The first premise expressed at 180 ("given that it is not made of ice it is necessarily not made of ice") is a priori. — Metaphysician Undercover
Formal logic and its various notions of ‘truth’ depends for its sense on faith in intrinsicality. — Joshs
I know water boils at 100℃ at normal pressure, as a result of experiments done at high school and reassurance from various authorities.We know post hoc and a priori, as mere inference, water under a certain set of conditions will always boil at 100C. — Mww
First published Wed Jul 31, 1996; substantive revision Sun Aug 15, 2010
The Identity of Indiscernibles is a principle of analytic ontology first explicitly formulated by Wilhelm Gottfried Leibniz in his Discourse on Metaphysics, Section 9 (Loemker 1969: 308). It states that no two distinct things exactly resemble each other. This is often referred to as ‘Leibniz’s Law’ and is typically understood to mean that no two objects have exactly the same properties...
The Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:
∀F(Fx ↔ Fy) → x=y. — SEP
this lectern may have been in the other room, but may not have been made of ice - since it is made of wood, if we suppose that it might have been made of ice, we would better say that this lectern might have been replaced by another, made of ice. — Banno
Let us just take the weaker statement that it is not made of ice. That will establish it as strongly as we need it, perhaps as dramatically. — top p.179
I take him here to be saying that the argument (1-4) applies when a and b are proper names and F a property.It would seem that Leibniz law and the law (1) should not only hold in the universally quantified form, but also in the form "if a = b and Fa, then Fb", wherever 'a' and 'b' stand in place of names and 'F' stands in place of a predicate expressing a genuine
property of the object: ( a = b• F a ) > F b — p. 167
P⊃□PP⊃◻P
is invalid. It is certainly not a priori.
It seems you have not understood the argument, the whole point of which is that P⊃☐P in the case of the lectern is known a posteriori. — Banno
It's clear from the examples given that statements of the form x=y can be discovered empirically, and hence at least some are not discovered a priori. — Banno
It seems to me that the use of the word necessary is redundant between objects, in that what does "if two objects have all the same properties, they are in fact necessarily one and the same" add to "if two objects have all the same properties, they are in fact one and the same"
Necessity between an object and its properties - between a lectern and its property wood
As regards the lectern, necessity is being used between an object and its properties, where he writes "So we have to say that though we cannot know a priori whether this table was made of ice or not, given that it is not made of ice, it is necessarily not made of ice. — RussellA
Yeah it is.whether or not it is valid is not in question. — Metaphysician Undercover
(my bolding)The first premise expressed at 180 ("given that it is not made of ice it is necessarily not made of ice") is a priori. — Metaphysician Undercover
….some may suppose that all statements of the form x=y are necessary, and hence a priori (Is this Mww's view?) — Banno
It isn't. It is invalid, so it can't be a priori. If it is true, it is true a posteriori, as Kripke uses it. — Banno
no statement in itself is ever necessary in the domain of pure logic, to which the very idea of necessity solely belongs. — Mww
x = x is necessarily true under any conditions — Mww
OK, so we got x = y. X is a dog, y is a mammal. — Mww
Dogs are mammals is an example of F(S)-type "is". The "=" means that the thing on the left is the very same as the thing on the right. dog=mammal appears ill-formed....folk have been using cognates of "S is F" without explaining what they are talking about. Is it that S=F (they are equal)? Or S ≡ F (they are materially equivalent)? Or just F(S) (predicating F to S)? or S∈F (S is an element of the set or class S), or none of these, or some combination, or something else? — Banno
"the law of identity"... is used by Kripke in the first premise — Metaphysician Undercover
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