Changes

<p>On the contrary, the succession of Predicates of Predicates is different in the different Modes of Being.  Meantime, it will be proper that in our system of diagrammatization we should provide for the division, whenever needed, of each of our three Universes of modes of reality into ''Realms'' for the different Predicaments.</p>

<p>On the contrary, the succession of Predicates of Predicates is different in the different Modes of Being.  Meantime, it will be proper that in our system of diagrammatization we should provide for the division, whenever needed, of each of our three Universes of modes of reality into ''Realms'' for the different Predicaments.</p>

<p>Peirce, CP&nbsp;4.549, &ldquo;Prolegomena to an Apology for Pragmaticism&rdquo;, ''The Monist'' 16, 492&ndash;546 (1906), CP&nbsp;4.530&ndash;572.</p>

<p>C.S. Peirce, CP&nbsp;4.549, &ldquo;Prolegomena to an Apology for Pragmaticism&rdquo;, ''The Monist'' 16, 492&ndash;546 (1906), CP&nbsp;4.530&ndash;572.</p>

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{| align="center" width="90%"

{| align="center" width="90%"

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<p><math>\operatorname{Ref}(R) \colon (x)R(x, x),</math><br>

<math>\begin{array}{l}

<math>\operatorname{Sym}(R) \colon (x)(y)(R(x, y) \rightarrow R(y, x)),</math><br>

\operatorname{Ref}(R) \colon (x)R(x, x),

<math>\operatorname{Tr}(R) \colon (x)(y)(z)(R(x, y) \And R(y, z) \rightarrow R(x, z)).</math></p>

\operatorname{Sym}(R) \colon (x)(y)(R(x, y) \rightarrow R(y, x)),

\operatorname{Tr}(R) \colon (x)(y)(z)(R(x, y) \And R(y, z) \rightarrow R(x, z)).

\end{array}</math>

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===Selection 2===

===Selection 2===

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<table align="center" cellpadding="6" style="border:none" width="90%"><td style="border:none">

<p>We have, first, predicates of individuals, and these are classified into predicates of different categories, or types, according to the number of their argument places.  Such predicates are called ''predicates of first level''.</p>

<p>We have, first, predicates of individuals, and these are classified into predicates of different categories, or types, according to the number of their argument places.  Such predicates are called <i>predicates of first level</i>.</p>

<p>By a ''predicate of second level'', we understand one whose argument places are occupied by names of individuals or by predicates of first level, where a predicate of first level must occur at least once as an argument.  The categories, or types, of predicates second level are differentiated according to the number and kind of their argument places.  (p.&nbsp;152).</p>

<p>Hilbert and Ackermann, ''Principles of Mathematical Logic'', Robert E. Luce (trans.), Chelsea Publishing Company, New York, NY, 1950.  First published, ''Grundzüge der Theoretischen Logik'', 1928.  Second edition, 1938.  English translation with revisions, corrections, and added notes by Robert E. Luce, 1950.</p>

 

<p>Hilbert and Ackermann, <i>Principles of Mathematical Logic</i>, Robert E. Luce (trans.), Chelsea Publishing Company, New York, NY, 1950.  First published, <i>Grundzüge der Theoretischen Logik</i>, 1928.  Second edition, 1938.  English translation with revisions, corrections, and added notes by Robert E. Luce, 1950.</p>

 

==References==

==References==

* Aristotle, &ldquo;The Categories&rdquo;, Harold P. Cooke (trans.), pp. 1&ndash;109 in ''Aristotle, Volume&nbsp;1'', Loeb Classical Library, William Heinemann, London, UK, 1938.

* Aristotle, "The Categories", Harold P. Cooke (trans.), pp. 1&ndash;109 in _Aristotle, Volume&nbsp;1_, Loeb Classical Library, William Heinemann, London, UK, 1938.

* Aristotle, "Categories", E.M. Edghill (trans.), eBooks@Adelaide, University of Adelaide, South Australia, 2007.  [Online](http://ebooks.adelaide.edu.au/a/aristotle/categories/).

* Aristotle, &ldquo;Categories&rdquo;, E.M. Edghill (trans.), eBooks@Adelaide, University of Adelaide, South Australia, 2007.  [http://ebooks.adelaide.edu.au/a/aristotle/categories/ Online].

* van Heijenoort, Jean (1967/1977), _From Frege to Gödel : A Source Book in Mathematical Logic, 1879&ndash;1931_, Harvard University Press, Cambridge, MA, 1967.  2nd printing, 1972.  3rd printing, 1977.

* van Heijenoort, Jean (1967/1977), ''From Frege to Gödel : A Source Book in Mathematical Logic, 1879&ndash;1931'', Harvard University Press, Cambridge, MA, 1967.  2nd printing, 1972.  3rd printing, 1977.

* Hilbert, D., and Ackermann, W. (1938/1950), _Principles of Mathematical Logic_, Robert E. Luce (trans.), Chelsea Publishing Company, New York, NY, 1950.  First published, _Grundzüge der Theoretischen Logik_, 1928.  Second edition, 1938.  English translation with revisions, corrections, and added notes by Robert E. Luce, 1950.

* Hilbert, D., and Ackermann, W. (1938/1950), ''Principles of Mathematical Logic'', Robert E. Luce (trans.), Chelsea Publishing Company, New York, NY, 1950.  First published, ''Grundzüge der Theoretischen Logik'', 1928.  Second edition, 1938.  English translation with revisions, corrections, and added notes by Robert E. Luce, 1950.

* Kant

* Kant

* C.S. Peirce, &ldquo;[On a New List of Categories](http://www.cspeirce.com/menu/library/bycsp/newlist/nl-frame.htm)&rdquo;

* C.S. Peirce, &ldquo;On a New List of Categories&rdquo;, [http://www.cspeirce.com/menu/library/bycsp/newlist/nl-frame.htm Online].

* Carnap, _[The Logical Syntax of Language](http://books.google.com/books?id=Yf9R6WFFLhYC&printsec=frontcover)_, _cf._ &ldquo;[Functor](http://books.google.com/books?id=Yf9R6WFFLhYC&printsec=frontcover#v=onepage&q=Functor&f=false)&rdquo;

* Carnap, ''[http://books.google.com/books?id=Yf9R6WFFLhYC&printsec=frontcover The Logical Syntax of Language]'', ''vide'' [http://books.google.com/books?id=Yf9R6WFFLhYC&printsec=frontcover#v=onepage&q=Functor&f=false &ldquo;Functor&rdquo;]

==Related Topics==

==Related Topics==

==Document History==

==Document History==

* [http://ncatlab.org/nlab/revision/precursors+%3E+history/15 Precursors @ nLab]

* [http://ncatlab.org/nlab/revision/precursors/15 Precursors @ nLab]