ONT Re: De In Esse Predication
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DEIP. Note 11
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| It remains to show in what manner I suppose the ideas of the other forms
| of propositions to be evolved; and this will be a chapter of what I have
| called "speculative rhetoric". I may begin by remarking that I use the
| sign -< for the sign of inclusion. I believe I was the first to show,
| in 1867, that Boole's algebra, as he left it, was unfit to express
| particular propositions. Following out that idea, I showed, in 1870,
| before anybody else, that we needed in logic a sign corresponding to
| the sign =<, but that sign is unsatisfactory because it implies that
| the relation is a combination of the relations expressed by < and =,
| whereas in truth, as I demonstrated, it is more simple than either. ...
|
| Accordingly,
|
| h_i -< d_i
|
| means that on the occasion i, if the idea h is definitively
| forced upon the mind, then on the same occasion the idea d
| is definitively forced upon the mind. On the Philonian view
| this is the same as to say that on the occasion i, either the
| idea h is not definitively forced upon the mind or on the same
| occasion the idea d is definitively forced upon the mind. From
| that hypothesis, the rules of the sign -< may be mathematically
| deduced. ...
|
| C.S. Peirce, 'Collected Papers', CP 2.356,
|"That Categorical and Hypothetical Propositions
| are one in essence, with some connected matters",
| circa 1895.
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