Introduction to Mathematical Philosophy
Introduction to Mathematical Philosophy
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In our eReader you can find the full English version of the book. Read Introduction to Mathematical Philosophy Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Introduction to Mathematical Philosophy
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A figure will make this clearer. Let x and y be two terms having the relation P.
Then there are to be two terms z, w, such that x has the rela- tion S to z, y has the relation S to w, and z has the relation Q to w. If this happens with every pair of terms such as x and y, and if the converse happens with every pair of terms such as z and w, it is clear that for every instance in which the relation P holds there is a corresponding instance in which the relation Q holds, and vice versa ; and this... is what we desire to secure by our definition. We can eliminate some redundancies in the above sketch of a definition, by observing that, when the above conditions are realised, the relation P is the same as the relative product of S and Q and the converse of S, i.e. the P-step from x to y may be replaced by the succession of the S-step from x to z, the Q-step from z to w, and the backward S-step from w to y. Thus we may set up the following definitions : — A relation S is said to be a " correlator " or an " ordinal correlator " of two relations P and Q if S is one-one, has the field of Q for its converse domain, and is such that P is the relative product of S and Q and the converse of S.
What to read after Introduction to Mathematical Philosophy?
You can find similar books in the "Read Also" column, or choose other free books by Russell Bertrand to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
A figure will make this clearer. Let x and y be two terms having the relation P.
Then there are to be two terms z, w, such that x has the rela- tion S to z, y has the relation S to w, and z has the relation Q to w. If this happens with every pair of terms such as x and y, and if the converse happens with every pair of terms such as z and w, it is clear that for every instance in which the relation P holds there is a corresponding instance in which the relation Q holds, and vice versa ; and this... is what we desire to secure by our definition. We can eliminate some redundancies in the above sketch of a definition, by observing that, when the above conditions are realised, the relation P is the same as the relative product of S and Q and the converse of S, i.e. the P-step from x to y may be replaced by the succession of the S-step from x to z, the Q-step from z to w, and the backward S-step from w to y. Thus we may set up the following definitions : — A relation S is said to be a " correlator " or an " ordinal correlator " of two relations P and Q if S is one-one, has the field of Q for its converse domain, and is such that P is the relative product of S and Q and the converse of S.
What to read after Introduction to Mathematical Philosophy?
You can find similar books in the "Read Also" column, or choose other free books by Russell Bertrand to read onlineMoreLess
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