Talk:Existential generalization
Universal instantiation and Existential Generalization are two aspects of a single principle, for instead of saying that '(x(x=x)' implies 'Socrates is Socrates
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Quine
- I am reading Quine at the moment (quintessence, extensionalism, Reference and Modality. From this I would like to add to this article:
Universal instantiation and Existential Generalization are two aspects of a single principle, for instead of saying that '(x(x=x)' implies 'Socrates is Socrates', we could as well say that the denial 'Socrates≠Socrates' implies '(∃x(x≠x)'. The principle embodied in these two operations is the link between quantifications and the singular statements that are related to them as instances. Yet it is a principle only by courtesy. It holds only in the case where a term names and, furthermore, occurs referentially[1].
- Any ideas, remarks, or changes?
- --Fan Singh Long (talk) 05:57, 6 February 2012 (UTC)
- Ok, since no one has seen fit to leave any comments at all, I will edit the article now.
- --Fan Singh Long (talk) 06:42, 13 February 2012 (UTC)
References
- ^ Quine,W.V.O., Quintessence, Extensionalism, Reference and Modality, P366
Fitch notation
An example for only some free occurrences of x replaced by a would be
- x R a → ∃x x R x
for some relation R. Assuming that the free occurrence of x is tacitly universally quantified, this looks ok. However, another example would be
- x R x → ∃x x R x .
(no occurrences at all instantiated) this is wrong on an empty domain. - Jochen Burghardt (talk) 16:25, 26 February 2022 (UTC)
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