Changes

</blockquote>

</blockquote>

====Note 8.====

====Note 8. Peirce (CE 1, 280)====

<pre>

<blockquote>

| But there are three distinct kinds of inference;

<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>

| 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.

</pre>

====Note 9.====

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 280</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&ndash;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

| 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 10.====

====Note 9. Peirce (CE 1, 280&ndash;281)====

<pre>

<blockquote>

| 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.

 

| 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

<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>

| rest on nothing but deduction, and therefore it must relate

 

| to something whose character depends upon its definition.

<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>

| Now the only objects of which this is true are symbols;

 

| they indeed are created by their definition;  while

<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>

| neither forms nor things are.  Hence, the principle

 

| of deduction must relate to the symbolizability of

<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 &mdash; the same matter &mdash; that they were before.  Hence, the principle of induction must relate to the symbolizability of things.</p>

| symbols.

 

<p>All these principles must as principles be universal. Hence they are as follows: &mdash;</p>

| The principle of hypothetic inference must be established hypothetically,

 

| that is by reasoning from determinate to determinant.  Now it is clear that

<p>All things, forms, symbols are symbolizable.</p>

| 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

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 281&ndash;282</p>

| 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

<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>

| far as they determine some symbol or object.  Hence the principle of hypothetic

</blockquote>

| inference must relate to the symbolizability of forms.

| 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 dissappeared 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.

| All these principles must as principles be universal.

| Hence they are as follows: --

| All things, forms, symbols are symbolizable.

| C.S. Peirce, 'Chronological Edition', CE 1, pp. 281-282.

| 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>

==Locations Cited==

==Locations Cited==

# 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