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For we can now ask about the very identity statement that is grounding the biconditional principle.
biconditional: for any states of affairs A and B, S is rational to
For example, the biconditional C [equivalent to] E meets Eells's definition of a factor that interacts with C with respect to E.
(40) As to the problem of the supposed lack of fit between the disjunctive judgment and the category of community to follow, replacing disjunction with the biconditional would suffice.
Using the biconditional obtainable from this definition, in conjunction with the modal fact that
138; my boldface emphasis.) In this passage, Kripke gives two examples of necessary, a posteriori, theoretical identification sentences that have the form of universally quantified biconditionals. He also seems to suggest that the doubly quantified biconditional (1b) is a proper analysis of the identity (1a).
And what about the Biconditional? Given an argument with an even number of Ts it behaves like Material Conditional and given an argument with an odd number of Ts it behaves like Conjunction.
But, even in this case, to assume that the biconditional is tautologically true may be risky.
Since only the present truth of the statements is implicated across the biconditional, no implications about the timelessness of truth follow.
The aim here is to define some new conditional, ] , such that: (a) ] satisfies contraction, (b) we have the version of the T-schema with ] (or rather, its corresponding biconditional) as the main connective.
Here are moves in thought, with some ellisions,(8) leading to belief in the left-to-right half of this biconditional. The listing is not meant to indicate temporal sequence; obviously an inferred thought occurs after activation of the relevant inferential disposition, but we should not rule out the possibility of inferences occurring in parallel.
To determine the ontological commitment of (i) we determine the commitment of (iii) and (iv), and the commitment of (iii) (and (iv), making appropriate changes) is read off from the right hand side of the biconditional of Quine's semantic theory: (iii) is true if and only if there exists an x such that "a" designates x and "F" applies to x.