6 ms·
Does anyone know what it's called when the argument is of the form: ∀x. P(x) x Therefore, P(x) Is P(x) "trivially true" in this case? This tends to come up
by googthrowaway42 6y ago
Does anyone know what it's called when the argument is of the form:
∀x. P(x)
x
Therefore, P(x)
Is P(x) "trivially true" in this case?
This tends to come up in some political arguments (e.g. about systemic bias where everything can be seen as influenced by that bias).
- istjohn 6y agoDo you mind translating that into English? Edit: I gather the translation is something like: For all x, predicate P is true of x. x is true. Therefore, predicate P is true of x.
- contravariant 6y agoIt's probably not a good idea to use the same variable for both, also 'x' is not a logical statement so the proof would look more like: ∀x. P(x) P(c) where c can be anything. This is usually called something like instantation or ∀-elimination. I suppose you could call P(c) a trivial consequence of ∀x. P(x), no matter what c is. The formula P(x) could be something like 'if x is human they are mortal, so something like 'if "Scorates" is human they are mortal" is a trivial consequence, as is 'If "Blue" is human they are mortal".
- googthrowaway42 6y agoThank you and yes I should have used a different symbol.
- dooglius 6y agoUniversal Instantiation
- googthrowaway42 6y agoThank you
- Der_Einzige 6y agoSounds like the law of identity...