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<p>In like manner, it is impossible to find any simple term.  This is obvious from this consideration.  If there is any simple term, simple terms are innumerable for in that case all attributes which are not simple are made up of simple attributes.  Now none of these attributes can be affirmed or denied universally of whatever has any one.  For let ''A'' be one simple term and ''B'' be another.  Now suppose we can say All ''A'' is ''B'';  then ''B'' is contained in ''A''.  If, therefore, ''A'' contains anything but ''B'' it is a compound term, but ''A'' is different from ''B'', and is simple;  hence it cannot be that All ''A'' is ''B''.  Suppose No ''A'' is ''B'', then not-''B'' is contained in ''A'';  if therefore ''A'' contains anything besides not-''B'' it is not a simple term;  but if it is the same as not-''B'', it is not a simple term but is a term relative to ''B''.  Now it is a simple term and therefore Some ''A'' is ''B''.  Hence if we take any two simple terms and call one ''A'' and the other ''B'' we have:</p>

<p>In like manner, it is impossible to find any simple term.  This is obvious from this consideration.  If there is any simple term, simple terms are innumerable for in that case all attributes which are not simple are made up of simple attributes.  Now none of these attributes can be affirmed or denied universally of whatever has any one.  For let ''A'' be one simple term and ''B'' be another.  Now suppose we can say All ''A'' is ''B'';  then ''B'' is contained in ''A''.  If, therefore, ''A'' contains anything but ''B'' it is a compound term, but ''A'' is different from ''B'', and is simple;  hence it cannot be that All ''A'' is ''B''.  Suppose No ''A'' is ''B'', then not-''B'' is contained in ''A'';  if therefore ''A'' contains anything besides not-''B'' it is not a simple term;  but if it is the same as not-''B'', it is not a simple term but is a term relative to ''B''.  Now it is a simple term and therefore Some ''A'' is ''B''.  Hence if we take any two simple terms and call one ''A'' and the other ''B'' we have:</p>

<p><center>Some ''A'' is ''B''</center>

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

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