A Particular Proposition does not assert the existence of its Subject.
Then you generalize the result to all propositions, since nothing in the argument hinges on the fact that this particular proposition was selected.
It takes its most important job to be specifying the conditions under which an individual knows a particular proposition at a particular time.
But to represent any Particular Proposition, at least three Diagrams would be needed (in order to include all the possible cases), and, for “Some not-x are not-y”, all the four.
This is because Aristotle did not discuss weakened forms of syllogisms, in which one concludes a particular proposition when one could already conclude the coresponding universal.
I can't, strictly speaking, change my mind about any particular proposition, since if I went from believing, say, “Dogs are good pets” to believing “Dogs are not good pets”, what I mean by “Dog” and “Pet” would have changed.
Against completeness, one might say that there are circumstances in which the level of disagreement on a particular proposition (or set of propositions) is so great that forming a collective view on it is undesirable or counterproductive.
It is thought to be highly implausible that belief in a particular proposition, or desire for a particular state of affairs, is identical with the same state of a brain (or a part of a brain) in different people, or even in the same person at different times.
For although the indefinite ‘A dodo ate my lunch’ might be held to be equivalent to the particular proposition ‘Some dodo ate my lunch’, generic indefinites like ‘A dodo is a bird’, are quite different, and their semantics does not bear on the quantified sentences in the square of opposition.
Now it is true that the most readily available belief-inducing technologies – selectively using the evidence for instance – all involve a degree of self-deception, since one ordinarily cannot attend only to the favorable evidence in support of a particular proposition while neglecting the adverse evidence arrayed against it and, being conscious of all this, expect that one will acquire that belief.
Consider, in particular, Proposition 13, a citizens' initiative put on the 1978 ballot by Howard Jarvis, an anti-tax crusader in Los Angeles.
Alternatively, we can say that a proposition is that which is expressed by a sentence on a particular occasion of use.
If a propositional function is applied to a proposition of a particular order, then it yields a proposition of a higher order.
Conversion yields an equivalent proposition (and is hence a valid inference) in general only with so-called E and I propositions (universal negatives and particular affirmatives).
It is often objected to deflationism, however, that the doctrine has particular trouble meeting this adequacy condition.
(Roughly speaking, a proposition is a proposition considered solely with respect to its logical features.)
Finally, for Bolzano, the proposition “A is the cause of B” means that the proposition “A exists” contains the ground of the proposition “B exists”.
Existential import, in syllogistic, the logical implication by a universal proposition (i.e., a proposition of the form “All S is P” or “No S is P”) of the corresponding particular statement (i.e., “Some S is P” or “Some S is not P,” respectively).
The demonstration thus proves, according to Berkeley, a general proposition about triangles.
If you think that a negation of a proposition is a proposition (so that in particular a negation of an atomic proposition is a proposition) then you also believe that a negation (or complement or whatever you want to call it) of a predicate is another predicate.
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