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MyWikiBiz, Author Your Legacy — Thursday March 28, 2024
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<p>All these principles must as principles be universal.  Hence they are as follows:</p>
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<p>All these principles must as principles be universal.  Hence they are as follows:&mdash;</p>
 
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<p>All things, forms, symbols are symbolizable.</p>
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| align="center" | <math>\text{All things, forms, symbols are symbolizable.}\!</math>
 
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<p>The next step is to prove each of these principles.  First then, to prove deductively that all symbols are symbolizable.  In every syllogism there is a term which is predicate and subject.  But a predicate is a symbol of its subject.  Hence, in every deduction a symbol is symbolized.  Now deduction is valid independently of the matter of the judgment.  Hence all symbols are symbolizable.</p>
 
<p>The next step is to prove each of these principles.  First then, to prove deductively that all symbols are symbolizable.  In every syllogism there is a term which is predicate and subject.  But a predicate is a symbol of its subject.  Hence, in every deduction a symbol is symbolized.  Now deduction is valid independently of the matter of the judgment.  Hence all symbols are symbolizable.</p>
    
<p>Next;  to prove inductively that all things are symbolizable.  For this purpose we must take all the collocations of things we can and judge by them.  Now all these collocations of things have been selected upon some principle;  this principle of selection is a predicate of them and a ''concept''.  Being a concept it is a symbol.  And it partakes of that peculiarity of symbols that it must have information.  We have no concepts which do not denote some things as well as connoting;  because all our thought begins with experience.  But a symbol which has connotation and denotation contains information.  Whatever symbol contains information contains more connotation than is necessary to limit its possible denotation to those things which it may denote.  That is every symbol contains more than is sufficient for a principle of selection.  Hence every selected collocation of things must have something more than a mere principle of selection, it must have another common quality.  Now by induction this common quality may be predicated of the whole possible denotation of the concept which serves as principle of selection.  And thus every collocation of things we can select is symbolized by its principle of selection.  Now by induction we pass from this statement that all things we can take are symbolizable to the principle that all things are symbolzable.  Q.E.D.  This argument though inductive in form is of the highest possible validity, for no case can possibly arise to contradict it.</p>
 
<p>Next;  to prove inductively that all things are symbolizable.  For this purpose we must take all the collocations of things we can and judge by them.  Now all these collocations of things have been selected upon some principle;  this principle of selection is a predicate of them and a ''concept''.  Being a concept it is a symbol.  And it partakes of that peculiarity of symbols that it must have information.  We have no concepts which do not denote some things as well as connoting;  because all our thought begins with experience.  But a symbol which has connotation and denotation contains information.  Whatever symbol contains information contains more connotation than is necessary to limit its possible denotation to those things which it may denote.  That is every symbol contains more than is sufficient for a principle of selection.  Hence every selected collocation of things must have something more than a mere principle of selection, it must have another common quality.  Now by induction this common quality may be predicated of the whole possible denotation of the concept which serves as principle of selection.  And thus every collocation of things we can select is symbolized by its principle of selection.  Now by induction we pass from this statement that all things we can take are symbolizable to the principle that all things are symbolzable.  Q.E.D.  This argument though inductive in form is of the highest possible validity, for no case can possibly arise to contradict it.</p>
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<p>Thirdly, we have to prove hypothetically that all forms are symbolizable.  For this purpose we must consider that 'forms' are nothing unless they are embodied, and then they constitute the synthesis of the matter.  Hence the knowledge of them cannot be directly given but must be obtained by hypothesis.  Now we have to explain this fact, that all forms are to be regarded as subjects for hypothesis, by a hypothesis.  For this purpose, we should reflect that whatever is symbolizable is symbolized by terms and their combinations.  Now we saw at the last lecture that the process of obtaining a new term is a hypothetic inference.  So that everything which is symbolizable is to be regarded as a subject for hypothesis.  This accounts for the same thing being true of forms, if we make the hypothesis that all forms are symbolizable.  Q.E.D.  This argument though only an hypothesis could not have been stronger for the conclusion involves no matter of fact at all. (Peirce 1865, "Harvard Lecture 10Grounds of Induction", CE 1, 282–283).</p>
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<p>Thirdly, we have to prove hypothetically that all forms are symbolizable.  For this purpose we must consider that 'forms' are nothing unless they are embodied, and then they constitute the synthesis of the matter.  Hence the knowledge of them cannot be directly given but must be obtained by hypothesis.  Now we have to explain this fact, that all forms are to be regarded as subjects for hypothesis, by a hypothesis.  For this purpose, we should reflect that whatever is symbolizable is symbolized by terms and their combinations.  Now we saw at the last lecture that the process of obtaining a new term is a hypothetic inference.  So that everything which is symbolizable is to be regarded as a subject for hypothesis.  This accounts for the same thing being true of forms, if we make the hypothesis that all forms are symbolizable.  Q.E.D.  This argument though only an hypothesis could not have been stronger for the conclusion involves no matter of fact at all.</p>
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<p>(Peirce 1865, Harvard Lecture 10 : Grounds of Induction, CE 1, 282&ndash;283).</p>
 
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