Changes

</blockquote>

</blockquote>

====LAS.  Note 6====

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

<pre>

<blockquote>

| To prove then, first, that all symbols are symbolizable.

<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>

| Every syllogism consists of three propositions with two terms

 

| each, a subject and a predicate, and three terms in all each term

<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>

| 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.

<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>

| Hence in all reasoning 'à priori' a symbol must be symbolized.

 

| But as reasoning 'à priori' is possible about a statement

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

| without reference to its predicate, all symbols must be

 

| symbolizable.

<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>

| 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====

====LAS.  Note 7====