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<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, "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>
 
</blockquote>
 
</blockquote>
 +
 +
===LAS.  Logic As Semiotic===
 +
 +
====LAS.  Note 1====
 +
 +
<pre>
 +
| 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.
 +
|
 +
| 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.
 +
|
 +
| Charles Sanders Peirce, 'Collected Papers', CP 2.227.
 +
| Eds. Note.  "From an unidentified fragment, c. 1897".
 +
</pre>
 +
 +
====LAS.  Note 2====
 +
 +
<pre>
 +
| 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, p. 217.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 3====
 +
 +
<pre>
 +
| 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.
 +
|
 +
| The first and simplest kind of truth is the resemblance of a copy.
 +
| It may be roughly stated to consist in a sameness of predicates.
 +
| Leibniz would say that carried to its highest point, it would
 +
| destroy itself by becoming identity.  Whether that is true or
 +
| not, all known resemblance has a limit.  Hence, resemblance
 +
| is always partial truth.  On the other hand, no two things
 +
| are so different as to resemble each other in no particular.
 +
| Such a case is supposed in the proverb that Dreams go by
 +
| contraries, -- an absurd notion, since concretes have no
 +
| contraries.  A false copy is one which claims to resemble
 +
| an object which it does not resemble.  But this never fully
 +
| occurs, for two reasons;  in the first place, the falsehood
 +
| does not lie in the copy itself but in the 'claim' which is
 +
| made for it, in the 'superscription' for instance;  in the
 +
| second place, as there must be 'some' resemblance between
 +
| the copy and its object, this falsehood cannot be entire.
 +
| Hence, there is no absolute truth or falsehood of copies.
 +
| Now logical representations have absolute truth and
 +
| falsehood as we know 'à posteriori' from the law
 +
| of excluded middle.  Hence, logic does not treat
 +
| of copies.
 +
|
 +
| The second kind of truth, is the denotation of a sign,
 +
| according to a previous convention.  A child's name, for
 +
| example, by a convention made at baptism, denotes that person.
 +
| Signs may be plural but they cannot have genuine generality because
 +
| each of the objects to which they refer must have been fixed upon
 +
| by convention.  It is true that we may agree that a certain sign
 +
| shall denote a certain individual conception, an individual act
 +
| of an individual mind, and that conception may stand for all
 +
| conceptions resembling it;  but in this case, the generality
 +
| belongs to the 'conception' and not to the sign.  Signs,
 +
| therefore, in this narrow sense are not treated of in
 +
| logic, because logic deals only with general terms.
 +
|
 +
| 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'.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 169-170.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 4====
 +
 +
<pre>
 +
| 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 -- whether reflected on
 +
| or not -- 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, p. 173.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 5====
 +
 +
<pre>
 +
| 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.
 +
|
 +
| 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 184-185.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 6====
 +
 +
<pre>
 +
| 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.
 +
|
 +
| 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.
 +
|
 +
| 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 185-186.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 7====
 +
 +
<pre>
 +
| 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.
 +
|
 +
| 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, p. 186.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 8====
 +
 +
<pre>
 +
| The first distinction we found it necessary to draw --
 +
| the first set of conceptions we have to signalize --
 +
| forms a triad
 +
|
 +
|    Thing  Representation  Form.
 +
|
 +
| 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 -- that which we can comprehend -- is
 +
| a world of representations.
 +
|
 +
| 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 256-257.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 9====
 +
 +
<pre>
 +
| We found representations to be of three kinds
 +
|
 +
|    Signs  Copies  Symbols.
 +
|
 +
| By a 'copy', I mean a representation whose agreement with
 +
| its object depends merely upon a sameness of predicates.
 +
|
 +
| By a 'sign', I mean a representation whose reference to
 +
| its object is fixed by convention.
 +
|
 +
| By a 'symbol', I mean one which upon being presented to the mind --
 +
| without any resemblance to its object and without any reference to
 +
| a previous convention -- calls up a concept.  I consider concepts,
 +
| themselves, as a species of symbols.
 +
|
 +
| A symbol is subject to three conditions.  First it must represent an object,
 +
| or informed and representable thing.  Second it must be a manifestation of
 +
| a 'logos', or represented and realizable form.  Third it must be translatable
 +
| into another language or system of symbols.
 +
|
 +
| 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 257-258.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
 +
 +
====LAS.  Note 10====
 +
 +
<pre>
 +
| When have then three different kinds of inference.
 +
|
 +
|    Deduction or inference 'à priori',
 +
|
 +
|    Induction or inference 'à particularis', and
 +
|
 +
|    Hypothesis or inference 'à posteriori'.
 +
|
 +
| It is necessary now to examine this classification critically.
 +
|
 +
| 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 -- 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.
 +
|
 +
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 267-268.
 +
|
 +
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
 +
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
 +
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
 +
</pre>
    
===Inquiry Into Information===
 
===Inquiry Into Information===
Line 718: Line 1,129:  
|
 
|
 
| Joe Ransdell
 
| Joe Ransdell
</pre>
  −
  −
===LAS.  Logic As Semiotic===
  −
  −
====LAS.  Note 1====
  −
  −
<pre>
  −
| 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.
  −
|
  −
| 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.
  −
|
  −
| Charles Sanders Peirce, 'Collected Papers', CP 2.227.
  −
| Eds. Note.  "From an unidentified fragment, c. 1897".
  −
</pre>
  −
  −
====LAS.  Note 2====
  −
  −
<pre>
  −
| 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, p. 217.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 3====
  −
  −
<pre>
  −
| 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.
  −
|
  −
| The first and simplest kind of truth is the resemblance of a copy.
  −
| It may be roughly stated to consist in a sameness of predicates.
  −
| Leibniz would say that carried to its highest point, it would
  −
| destroy itself by becoming identity.  Whether that is true or
  −
| not, all known resemblance has a limit.  Hence, resemblance
  −
| is always partial truth.  On the other hand, no two things
  −
| are so different as to resemble each other in no particular.
  −
| Such a case is supposed in the proverb that Dreams go by
  −
| contraries, -- an absurd notion, since concretes have no
  −
| contraries.  A false copy is one which claims to resemble
  −
| an object which it does not resemble.  But this never fully
  −
| occurs, for two reasons;  in the first place, the falsehood
  −
| does not lie in the copy itself but in the 'claim' which is
  −
| made for it, in the 'superscription' for instance;  in the
  −
| second place, as there must be 'some' resemblance between
  −
| the copy and its object, this falsehood cannot be entire.
  −
| Hence, there is no absolute truth or falsehood of copies.
  −
| Now logical representations have absolute truth and
  −
| falsehood as we know 'à posteriori' from the law
  −
| of excluded middle.  Hence, logic does not treat
  −
| of copies.
  −
|
  −
| The second kind of truth, is the denotation of a sign,
  −
| according to a previous convention.  A child's name, for
  −
| example, by a convention made at baptism, denotes that person.
  −
| Signs may be plural but they cannot have genuine generality because
  −
| each of the objects to which they refer must have been fixed upon
  −
| by convention.  It is true that we may agree that a certain sign
  −
| shall denote a certain individual conception, an individual act
  −
| of an individual mind, and that conception may stand for all
  −
| conceptions resembling it;  but in this case, the generality
  −
| belongs to the 'conception' and not to the sign.  Signs,
  −
| therefore, in this narrow sense are not treated of in
  −
| logic, because logic deals only with general terms.
  −
|
  −
| 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'.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 169-170.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 4====
  −
  −
<pre>
  −
| 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 -- whether reflected on
  −
| or not -- 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, p. 173.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 5====
  −
  −
<pre>
  −
| 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.
  −
|
  −
| 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 184-185.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 6====
  −
  −
<pre>
  −
| 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.
  −
|
  −
| 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.
  −
|
  −
| 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 185-186.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 7====
  −
  −
<pre>
  −
| 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.
  −
|
  −
| 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, p. 186.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 8====
  −
  −
<pre>
  −
| The first distinction we found it necessary to draw --
  −
| the first set of conceptions we have to signalize --
  −
| forms a triad
  −
|
  −
|    Thing  Representation  Form.
  −
|
  −
| 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 -- that which we can comprehend -- is
  −
| a world of representations.
  −
|
  −
| 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 256-257.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 9====
  −
  −
<pre>
  −
| We found representations to be of three kinds
  −
|
  −
|    Signs  Copies  Symbols.
  −
|
  −
| By a 'copy', I mean a representation whose agreement with
  −
| its object depends merely upon a sameness of predicates.
  −
|
  −
| By a 'sign', I mean a representation whose reference to
  −
| its object is fixed by convention.
  −
|
  −
| By a 'symbol', I mean one which upon being presented to the mind --
  −
| without any resemblance to its object and without any reference to
  −
| a previous convention -- calls up a concept.  I consider concepts,
  −
| themselves, as a species of symbols.
  −
|
  −
| A symbol is subject to three conditions.  First it must represent an object,
  −
| or informed and representable thing.  Second it must be a manifestation of
  −
| a 'logos', or represented and realizable form.  Third it must be translatable
  −
| into another language or system of symbols.
  −
|
  −
| 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 257-258.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  −
</pre>
  −
  −
====LAS.  Note 10====
  −
  −
<pre>
  −
| When have then three different kinds of inference.
  −
|
  −
|    Deduction or inference 'à priori',
  −
|
  −
|    Induction or inference 'à particularis', and
  −
|
  −
|    Hypothesis or inference 'à posteriori'.
  −
|
  −
| It is necessary now to examine this classification critically.
  −
|
  −
| 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 -- 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.
  −
|
  −
| C.S. Peirce, 'Chronological Edition', CE 1, pp. 267-268.
  −
|
  −
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
  −
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
  −
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
   
</pre>
 
</pre>
  
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