Changes

</blockquote>

</blockquote>

====LAS.  Note 10====

====Excerpt 10.  Peirce (CE 1, 267&ndash;268)====

<pre>

<blockquote>

| When have then three different kinds of inference.

<p>When have then three different kinds of inference.</p>

 

|    Deduction or inference 'à priori',

:<p>Deduction or inference ''à priori'',</p>

 

|    Induction or inference 'à particularis', and

:<p>Induction or inference ''à particularis'', and</p>

 

|    Hypothesis or inference 'à posteriori'.

:<p>Hypothesis or inference ''à posteriori''.</p>

 

| It is necessary now to examine this classification critically.

<p>It is necessary now to examine this classification critically.</p>

 

| And first let me specify what I claim for my invention.  I do not claim that it is

<p>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 &mdash; 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.</p>

| 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

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 267&ndash;268</p>

| 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.

<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>

| It is true that in the solutions of quadratic equations, there are generally two

</blockquote>

| 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>

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