Changes

</blockquote>

</blockquote>

====Note 3.====

====Note 3. Peirce (CE 1, 187&ndash;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.

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.

| For example, take 'cat';  now increase the extension of that greatly --

| 'cat' or 'rabbit' or 'dog';  now apply to this extended class the

<p>For example, take ''cat'';  now increase the extension of that greatly &mdash; ''cat'' or ''rabbit'' or ''dog'';  now apply to this extended class the additional intension ''feline''; &mdash; ''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>

| additional intension 'feline'; -- 'feline cat' or 'feline rabbit'

 

| or 'feline dog' is equal to 'cat' again.  This law holds good as

<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>

| long as the information remains constant, but when this is changed

 

| the relation is changed.  Thus 'cats' are before we know about them

<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>

| separable into 'blue cats" and 'cats not blue' of which classes 'cats'

 

| is the most extensive and least intensive.  But afterwards we find out

<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>

| that one of those classes cannot exist;  so that 'cats' increases its

 

| intension to equal 'cats not blue' while 'cats not blue' increases its

<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>

| extension to equal 'cats'.

 

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 187&ndash;188</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'

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

| is 'immortal' and this fact is symbolized in the word 'man'.  'Man', therefore, has at

</blockquote>

| 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'.

| 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.

| 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'.

| 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.

| C.S. Peirce, 'Chronological Edition', CE 1, pp. 187-188.

| 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>

====Note 4.====

====Note 4.====