necessary elements of experience are not determined from without.  But are they, therefore, determined from within?  Are they determined at all?  Does not this very conception of determination imply causality and thus beg the whole question of causality at the very outset?  Not at all.  The determination here meant is not real determination but logical determination.  A cognition ''à priori'' is one which any experience contains reason for and therefore which no experience determines but which contains elements such as the mind introduces in working up the materials of sense, or rather as they are not new materials, they are the working up.</p>

<p>Is there any knowledge ''à priori''?  All our thought begins with experience, the mind furnishes no material for thought whatever.  This is acknowledged by all the philosophers with whom we need concern ourselves at all.  The mind only works over the materials furnished by sense;  no dream is so strange but that all its elementary parts are reminiscences of appearance, the collocation of these alone are we capable of originating.</p>

 

<p>In one sense, therefore, everything may be said to be inferred from experience;  everything that we know, or think or guess or make up may be said to be inferred by some process valid or fallacious from the impressions of sense.  But though everything in this loose sense is inferred from experience, yet everything does not require experience to be as it is in order to afford data for the inference.  Give me the relations of ''any'' geometrical intuition you please and you give me the data for proving all the propositions of geometry.  In other words, everything is not determined by experience.</p>

 

<p>And this admits of proof.  For suppose there may be universal and necessary judgements;  as for example the moon must be made of green cheese.  But there is no element of necessity in an impression of sense for necessity implies that things would be the same as they are were certain accidental circumstances different from what they are.  I may here note that it is very common to misstate this point, as though the necessity here intended were a necessity of thinking.  But it is not meant to say that what we feel compelled to think we are absolutely compelled to think, as this would imply;  but that if we think a fact ''must be'' we cannot have observed that it ''must be''.  The principle is thus reduced to an analytical one.  In the same way universality implies that the event would be the same were the things within certain limits different from what they are.</p>

 

<p>Hence universal and necessary elements of experience are not determined from without.  But are they, therefore, determined from within?  Are they determined at all?  Does not this very conception of determination imply causality and thus beg the whole question of causality at the very outset?  Not at all.  The determination here meant is not real determination but logical determination.  A cognition ''à priori'' is one which any experience contains reason for and therefore which no experience determines but which contains elements such as the mind introduces in working up the materials of sense, or rather as they are not new materials, they are the working up.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 246&ndash;247</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 246&ndash;247</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 22. Peirce (CE 1, 256)====

====Excerpt 22. Peirce (CE 1, 256)====

<p>Though I talk of forms as something independent of the mind, I only mean that the mind so conceives them and that that conception is valid.  I thus say that all the qualities we know are determinations of the pure idea.  But that we have any further knowledge of the idea or that this is to know it in itself I entirely deny.</p>

<p>Though I talk of forms as something independent of the mind, I only mean that the mind so conceives them and that that conception is valid.  I thus say that all the qualities we know are determinations of the pure idea.  But that we have any further knowledge of the idea or that this is to know it in itself I entirely deny.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 256</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 256</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

===Definition===

===Definition===

====Excerpt 1. Peirce (CP 2.271)====

====Excerpt 1. Peirce (CP 2.315)====

 

 

 

====Excerpt 2. Peirce (CP 2.315)====

====Excerpt 2. Peirce (CP 2.315)====

====Excerpt 3. Peirce (CP 2.330)====

====Excerpt 3. Peirce (CP 2.330)====

====Excerpt 1. Peirce (CP 2.227)====

====Excerpt 1. Peirce (CP 2.227)====

<p>Logic, in its general sense, is, as I believe I have shown, only another name for ''semiotic'' (Greek ''semeiotike''), the quasi-necessary, or formal, doctrine of signs.  By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the characters of such signs as we know, and from such an observation, by a process which I will not object to naming Abstraction, we are led to statements, eminently fallible, and therefore in one sense by no means necessary, as to what ''must be'' the characters of all signs used by a "scientific" intelligence, that is to say, by an intelligence capable of learning by experience.  As to that process of abstraction, it is itself a sort of observation.</p>

<p>Logic, in its general sense, is, as I believe I have shown, only another name for ''semiotic'' (&sigma;&eta;&mu;&epsilon;&iota;&omega;&tau;&iota;&kappa;&#942;), the quasi-necessary, or formal, doctrine of signs.  By describing the doctrine as &ldquo;quasi-necessary&rdquo;, or formal, I mean that we observe the characters of such signs as we know, and from such an observation, by a process which I will not object to naming Abstraction, we are led to statements, eminently fallible, and therefore in one sense by no means necessary, as to what ''must&nbsp;be'' the characters of all signs used by a &ldquo;scientific&rdquo; intelligence, that is to say, by an intelligence capable of learning by experience.  As to that process of abstraction, it is itself a sort of observation.</p>

<p>The faculty which I call abstractive observation is one which ordinary people perfectly recognize, but for which the theories of philosophers sometimes hardly leave room.  It is a familiar experience to every human being to wish for something quite beyond his present means, and to follow that wish by the question, "Should I wish for that thing just the same, if I had ample means to gratify it?" To answer that question, he searches his heart, and in doing so makes what I term an abstractive observation.  He makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would require to be made in that picture, and then examines it, that is, ''observes'' what he has imagined, to see whether the same ardent desire is there to be discerned.  By such a process, which is at bottom very much like mathematical reasoning, we can reach conclusions as to what ''would be'' true of signs in all cases, so long as the intelligence using them was scientific.</p>

<p>The faculty which I call abstractive observation is one which ordinary people perfectly recognize, but for which the theories of philosophers sometimes hardly leave room.  It is a familiar experience to every human being to wish for something quite beyond his present means, and to follow that wish by the question, &ldquo;Should I wish for that thing just the same, if I had ample means to gratify it?&rdquo; To answer that question, he searches his heart, and in doing so makes what I term an abstractive observation.  He makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would require to be made in that picture, and then examines it, that is, ''observes'' what he has imagined, to see whether the same ardent desire is there to be discerned.  By such a process, which is at bottom very much like mathematical reasoning, we can reach conclusions as to what ''would be'' true of signs in all cases, so long as the intelligence using them was scientific.</p>

<p>C.S. Peirce, ''Collected Papers'', CP 2.227.  (Eds. Note.  "From an unidentified fragment, ''c.'' 1897")</p>

<p align="right">C.S. Peirce, ''Collected Papers'', CP 2.227<br>

(&ldquo;From an unidentified fragment, ''c.'' 1897&rdquo;)</p>

====Excerpt 2. Peirce (CE 1, 217)====

====Excerpt 2. Peirce (CE 1, 217)====

<p>Logic is an analysis of forms not a study of the mind.  It tells ''why'' an inference follows not ''how'' it arises in the mind.  It is the business therefore of the logician to break up complicated inferences from numerous premisses into the simplest possible parts and not to leave them as they are.</p>

<p>Logic is an analysis of forms not a study of the mind.  It tells ''why'' an inference follows not ''how'' it arises in the mind.  It is the business therefore of the logician to break up complicated inferences from numerous premisses into the simplest possible parts and not to leave them as they are.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 217</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 217</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 3. Peirce (CE 1, 169&ndash;170)====

====Excerpt 3. Peirce (CE 1, 169&ndash;170)====

<p>Some reasons having now been given for adopting the unpsychological conception of the science, let us now seek to make this conception sufficiently distinct to serve for a definition of logic.  For this purpose we must bring our ''logos'' from the abstract to the concrete, from the absolute to the dependent.  There is no science of absolutes.  The metaphysical logos is no more to us than the metaphysical soul or the metaphysical matter.  To the absolute Idea or Logos, the dependent or relative ''word'' corresponds.  The word ''horse'', is thought of as being a word though it be unwritten, unsaid, and unthought.  It is true, it must be considered as having been thought;  but it need not have been thought by the same mind which regards it as being a word.  I can think of a word in Feejee, though I can attach no definite articulation to it, and do not guess what it would be like.  Such a word, abstract but not absolute, is no more than the genus of all symbols having the same meaning.  We can also think of the higher genus which contains words of all meanings.  A first approximation to a definition, then, will be that logic is the science of representations in general, whether mental or material.  This definition coincides with Locke's.  It is however too wide for logic does not treat of all kinds of representations.  The resemblance of a portrait to its object, for example, is not logical truth.  It is necessary, therefore, to divide the genus representation according to the different ways in which it may accord with its object.</p>

<p>Some reasons having now been given for adopting the unpsychological conception of the science, let us now seek to make this conception sufficiently distinct to serve for a definition of logic.  For this purpose we must bring our ''logos'' from the abstract to the concrete, from the absolute to the dependent.  There is no science of absolutes.  The metaphysical logos is no more to us than the metaphysical soul or the metaphysical matter.  To the absolute Idea or Logos, the dependent or relative ''word'' corresponds.  The word ''horse'', is thought of as being a word though it be unwritten, unsaid, and unthought.  It is true, it must be considered as having been thought;  but it need not have been thought by the same mind which regards it as being a word.  I can think of a word in Feejee, though I can attach no definite articulation to it, and do not guess what it would be like.  Such a word, abstract but not absolute, is no more than the genus of all symbols having the same meaning.  We can also think of the higher genus which contains words of all meanings.  A first approximation to a definition, then, will be that logic is the science of representations in general, whether mental or material.  This definition coincides with Locke's.  It is however too wide for logic does not treat of all kinds of representations.  The resemblance of a portrait to its object, for example, is not logical truth.  It is necessary, therefore, to divide the genus representation according to the different ways in which it may accord with its object.</p>

<p>The third kind of truth or accordance of a representation with its object, is that which inheres in the very nature of the representation whether that nature be original or acquired.  Such a representation I name a ''symbol''.</p>

<p>The third kind of truth or accordance of a representation with its object, is that which inheres in the very nature of the representation whether that nature be original or acquired.  Such a representation I name a ''symbol''.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 169&ndash;170</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 169&ndash;170</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 4. Peirce (CE 1, 173)====

====Excerpt 4. Peirce (CE 1, 173)====

<p>How often do we think of the thing in algebra?  When we use the symbol of multiplication we do not even think out the conception of multiplication, we think merely of the laws of that symbol, which coincide with the laws of the conception, and what is more to the purpose, coincide with the laws of multiplication in the object.  Now, I ask, how is it that anything can be done with a symbol, without reflecting upon the conception, much less imagining the object that belongs to it?  It is simply because the symbol has acquired a nature, which may be described thus, that when it is brought before the mind certain principles of its use &mdash; whether reflected on or not &mdash; by association immediately regulate the action of the mind;  and these may be regarded as laws of the symbol itself which it cannot ''as a symbol'' transgress.</p>

<p>How often do we think of the thing in algebra?  When we use the symbol of multiplication we do not even think out the conception of multiplication, we think merely of the laws of that symbol, which coincide with the laws of the conception, and what is more to the purpose, coincide with the laws of multiplication in the object.  Now, I ask, how is it that anything can be done with a symbol, without reflecting upon the conception, much less imagining the object that belongs to it?  It is simply because the symbol has acquired a nature, which may be described thus, that when it is brought before the mind certain principles of its use &mdash; whether reflected on or not &mdash; by association immediately regulate the action of the mind;  and these may be regarded as laws of the symbol itself which it cannot ''as a symbol'' transgress.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 173</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 173</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 5. Peirce (CE 1, 184&ndash;185)====

====Excerpt 5. Peirce (CE 1, 184&ndash;185)====

<p>Finally, these principles as principles applying not to this or that symbol, form, thing, but to all equally, must be universal.  And as grounds of possibility they must state what is possible.  Now what is the universal principle of the possible symbolization of symbols?  It is that all symbols are symbolizable.  And the other principles must predicate the same thing of forms and things.</p>

<p>Finally, these principles as principles applying not to this or that symbol, form, thing, but to all equally, must be universal.  And as grounds of possibility they must state what is possible.  Now what is the universal principle of the possible symbolization of symbols?  It is that all symbols are symbolizable.  And the other principles must predicate the same thing of forms and things.</p>

<p>These, then, are the three principles of inference.  Our next business is to demonstrate their truth.  But before doing so, let me repeat that these principles do not serve to prove that the kinds of inference are valid, since their own proof, on the contrary, must rest on the assumption of that validity.  Their use is only to show what the condition of that validity is.  Hence, the only proof of the truth of these principles is this;  to show, that if these principles be admitted as sufficient, and if the validity of the several kinds of inference be also admitted, that then the truth of these principles follows by the respective kinds of inference which each establishes.</p>

<p>These, then, are the three principles of inference.  Our next business is to demonstrate their truth.  But before doing so, let me repeat that these principles do not serve to prove that the kinds of inference are valid, since their own proof, on the contrary, must rest on the assumption of that validity.  Their use is only to show what the condition of that validity is.  Hence, the only proof of the truth of these principles is this;  to show, that if these principles be admitted as sufficient, and if the validity of the several kinds of inference be also admitted, that then the truth of these principles follows by the respective kinds of inference which each establishes.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 184&ndash;185</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 184&ndash;185</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 6. Peirce (CE 1, 185&ndash;186)====

====Excerpt 6. Peirce (CE 1, 185&ndash;186)====

<p>To prove then, first, that all symbols are symbolizable.  Every syllogism consists of three propositions with two terms each, a subject and a predicate, and three terms in all each term being used twice.  It is obvious that one term must occur both as subject and predicate.  Now a predicate is a symbol of its subject.  Hence in all reasoning ''à priori'' a symbol must be symbolized.  But as reasoning ''à priori'' is possible about a statement without reference to its predicate, all symbols must be symbolizable.</p>

<p>To prove then, first, that all symbols are symbolizable.  Every syllogism consists of three propositions with two terms each, a subject and a predicate, and three terms in all each term being used twice.  It is obvious that one term must occur both as subject and predicate.  Now a predicate is a symbol of its subject.  Hence in all reasoning ''à priori'' a symbol must be symbolized.  But as reasoning ''à priori'' is possible about a statement without reference to its predicate, all symbols must be symbolizable.</p>

<p>2nd To prove that all forms are symbolizable.  Since this proposition relates to pure form it is sufficient to show that its consequences are true.  Now the consequence will be that if a symbol of any object be given, but if this symbol does not adequately represent any form then another symbol more formal may always be substituted for it, or in other words as soon as we know what form it ought to symbolize the symbol may be so changed as to symbolize that form.  But this process is a description of inference ''à posteriori''.  Thus in the example relating to light;  the symbol of "giving such and such phenomena" which is altogether inadequate to express a form is replaced by "ether-waves" which is much more formal.  The consequence then of the universal symbolization of forms is the inference ''à posteriori'', and there is no truth or falsehood in the principle except what appears in the consequence.  Hence, the consequence being valid, the principle may be accepted.</p>

<p>2nd To prove that all forms are symbolizable.  Since this proposition relates to pure form it is sufficient to show that its consequences are true.  Now the consequence will be that if a symbol of any object be given, but if this symbol does not adequately represent any form then another symbol more formal may always be substituted for it, or in other words as soon as we know what form it ought to symbolize the symbol may be so changed as to symbolize that form.  But this process is a description of inference ''à posteriori''.  Thus in the example relating to light;  the symbol of &ldquo;giving such and such phenomena&rdquo; which is altogether inadequate to express a form is replaced by &ldquo;ether-waves&rdquo; which is much more formal.  The consequence then of the universal symbolization of forms is the inference ''à posteriori'', and there is no truth or falsehood in the principle except what appears in the consequence.  Hence, the consequence being valid, the principle may be accepted.</p>

<p>3rd To prove that all things may be symbolized.  If we have a proposition, the subject of which is not properly a symbol of the thing it signifies;  then in case everything may be symbolized, it is possible to replace this subject by another which is true of it and which does symbolize the subject.  But this process is inductive inference.  Thus having observed of a great variety of animals that they all eat herbs, if I substitute for this subject which is not a true symbol, the symbol "cloven-footed animals" which is true of these animals, I make an induction.  Accordingly I must acknowledge that this principle leads to induction;  and as it is a principle of objects, what is true of its subalterns is true of it;  and since induction is always possible and valid, this principle is true.</p>

<p>3rd To prove that all things may be symbolized.  If we have a proposition, the subject of which is not properly a symbol of the thing it signifies;  then in case everything may be symbolized, it is possible to replace this subject by another which is true of it and which does symbolize the subject.  But this process is inductive inference.  Thus having observed of a great variety of animals that they all eat herbs, if I substitute for this subject which is not a true symbol, the symbol &ldquo;cloven-footed animals&rdquo; which is true of these animals, I make an induction.  Accordingly I must acknowledge that this principle leads to induction;  and as it is a principle of objects, what is true of its subalterns is true of it;  and since induction is always possible and valid, this principle is true.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 185&ndash;186</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 185&ndash;186</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 7. Peirce (CE 1, 186)====

====Excerpt 7. Peirce (CE 1, 186)====

<p>Having discovered and demonstrated the grounds of the possibility of the three inferences, let us take a preliminary glance at the manner in which additions to these principles may make them grounds of proceedure.</p>

<p>Having discovered and demonstrated the grounds of the possibility of the three inferences, let us take a preliminary glance at the manner in which additions to these principles may make them grounds of proceedure.</p>

<p>The principle of inference ''à priori'' has been apodictically demonstrated;  the principle of inductive inference has been shown upon sufficient evidence to be true;  the principle of inference ''à posteriori'' has been shown to be one which nothing can contradict.  These three degrees of modality in the principles of the three inferences show the amount of certainty which each is capable of affording.  Inference ''à priori'' is as we all know the only apodictic proceedure;  yet no one thinks of questioning a good induction;  while inference ''à posteriori'' is proverbially uncertain.  ''Hypotheses non fingo'', said Newton;  striving to place his theory on a firm inductive basis.  Yet provisionally we must make hypotheses;  we start with them;  the baby when he lies turning his fingers before his eyes is testing a hypothesis he has already formed, as to the connection of touch and sight.  Apodictic reasoning can only be applied to the manipulation of our knowledge;  it never can extend it.  So that it is an induction which eventually settles every question of science;  and nine-tenths of the inferences we draw in any hour not of study are of this kind.</p>

<p>The principle of inference ''à priori'' has been apodictically demonstrated;  the principle of inductive inference has been shown upon sufficient evidence to be true;  the principle of inference ''à posteriori'' has been shown to be one which nothing can contradict.  These three degrees of modality in the principles of the three inferences show the amount of certainty which each is capable of affording.  Inference ''à priori'' is as we all know the only apodictic proceedure;  yet no one thinks of questioning a good induction;  while inference ''à posteriori'' is proverbially uncertain.  ''Hypotheses non fingo'', said Newton;  striving to place his theory on a firm inductive basis.  Yet provisionally we must make hypotheses;  we start with them;  the baby when he lies turning his fingers before his eyes is testing a hypothesis he has already formed, as to the connection of touch and sight.  Apodictic reasoning can only be applied to the manipulation of our knowledge;  it never can extend it.  So that it is an induction which eventually settles every question of science;  and nine-tenths of the inferences we draw in any hour not of study are of this kind.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 186</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 186</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 8. Peirce (CE 1, 256&ndash;257)====

====Excerpt 8. Peirce (CE 1, 256&ndash;257)====

<p>The first distinction we found it necessary to draw &mdash; the first set of conceptions we have to signalize &mdash; forms a triad:</p>

<p>The first distinction we found it necessary to draw &mdash; the first set of conceptions we have to signalize &mdash; forms a triad:</p>

<center>

<p align="center">Thing &nbsp;&nbsp;&nbsp;&nbsp; Representation &nbsp;&nbsp;&nbsp;&nbsp; Form.</p>

<p>Thing &nbsp;&nbsp;&nbsp; Representation &nbsp;&nbsp;&nbsp; Form.</p>

</center>

<p>Kant you remember distinguishes in all mental representations the matter and the form.  The distinction here is slightly different.  In the first place, I do not use the word ''Representation'' as a translation of the German ''Vorstellung'' which is the general term for any product of the cognitive power.  Representation, indeed, is not a perfect translation of that term, because it seems necessarily to imply a mediate reference to its object, which ''Vorstellung'' does not.  I however would limit the term neither to that which is mediate nor to that which is mental, but would use it in its broad, usual, and etymological sense for anything which is supposed to stand for another and which might express that other to a mind which truly could understand it.  Thus our whole world &mdash; that which we can comprehend &mdash; is a world of representations.</p>

<p>Kant you remember distinguishes in all mental representations the matter and the form.  The distinction here is slightly different.  In the first place, I do not use the word ''Representation'' as a translation of the German ''Vorstellung'' which is the general term for any product of the cognitive power.  Representation, indeed, is not a perfect translation of that term, because it seems necessarily to imply a mediate reference to its object, which ''Vorstellung'' does not.  I however would limit the term neither to that which is mediate nor to that which is mental, but would use it in its broad, usual, and etymological sense for anything which is supposed to stand for another and which might express that other to a mind which truly could understand it.  Thus our whole world &mdash; that which we can comprehend &mdash; is a world of representations.</p>

<p>No one can deny that there are representations, for every thought is one.  But with ''things'' and ''forms'' scepticism, though still unfounded, is at first possible.  The ''thing'' is that for which a representation might stand prescinded from all that would constitute a relation with any representation.  The ''form'' is the respect in which a representation might stand for a thing, prescinded from both thing and representation.  We thus see that ''things'' and ''forms'' stand very differently with us from ''representations''.  Not in being prescinded elements, for representations also are prescinded from other representations.  But because we know representations absolutely, while we only know ''forms'' and ''things'' through representations.  Thus scepticism is possible concerning ''them''.  But for the very reason that they are known only relatively and therefore do not belong to our world, the hypothesis of ''things'' and ''forms'' introduces nothing false.  For truth and falsity only apply to an object as far as it can be known.  If indeed we could know things and forms in themselves, then perhaps our representations of them might contradict this knowledge.  But since all that we know of them we know through representations, if our representations be consistent they have all the truth that the case admits of.</p>

<p>No one can deny that there are representations, for every thought is one.  But with ''things'' and ''forms'' scepticism, though still unfounded, is at first possible.  The ''thing'' is that for which a representation might stand prescinded from all that would constitute a relation with any representation.  The ''form'' is the respect in which a representation might stand for a thing, prescinded from both thing and representation.  We thus see that ''things'' and ''forms'' stand very differently with us from ''representations''.  Not in being prescinded elements, for representations also are prescinded from other representations.  But because we know representations absolutely, while we only know ''forms'' and ''things'' through representations.  Thus scepticism is possible concerning ''them''.  But for the very reason that they are known only relatively and therefore do not belong to our world, the hypothesis of ''things'' and ''forms'' introduces nothing false.  For truth and falsity only apply to an object as far as it can be known.  If indeed we could know things and forms in themselves, then perhaps our representations of them might contradict this knowledge.  But since all that we know of them we know through representations, if our representations be consistent they have all the truth that the case admits of.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 256&ndash;257</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 256&ndash;257</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 9. Peirce (CE 1, 257&ndash;258)====

====Excerpt 9. Peirce (CE 1, 257&ndash;258)====

<p>We found representations to be of three kinds:</p>

<p>We found representations to be of three kinds:</p>

<center>

<p align="center">Signs &nbsp;&nbsp;&nbsp;&nbsp; Copies &nbsp;&nbsp;&nbsp;&nbsp; Symbols.</p>

<p>Signs &nbsp;&nbsp;&nbsp; Copies &nbsp;&nbsp;&nbsp; Symbols.</p>

</center>

<p>By a ''copy'', I mean a representation whose agreement with its object depends merely upon a sameness of predicates.</p>

<p>By a ''copy'', I mean a representation whose agreement with its object depends merely upon a sameness of predicates.</p>

<p>The science of the general laws of relations of symbols to logoi is general grammar.  The science of the general laws of their relations to objects is logic.  And the science of the general laws of their relations to other systems of symbols is general rhetoric.</p>

<p>The science of the general laws of relations of symbols to logoi is general grammar.  The science of the general laws of their relations to objects is logic.  And the science of the general laws of their relations to other systems of symbols is general rhetoric.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 257&ndash;258</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 257&ndash;258</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

====Excerpt 10. Peirce (CE 1, 267&ndash;268)====

====Excerpt 10. Peirce (CE 1, 267&ndash;268)====

<p>When have then three different kinds of inference.</p>

<p>When have then three different kinds of inference.</p>

:<p>Deduction or inference ''à priori'',</p>

:: <p>Deduction or inference ''à priori'',</p>

:<p>Induction or inference ''à particularis'', and</p>

:: <p>Induction or inference ''à particularis'', and</p>

:<p>Hypothesis or inference ''à posteriori''.</p>

:: <p>Hypothesis or inference ''à posteriori''.</p>

<p>It is necessary now to examine this classification critically.</p>

<p>It is necessary now to examine this classification critically.</p>

<p>And first let me specify what I claim for my invention.  I do not claim that it is a natural classification, in the sense of being right while all others are wrong.  I do not know that such a thing as a natural classification is possible in the nature of the case.  The science which most resembles logic is mathematics.  Now among mathematical forms there does not seem to be any natural classification.  It is true that in the solutions of quadratic equations, there are generally two solutions from the positive and negative values of the root with an impossible gulf between them.  But this classing is owing to the forms being restricted by the conditions of the problem;  and I believe that all natural classes arise from some problem &mdash; something which was to be accomplished and which could be accomplished only in certain ways.  Required to make a musical instrument;  you must set either a plate or a string in vibration.  Required to make an animal;  it must be either a vertebrate, an articulate, a mollusk, or a radiate.  However this may be, in Geometry we find ourselves free to make several different classifications of curves, either of which shall be equally good.  In fact, in order to make any classification of them whatever we must introduce the purely arbitrary element of a system of coördinates or something of the kind which constitutes the point of view from which we regard the curves and which determines their classification completely.  Now it may be said that one system of coördinates is more ''natural'' than another;  and it is obvious that the conditions of binocular vision limit us in our use of our eyes to the use of particular coördinates.  But this fact that one such system is more natural to us has clearly nothing to do with pure mathematics but is merely introducing a problem;  given two eyes, required to form geometrical judgements, how can we do it?  In the same way, I conceive that the syllogism is nothing but the system of coördinates or method of analysis which we adopt in logic.  There is no reason why arguments should not be analyzed just as correctly in some other way.  It is a great mistake to suppose that arguments as they are thought are often syllogisms, but even if this were the case it would have no bearing upon pure logic as a formal science.  It is the principal business of the logician to analyze arguments into their elements just as it is part of the business of the geometer to analyze curves;  but the one is no more bound to follow the natural process of the intellect in his analysis, than the other is bound to follow the natural process of perception.</p>

<p>And first let me specify what I claim for my invention.  I do not claim that it is a natural classification, in the sense of being right while all others are wrong.  I do not know that such a thing as a natural classification is possible in the nature of the case.  The science which most resembles logic is mathematics.  Now among mathematical forms there does not seem to be any natural classification.  It is true that in the solutions of quadratic equations, there are generally two solutions from the positive and negative values of the root with an impossible gulf between them.  But this classing is owing to the forms being restricted by the conditions of the problem;  and I believe that all natural classes arise from some problem &mdash; something which was to be accomplished and which could be accomplished only in certain ways.  Required to make a musical instrument;  you must set either a plate or a string in vibration.  Required to make an animal;  it must be either a vertebrate, an articulate, a mollusk, or a radiate.  However this may be, in Geometry we find ourselves free to make several different classifications of curves, either of which shall be equally good.  In fact, in order to make any classification of them whatever we must introduce the purely arbitrary element of a system of coördinates or something of the kind which constitutes the point of view from which we regard the curves and which determines their classification completely.  Now it may be said that one system of coördinates is more ''natural'' than another;  and it is obvious that the conditions of binocular vision limit us in our use of our eyes to the use of particular coördinates.  But this fact that one such system is more natural to us has clearly nothing to do with pure mathematics but is merely introducing a problem;  given two eyes, required to form geometrical judgements, how can we do it?  In the same way, I conceive that the syllogism is nothing but the system of coördinates or method of analysis which we adopt in logic.  There is no reason why arguments should not be analyzed just as correctly in some other way.  It is a great mistake to suppose that arguments as they are thought are often syllogisms, but even if this were the case it would have no bearing upon pure logic as a formal science.  It is the principal business of the logician to analyze arguments into their elements just as it is part of the business of the geometer to analyze curves;  but the one is no more bound to follow the natural process of the intellect in his analysis, than the other is bound to follow the natural process of perception.</p>

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 267&ndash;268</p>

<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 267&ndash;268</p>

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

<p>Charles Sanders Peirce, &ldquo;Harvard Lectures ''On the Logic of Science''&rdquo; (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume&nbsp;1, 1857&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

===Inquiry Into Information===

===Inquiry Into Information===

# http://stderr.org/pipermail/inquiry/2004-December/002238.html

# http://stderr.org/pipermail/inquiry/2004-December/002238.html

# http://stderr.org/pipermail/inquiry/2004-December/002239.html

# http://stderr.org/pipermail/inquiry/2004-December/002239.html

[[Category:Charles Sanders Peirce]]

[[Category:Charles Sanders Peirce]]