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<p>or in other words the universe will contain every possible kind of thing afforded by the permutation of simple qualities.  Now the universe does not contain all these things;  it contains no ''well-known green horse''.  Hence the consequence of supposing a simple term to exist is an error of fact.  There are several other ways of showing this besides the one that I have adopted.  They all concur to show that whatever has extension must be composite.</p>

<p>or in other words the universe will contain every possible kind of thing afforded by the permutation of simple qualities.  Now the universe does not contain all these things;  it contains no ''well-known green horse''.  Hence the consequence of supposing a simple term to exist is an error of fact.  There are several other ways of showing this besides the one that I have adopted.  They all concur to show that whatever has extension must be composite.</p>

<p>(Peirce 1866, "Lowell Lecture 7", CE 1, 461).</p>

<p>(Peirce 1866, Lowell Lecture 7, CE 1, 461).</p>

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<p>With me — the ''Sphere'' of a term is all the things we know that it applies to, or the disjunctive sum of the subjects to which it can be predicate in an affirmative subsumptive proposition.  The ''content'' of a term is all the attributes it tells us, or the conjunctive sum of the predicates to which it can be made subject in a universal necessary proposition.</p>

<p>With me — the ''Sphere'' of a term is all the things we know that it applies to, or the disjunctive sum of the subjects to which it can be predicate in an affirmative subsumptive proposition.  The ''content'' of a term is all the attributes it tells us, or the conjunctive sum of the predicates to which it can be made subject in a universal necessary proposition.</p>

<p>The maxim then which rules explicatory reasoning is that any part of the content of a term can be predicated of any part of its sphere.  (Peirce 1866, "Lowell Lecture 7", CE 1, 462).</p>

<p>The maxim then which rules explicatory reasoning is that any part of the content of a term can be predicated of any part of its sphere.  (Peirce 1866, Lowell Lecture 7, CE 1, 462).</p>

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We come next to consider inductions.  In inferences of this kind we proceed as if upon the principle that as is a sample of a class so is the whole class.  The word ''class'' in this connection means nothing more than what is denoted by one term, — or in other words the sphere of a term.  Whatever characters belong to the whole sphere of a term constitute the content of that term.  Hence the principle of induction is that whatever can be predicated of a specimen of the sphere of a term is part of the content of that term.  And what is a specimen?  It is something taken from a class or the sphere of a term, at random — that is, not upon any further principle, not selected from a part of that sphere;  in other words it is something taken from the sphere of a term and not taken as belonging to a narrower sphere.  Hence the principle of induction is that whatever can be predicated of something taken as belonging to the sphere of a term is part of the content of that term.  But this principle is not axiomatic by any means.  Why then do we adopt it?  (Peirce 1866, "Lowell Lecture 7", CE 1, 462–463).

We come next to consider inductions.  In inferences of this kind we proceed as if upon the principle that as is a sample of a class so is the whole class.  The word ''class'' in this connection means nothing more than what is denoted by one term, — or in other words the sphere of a term.  Whatever characters belong to the whole sphere of a term constitute the content of that term.  Hence the principle of induction is that whatever can be predicated of a specimen of the sphere of a term is part of the content of that term.  And what is a specimen?  It is something taken from a class or the sphere of a term, at random — that is, not upon any further principle, not selected from a part of that sphere;  in other words it is something taken from the sphere of a term and not taken as belonging to a narrower sphere.  Hence the principle of induction is that whatever can be predicated of something taken as belonging to the sphere of a term is part of the content of that term.  But this principle is not axiomatic by any means.  Why then do we adopt it?  (Peirce 1866, Lowell Lecture 7, CE 1, 462–463).

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(·X·)  (···)  (·X·)  (···)  ( X )  (  )  ( X )  (  )

(·X·)  (···)  (·X·)  (···)  ( X )  (  )  ( X )  (  )

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<p>Now suppose we make these two terms ''dotted circle'' and ''crossed and dotted circle'' equivalent.  This we can do by crossing our uncrossed dotted circles.  In that way, we increase the comprehension of ''dotted circle'' and at the same time increase the extension of ''crossed and dotted circle'' since we now make it denote ''all dotted circles''. (Peirce 1866, "Lowell Lecture 7", CE 1, 463–464).</p>

<p>Now suppose we make these two terms ''dotted circle'' and ''crossed and dotted circle'' equivalent.  This we can do by crossing our uncrossed dotted circles.  In that way, we increase the comprehension of ''dotted circle'' and at the same time increase the extension of ''crossed and dotted circle'' since we now make it denote ''all dotted circles''.</p>

 

<p>(Peirce 1866, Lowell Lecture 7, CE 1, 463&ndash;464).</p>

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Thus every increase in the number of equivalents of any term increases either its extension or comprehension and ''conversely''.  It may be said that there are no equivalent terms in logic, since the only difference between such terms would be merely external and grammatical, while in logic terms which have the same meaning are identical.  I fully admit that.  Indeed, the process of getting an equivalent for a term is an identification of two terms previously diverse.  It is, in fact, the process of nutrition of terms by which they get all their life and vigor and by which they put forth an energy almost creative — since it has the effect of reducing the chaos of ignorance to the cosmos of science.  Each of these equivalents is the explication of what there is wrapt up in the primary — they are the surrogates, the interpreters of the original term.  They are new bodies, animated by that same soul.  I call them the ''interpretants'' of the term.  And the quantity of these ''interpretants'', I term the ''information'' or ''implication'' of the term. (Peirce 1866, "Lowell Lecture 7", CE 1, 464–465).

<p>Thus every increase in the number of equivalents of any term increases either its extension or comprehension and ''conversely''.  It may be said that there are no equivalent terms in logic, since the only difference between such terms would be merely external and grammatical, while in logic terms which have the same meaning are identical.  I fully admit that.  Indeed, the process of getting an equivalent for a term is an identification of two terms previously diverse.  It is, in fact, the process of nutrition of terms by which they get all their life and vigor and by which they put forth an energy almost creative — since it has the effect of reducing the chaos of ignorance to the cosmos of science.  Each of these equivalents is the explication of what there is wrapt up in the primary &mdash; they are the surrogates, the interpreters of the original term.  They are new bodies, animated by that same soul.  I call them the ''interpretants'' of the term.  And the quantity of these ''interpretants'', I term the ''information'' or ''implication'' of the term.</p>

 

<p>(Peirce 1866, Lowell Lecture 7, CE 1, 464&ndash;465).

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<p>which means that when the information is increased there is an increase of either extension or comprehension without any diminution of the other of these quantities.</p>

<p>which means that when the information is increased there is an increase of either extension or comprehension without any diminution of the other of these quantities.</p>

<p>Now, ladies and gentlemen, as it is true that every increase of our knowledge is an increase in the information of a term — that is, is an addition to the number of terms equivalent to that term — so it is also true that the first step in the knowledge of a thing, the first framing of a term, is also the origin of the information of that term because it gives the first term equivalent to that term.  I here announce the great and fundamental secret of the logic of science.  There is no term, properly so called, which is entirely destitute of information, of equivalent terms.  The moment an expression acquires sufficient comprehension to determine its extension, it already has more than enough to do so.  (Peirce 1866, "Lowell Lecture 7", CE 1, 465).</p>

<p>Now, ladies and gentlemen, as it is true that every increase of our knowledge is an increase in the information of a term — that is, is an addition to the number of terms equivalent to that term — so it is also true that the first step in the knowledge of a thing, the first framing of a term, is also the origin of the information of that term because it gives the first term equivalent to that term.  I here announce the great and fundamental secret of the logic of science.  There is no term, properly so called, which is entirely destitute of information, of equivalent terms.  The moment an expression acquires sufficient comprehension to determine its extension, it already has more than enough to do so.  (Peirce 1866, Lowell Lecture 7, CE 1, 465).</p>

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<p>The interpretant of a term, then, and that which it stands to are identical.  Hence, since it is of the very essence of a symbol that it should stand ''to'' something, every symbol — every word and every ''conception'' — must have an interpretant — or what is the same thing, must have information or implication.</p>

<p>The interpretant of a term, then, and that which it stands to are identical.  Hence, since it is of the very essence of a symbol that it should stand ''to'' something, every symbol — every word and every ''conception'' — must have an interpretant — or what is the same thing, must have information or implication.</p>

<p>Let us now return to the information.  The information of a term is the measure of its superfluous comprehension.  That is to say that the proper office of the comprehension is to determine the extension of the term.  For instance, you and I are men because we possess those attributes — having two legs, being rational, &c. — which make up the comprehension of ''man''.  Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.  (Peirce 1866, "Lowell Lecture 7", CE 1, 466–467).</p>

<p>Let us now return to the information.  The information of a term is the measure of its superfluous comprehension.  That is to say that the proper office of the comprehension is to determine the extension of the term.  For instance, you and I are men because we possess those attributes — having two legs, being rational, &c. — which make up the comprehension of ''man''.  Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.  (Peirce 1866, Lowell Lecture 7, CE 1, 466–467).</p>

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<p>Now this maxim would not be true if the Extension and Comprehension were directly proportional to one another;  this is to say if the Greater the one the greater the other.  For in that case, though the whole Content would belong to the whole Sphere;  yet only a particular part of it would belong to a part of that Sphere and not every part to every part.  On the other hand if the Comprehension and Extension were not in some way proportional to one another, that is if terms of different spheres could have the same content or terms of the same content different spheres;  then there would be no such fact as a content's ''belonging'' to a sphere and hence again the maxim would fail.  For the maxim to be true, then, it is absolutely necessary that the comprehension and extension should be inversely proportional to one another.  That is that the greater the sphere, the less the content.</p>

<p>Now this maxim would not be true if the Extension and Comprehension were directly proportional to one another;  this is to say if the Greater the one the greater the other.  For in that case, though the whole Content would belong to the whole Sphere;  yet only a particular part of it would belong to a part of that Sphere and not every part to every part.  On the other hand if the Comprehension and Extension were not in some way proportional to one another, that is if terms of different spheres could have the same content or terms of the same content different spheres;  then there would be no such fact as a content's ''belonging'' to a sphere and hence again the maxim would fail.  For the maxim to be true, then, it is absolutely necessary that the comprehension and extension should be inversely proportional to one another.  That is that the greater the sphere, the less the content.</p>

<p>Now this evidently true.  If we take the term ''man'' and increase its ''comprehension'' by the addition of ''black'', we have ''black man'' and this has less ''extension'' than ''man''.  So if we take ''black man'' and add ''non-black man'' to its sphere, we have ''man'' again, and so have decreased the comprehension.  So that whenever the extension is increased the comprehension is diminished and ''vice versa''.  (Peirce 1866, "Lowell Lecture 7", CE 1, 459–460).</p>

<p>Now this evidently true.  If we take the term ''man'' and increase its ''comprehension'' by the addition of ''black'', we have ''black man'' and this has less ''extension'' than ''man''.  So if we take ''black man'' and add ''non-black man'' to its sphere, we have ''man'' again, and so have decreased the comprehension.  So that whenever the extension is increased the comprehension is diminished and ''vice versa''.  (Peirce 1866, Lowell Lecture 7, CE 1, 459–460).</p>

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<center>Some ''A'' is not ''B''</center></p>

<center>Some ''A'' is not ''B''</center></p>

<p>or in other words the universe will contain every possible kind of thing afforded by the permutation of simple qualities.  Now the universe does not contain all these things;  it contains no ''well-known green horse''.  Hence the consequence of supposing a simple term to exist is an error of fact.  There are several other ways of showing this besides the one that I have adopted.  They all concur to show that whatever has extension must be composite.  (Peirce 1866, "Lowell Lecture 7", CE 1, 460–461).</p>

<p>or in other words the universe will contain every possible kind of thing afforded by the permutation of simple qualities.  Now the universe does not contain all these things;  it contains no ''well-known green horse''.  Hence the consequence of supposing a simple term to exist is an error of fact.  There are several other ways of showing this besides the one that I have adopted.  They all concur to show that whatever has extension must be composite.  (Peirce 1866, Lowell Lecture 7, CE 1, 460–461).</p>

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<p>The consequence of this fact is that when we wish to enumerate the sphere of a term — a process termed ''division'' — or when we wish to run over the content of a term — a process called ''definition'' — since we cannot take the elements of our enumeration singly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some.  Hence the extension and comprehension which we know will be somewhat indeterminate.  But we must distinguish two kinds of these quantities.  If we were to subtilize we might make other distinctions but I shall be content with two.  They are the extension and comprehension relatively to our actual knowledge, and what these would be were our knowledge perfect.</p>

<p>The consequence of this fact is that when we wish to enumerate the sphere of a term — a process termed ''division'' — or when we wish to run over the content of a term — a process called ''definition'' — since we cannot take the elements of our enumeration singly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some.  Hence the extension and comprehension which we know will be somewhat indeterminate.  But we must distinguish two kinds of these quantities.  If we were to subtilize we might make other distinctions but I shall be content with two.  They are the extension and comprehension relatively to our actual knowledge, and what these would be were our knowledge perfect.</p>

<p>Logicians have hitherto left the doctrine of extension and comprehension in a very imperfect state owing to the blinding influence of a psychological treatment of the matter.  They have, therefore, not made this distinction and have reduced the comprehension of a term to what it would be if we had no knowledge of fact at all.  I mention this because if you should come across the matter I am now discussing in any book, you would find the matter left in quite a different state.  (Peirce 1866, "Lowell Lecture 7", CE 1, 462).</p>

<p>Logicians have hitherto left the doctrine of extension and comprehension in a very imperfect state owing to the blinding influence of a psychological treatment of the matter.  They have, therefore, not made this distinction and have reduced the comprehension of a term to what it would be if we had no knowledge of fact at all.  I mention this because if you should come across the matter I am now discussing in any book, you would find the matter left in quite a different state.  (Peirce 1866, Lowell Lecture 7, CE 1, 462).</p>

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<p>Hence if we find out that neat are herbivorous, swine are herbivorous, sheep are herbivorous, and deer are herbivorous;  we may be sure that there is some class of animals which covers all these, all the members of which are herbivorous.  Now a disjunctive term — such as ''neat swine sheep and deer'', or ''man, horse, kangaroo, and whale'' — is not a true symbol.  It does not denote what it does in consequence of its connotation, as a symbol does;  on the contrary, no part of its connotation goes at all to determine what it denotes — it is in that respect a mere accident if it denote anything.  Its ''sphere'' is determined by the concurrence of the four members, man, horse, kangaroo, and whale, or neat swine sheep and deer as the case may be.</p>

<p>Hence if we find out that neat are herbivorous, swine are herbivorous, sheep are herbivorous, and deer are herbivorous;  we may be sure that there is some class of animals which covers all these, all the members of which are herbivorous.  Now a disjunctive term — such as ''neat swine sheep and deer'', or ''man, horse, kangaroo, and whale'' — is not a true symbol.  It does not denote what it does in consequence of its connotation, as a symbol does;  on the contrary, no part of its connotation goes at all to determine what it denotes — it is in that respect a mere accident if it denote anything.  Its ''sphere'' is determined by the concurrence of the four members, man, horse, kangaroo, and whale, or neat swine sheep and deer as the case may be.</p>

<p>Now those who are not accustomed to the homologies of the conceptions of men and words, will think it very fanciful if I say that this concurrence of four terms to determine the sphere of a disjunctive term resembles the arbitrary convention by which men agree that a certain sign shall stand for a certain thing.  And yet how is such a convention made?  The men all look upon or think of the thing and each gets a certain conception and then they agree that whatever calls up or becomes an object of that conception in either of them shall be denoted by the sign.  In the one case, then, we have several different words and the disjunctive term denotes whatever is the object of either of them.  In the other case, we have several different conceptions — the conceptions of different men — and the conventional sign stands for whatever is an object of either of them.  It is plain the two cases are essentially the same, and that a disjunctive term is to be regarded as a conventional sign or index.  And we find both agree in having a determinate extension but an inadequate comprehension.  (Peirce 1866, "Lowell Lecture 7", CE 1, 468–469).</p>

<p>Now those who are not accustomed to the homologies of the conceptions of men and words, will think it very fanciful if I say that this concurrence of four terms to determine the sphere of a disjunctive term resembles the arbitrary convention by which men agree that a certain sign shall stand for a certain thing.  And yet how is such a convention made?  The men all look upon or think of the thing and each gets a certain conception and then they agree that whatever calls up or becomes an object of that conception in either of them shall be denoted by the sign.  In the one case, then, we have several different words and the disjunctive term denotes whatever is the object of either of them.  In the other case, we have several different conceptions — the conceptions of different men — and the conventional sign stands for whatever is an object of either of them.  It is plain the two cases are essentially the same, and that a disjunctive term is to be regarded as a conventional sign or index.  And we find both agree in having a determinate extension but an inadequate comprehension.  (Peirce 1866, Lowell Lecture 7, CE 1, 468–469).</p>

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<p>Now this maxim would not be true if the Extension and Comprehension were directly proportional to one another;  this is to say if the Greater the one the greater the other.  For in that case, though the whole Content would belong to the whole Sphere;  yet only a particular part of it would belong to a part of that Sphere and not every part to every part.  On the other hand if the Comprehension and Extension were not in some way proportional to one another, that is if terms of different spheres could have the same content or terms of the same content different spheres;  then there would be no such fact as a content's ''belonging'' to a sphere and hence again the maxim would fail.  For the maxim to be true, then, it is absolutely necessary that the comprehension and extension should be inversely proportional to one another.  That is that the greater the sphere, the less the content.</p>

<p>Now this maxim would not be true if the Extension and Comprehension were directly proportional to one another;  this is to say if the Greater the one the greater the other.  For in that case, though the whole Content would belong to the whole Sphere;  yet only a particular part of it would belong to a part of that Sphere and not every part to every part.  On the other hand if the Comprehension and Extension were not in some way proportional to one another, that is if terms of different spheres could have the same content or terms of the same content different spheres;  then there would be no such fact as a content's ''belonging'' to a sphere and hence again the maxim would fail.  For the maxim to be true, then, it is absolutely necessary that the comprehension and extension should be inversely proportional to one another.  That is that the greater the sphere, the less the content.</p>

<p>Now this evidently true.  If we take the term ''man'' and increase its ''comprehension'' by the addition of ''black'', we have ''black man'' and this has less ''extension'' than ''man''.  So if we take ''black man'' and add ''non-black man'' to its sphere, we have ''man'' again, and so have decreased the comprehension.  So that whenever the extension is increased the comprehension is diminished and ''vice versa''.  (Peirce 1866, "Lowell Lecture 7", CE 1, 459–460).</p>

<p>Now this evidently true.  If we take the term ''man'' and increase its ''comprehension'' by the addition of ''black'', we have ''black man'' and this has less ''extension'' than ''man''.  So if we take ''black man'' and add ''non-black man'' to its sphere, we have ''man'' again, and so have decreased the comprehension.  So that whenever the extension is increased the comprehension is diminished and ''vice versa''.  (Peirce 1866, Lowell Lecture 7, CE 1, 459–460).</p>

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<p>Thus, every addition to our information about a term is an addition to the number of equivalents which that term has.  Now, in whatever way a term gets to have a new equivalent, whether by an increase in our knowledge, or by a change in the things it denotes, this always results in an increase either of extension or comprehension without a corresponding decrease in the other quantity.</p>

<p>Thus, every addition to our information about a term is an addition to the number of equivalents which that term has.  Now, in whatever way a term gets to have a new equivalent, whether by an increase in our knowledge, or by a change in the things it denotes, this always results in an increase either of extension or comprehension without a corresponding decrease in the other quantity.</p>

<p>(Peirce 1866, "Lowell Lecture 7", CE 1, 462–464).</p>

<p>(Peirce 1866, Lowell Lecture 7, CE 1, 462–464).</p>

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