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Directory talk:Jon Awbrey/Projects/Notes And Queries (view source)
Revision as of 18:28, 8 November 2011
, 18:28, 8 November 2011Category:Charles Sanders Peirce
====Note 2. Peirce (CE 1, 187)====
====Note 2. Peirce (CE 1, 187)====
<pre>
<blockquote>
<p>In order to understand how these principles of ''à posteriori'' and inductive inference can be put into practice, we must consider by itself the substitution of one symbol for another. Symbols are alterable and comparable in three ways.</p>
</pre>
<p>In the first place they may denote more or fewer possible differing things; in this regard they are said to have ''extension''.</p>
<pre>
<p>In the second place, they may imply more or less as to the quality of these things; in this respect they are said to have ''intension''.</p>
<p>In the third place they may involve more or less real knowledge; in this respect they have ''information'' and ''distinctness''.</p>
</pre>
<p>Logical writers generally speak only of extension and intension and Kant has laid down the law that these quantities are inverse in respect of each other.</p>
<pre>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 187</p>
</pre>
<p>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.</p>
</blockquote>
====Note 3. Peirce (CE 1, 187–188)====
I am going to run through the series of concrete illustrations that Peirce lays out to explain his take on the conceptions of extension, intension, and information. It is a mite long, but helps better than anything else I know to bring what Peirce is talking about down to earth. For ease of comprehension I will divide this extended paragraph into more moderate-sized chunks.
<pre>
<blockquote>
<p>For example, take ''cat''; now increase the extension of that greatly — ''cat'' or ''rabbit'' or ''dog''; now apply to this extended class the additional intension ''feline''; — ''feline cat'' or ''feline rabbit'' or ''feline dog'' is equal to ''cat'' again. This law holds good as long as the information remains constant, but when this is changed the relation is changed. Thus ''cats'' are before we know about them separable into ''blue cats'' and ''cats not blue'' of which classes ''cats'' is the most extensive and least intensive. But afterwards we find out that one of those classes cannot exist; so that ''cats'' increases its intension to equal ''cats not blue'' while ''cats not blue'' increases its extension to equal ''cats''.</p>
</pre>
<p>Again, to give a better case, ''rational animal'' is divisible into ''mortal rational animal'' and ''immortal rational animal''; but upon information we find that no ''rational animal'' is ''immortal'' and this fact is symbolized in the word ''man''. ''Man'', therefore, has at once the extension of ''rational animal'' with the intension of ''mortal rational animal'', and far more beside, because it involves more ''information'' than either of the previous symbols. ''Man'' is more ''distinct'' than ''rational animal'', and more ''formal'' than ''mortal rational animal''.</p>
<pre>
<p>Now of two statements both of which are true, it is obvious that that contains the most truth which contains the most information. If two predicates of the same intension, therefore, are true of the same subject, the most formal one contains the most truth.</p>
</pre>
<p>Thus, it is better to say Socrates is a man, than to say Socrates is an animal who is rational mortal risible biped &c. because the former contains all the last and in addition it forms the synthesis of the whole under a definite ''form''.</p>
<pre>
<p>On the other hand if the same predicate is applicable to two equivalent subjects, that one is to be preferred which is the most ''distinct''; thus it conveys more truth to say All men are born of women, than All rational animals are born of women, because the former has at once as much extension as the latter, and a much closer reference to the things spoken of.</p>
</pre>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 187–188</p>
<pre>
<p>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.</p>
</blockquote>
</pre>
====Note 10.====
====Note 4. Peirce (CE 1, 188–189)====
<pre>
<blockquote>
<p>Let us now take the two statements, ''S'' is ''P'', Σ is ''P''; let us suppose that Σ is much more distinct than ''S'' and that it is also more extensive. But we ''know'' that ''S'' is ''P''. Now if Σ were not more extensive than ''S'', Σ is ''P'' would contain more truth than ''S'' is P; being more extensive it ''may'' contain more truth and it may also introduce a falsehood. Which of these probabilities is the greatest? Σ by being more extensive becomes less intensive; it is the intension which introduces truth and the extension which introduces falsehood. If therefore Σ increases the intension of ''S'' more than its extension, Σ is to be preferred to ''S''; otherwise not. Now this is the case of induction. Which contains most truth, ''neat'' and ''deer'' are herbivora, or cloven-footed animals are herbivora?</p>
<p>In the two statements, ''S'' is ''P'', ''S'' is Π, let Π be at once more ''formal'' and more ''intensive'' than ''P''; and suppose we only ''know'' that ''S'' is ''P''. In this case the increase of formality gives a chance of additional truth and the increase of intension a chance of error. If the extension of Π is more increased than than its intension, then ''S'' is Π is likely to contain more truth than ''S'' is ''P'' and ''vice versa''. This is the case of ''à posteriori'' reasoning. We have for instance to choose between:</p>
:{| cellpadding="4"
| || Light gives fringes of such and such a description
|-
| and || Light is ether-waves.
|}
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 188–189</p>
<p>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.</p>
</blockquote>
====Note 5. Peirce (CE 1, 276)====
<blockquote>
<p>Thus the process of information disturbs the relations of extension and comprehension for a moment and the class which results from the equivalence of two others has a greater intension than one and a greater extension than the other. Hence, we may conveniently alter the formula for the relations of extension and comprehension; thus, instead of saying that one is the reciprocal of the other, or:</p>
<center>
<p>comprehension × extension = constant,</p>
</center>
<p>we may say:</p>
<center>
|
<p>comprehension × extension = information.</p>
| The principle of inductive inference must be established inductively,
</center>
| that is by reasoning from parts to whole. This kind of reasoning can
| apply only to those objects whose parts collectively are their whole.
<p>We see then that all symbols besides their denotative and connotative objects have another; their informative object. The denotative object is the total of possible things denoted. The connotative object is the total of symbols translated or implied. The informative object is the total of forms manifested and is measured by the amount of intension the term has, over and above what is necessary for limiting its extension. For example, the denotative object of ''man'' is such collections of matter the word knows while it knows them, i.e., while they are organized. The connotative object of ''man'' is the total form which the word expresses. The informative object of ''man'' is the total fact which it embodies; or the value of the conception which is its equivalent symbol.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 276</p>
<p>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.</p>
</blockquote>
====Note 6. Peirce (CE 1, 278–279)====
<blockquote>
<p>The difference between connotation, denotation, and information supplies the basis for another division of terms and propositions; a division which is related to the one we have just considered in precisely the same way as the division of syllogism into 3 figures is related to the division into Deduction, Induction, and Hypothesis.</p>
<p>Every symbol which has connotation and denotation has also information. For by the denotative character of a symbol, I understand application to objects implied in the symbol itself. The existence therefore of objects of a certain kind is implied in every connotative denotative symbol; and this is information.</p>
<p>Now there are certain imperfect or false symbols produced by the combination of true symbols which have lost either their denotation or their connotation. When symbols are combined together in extension as for example in the compound term "cats and dogs", their sum possesses denotation but no connotation or at least no connotation which determines their denotation. Hence, such terms, which I prefer to call ''enumerative'' terms, have no information and it remains unknown whether there be any real kind corresponding to cats and dogs taken together. On the other hand when symbols are combined together in comprehension as for example in the compound "tailed men" the product possesses connotation but no denotation, it not being therein implied that there may be any ''tailed men''. Such conjunctive terms have therefore no information. Thirdly there are names purporting to be of real kinds as ''men''; and these are perfect symbols.</p>
<p>Enumerative terms are not truly symbols but only signs; and Conjunctive terms are copies; but these copies and signs must be considered in symbolistic because they are composed of symbols.</p>
<p>When an enumerative term forms the subject of a grammatical proposition, as when we say "cats and dogs have tails", there is no logical unity in the proposition at all. Logically, therefore, it is two propositions and not one. The same is the case when a conjunctive proposition forms the predicate of a sentence; for to say that "hens are feathered bipeds" is simply to predicate two unconnected marks of them.</p>
<p>When an enumerative term as such is the predicate of a proposition, that proposition cannot be a denotative one, for a denotative proposition is one which merely analyzes the denotation of its predicate, but the denotation of an enumerative term is analyzed in the term itself; hence if an enumerative term as such were the predicate of a proposition that proposition would be equivalent in meaning to its own predicate. On the other hand, if a conjunctive term as such is the subject of a proposition, that proposition cannot be connotative, for the connotation of a conjunctive term is already analyzed in the term itself, and a connotative proposition does no more than analyze the connotation of its subject. Thus we have</p>
<center>
<p>Conjunctive Simple Enumerative</p>
</pre>
</center>
<p>propositions so related to</p>
<center>
<p>Denotative Informative Connotative</p>
</center>
<p>propositions that what is on the left hand of one line cannot be on the right hand of the other.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 278–279</p>
<p>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.</p>
</blockquote>
====Note 7. Peirce (CE 1, 279–280)====
<blockquote>
<p>We are now in a condition to discuss the question of the grounds of scientific inference. This problem naturally divides itself into parts:</p>
:{| cellpadding="4"
| valign="top" | 1st
| To state and prove the principles upon which the possibility in general of each kind of inference depends,
|-
| valign="top" | 2nd
| To state and prove the rules for making inferences in particular cases.
|}
<p>The first point I shall discuss in the remainder of this lecture; the second I shall scarcely be able to touch upon in these lectures.</p>
<p>Inference in general obviously supposes symbolization; and all symbolization is inference. For every symbol as we have seen contains information. And in the last lecture we saw that all kinds of information involve inference. Inference, then, is symbolization. They are the same notions. Now we have already analyzed the notion of a ''symbol'', and we have found that it depends upon the possibility of representations acquiring a nature, that is to say an immediate representative power. This principle is therefore the ground of inference in general.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 279–280</p>
<p>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.</p>
</blockquote>
====Note 8. Peirce (CE 1, 280)====
<blockquote>
<p>But there are three distinct kinds of inference; inconvertible and different in their conception. There must, therefore, be three different principles to serve for their grounds. These three principles must also be indemonstrable; that is to say, each of them so far as it can be proved must be proved by means of that kind of inference of which it is the ground. For if the principle of either kind of inference were proved by another kind of inference, the former kind of inference would be reduced to the latter; and since the different kinds of inference are in all respects different this cannot be. You will say that it is no proof of these principles at all to support them by that which they themselves support. But I take it for granted at the outset, as I said at the beginning of my first lecture, that induction and hypothesis have their own validity. The question before us is ''why'' they are valid. The principles, therefore, of which we are in search, are not to be used to prove that the three kinds of inference are valid, but only to show how they come to be valid, and the proof of them consists in showing that they determine the validity of the three kinds of inference.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 280</p>
<p>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.</p>
</blockquote>
====Note 9. Peirce (CE 1, 280–281)====
<blockquote>
<p>But these three principles must have this in common that they refer to ''symbolization'' for they are principles of inference which is symbolization. As grounds of the possibility of inference they must refer to the possibility of symbolization or symbolizability. And as logical principles they must relate to the reference of symbols to objects; for logic has been defined as the science of the general conditions of the relations of symbols to objects. But as three different principles they must state three different relations of symbols to objects. Now we already found that a symbol has three different relations to objects; namely, connotation, denotation, and information, which are its relations to the object considered as a thing, a form, and an equivalent representation. Hence, it is obvious that these three principles must relate to the symbolizability of things, of forms, and of symbols.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 280–281</p>
<p>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.</p>
</blockquote>
====Note 10. Peirce (CE 1, 281–282)====
<blockquote>
<p>Our next business is to find out which is which. For this purpose we must consider that each principle is to be proved by the kind of inference which it supports.</p>
<p>The ground of deductive inference then must be established deductively; that is by reasoning from determinant to determinate, or in other words by reasoning from definition. But this kind of reasoning can only be applied to an object whose character depends upon its definition. Now of most objects it is the definition which depends upon the character; and so the definition must therefore itself rest on induction or hypothesis. But the principle of deduction must rest on nothing but deduction, and therefore it must relate to something whose character depends upon its definition. Now the only objects of which this is true are symbols; they indeed are created by their definition; while neither forms nor things are. Hence, the principle of deduction must relate to the symbolizability of symbols.</p>
<p>The principle of hypothetic inference must be established hypothetically, that is by reasoning from determinate to determinant. Now it is clear that this kind of reasoning is applicable only to that which is determined by what it determines; or that which is only subject to truth and falsehood so far as its determinate is, and is thus of itself pure ''zero''. Now this is the case with nothing whatever except the pure forms; they indeed are what they are only in so far as they determine some symbol or object. Hence the principle of hypothetic inference must relate to the symbolizability of forms.</p>
<p>The principle of inductive inference must be established inductively, that is by reasoning from parts to whole. This kind of reasoning can apply only to those objects whose parts collectively are their whole. Now of symbols this is not true. If I write ''man'' here and ''dog'' here that does not constitute the symbol of ''man and dog'', for symbols have to be reduced to the unity of symbolization which Kant calls the unity of apperception and unless this be indicated by some special mark they do not constitute a whole. In the same way forms have to determine the same matter before they are added; if the curtains are green and the wainscot yellow that does not make a ''yellow-green''. But with things it is altogether different; wrench the blade and handle of a knife apart and the form of the knife has disappeared but they are the same thing — the same matter — that they were before. Hence, the principle of induction must relate to the symbolizability of things.</p>
<p>All these principles must as principles be universal. Hence they are as follows: —</p>
<p>All things, forms, symbols are symbolizable.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 281–282</p>
<p>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.</p>
</blockquote>
==Locations Cited==
==Locations Cited==
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[[Category:Charles Sanders Peirce]]