A Logical Approach to Philosophy: Essays in Honour of Graham by David DeVidi, Tim Kenyon

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By David DeVidi, Tim Kenyon

The papers during this assortment are united via an method of philosophy. They illustrate the manifold contributions that good judgment makes to philosophical development, either by way of the applying of formal the way to conventional philosophical difficulties and by way of starting up new avenues of inquiry as philosophers deal with the results of latest and infrequently dazzling technical effects. Contributions contain new technical effects wealthy with philosophical importance for modern metaphysics, makes an attempt to diagnose the philosophical value of a few fresh technical effects, philosophically inspired proposals for brand spanking new methods to negation, investigations within the heritage and philosophy of common sense, and contributions to epistemology and philosophy of technology that make crucial use of logical thoughts and effects. the place the paintings is formal, the causes are patently philosophical, no longer only mathematical. the place the paintings is much less formal, it's deeply trained via the appropriate formal fabric. the amount contains contributions from one of the most fascinating philosophers now operating in philosophical common sense, philosophy of good judgment, epistemology and metaphysics.

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Let σ be any sentence and define α(x) ≡ x = 0 ∨ σ β(x) ≡ x = 1 ∨ σ . With these instances of α and β the antecedent of WESP is clearly satisfied, so that there exist members a, b of 2 for which (1) α(a) ∧ β(b) and (2) ∀x ∈ 2[a(x) ↔ b(x)] → a = b. It follows from (1) that σ ∨ (a = 0 ∧ b = 1), whence (3) σ ∨ a = b. And since clearly σ → ∀x ∈ 2[α(x) ↔ β(x)] we deduce from (2) that σ → a = b, whence a = b → ¬σ . Putting this last together with (3) yields σ ∨ ¬σ , and SLEM follows. For the converse, we argue informally.

Assuming AC∗ 1 , take ϕ(x, y) ≡ α(y) in its antecedent. , Ex. Conversely, define α(y) ≡ ϕ(0, y). Then, assuming Ex, there is b for which ∃yα(y) → α(b), so ∀x ∈ 1∃yϕ(x, y) → ∀x ∈ 1ϕ(x, b). Defining f ∈ Fun(1) by f = { 0, b } gives ∀x ∈ 1∃yϕ(x, y) → ∀x ∈ 1ϕ(x, f x), and AC∗ 1 follows. 3 DAC∗ 1 and Un are equivalent over IST. Proof. Given α, define ϕ(x, y) ≡ α(y). Then, for f ∈ Fun(1), ∃x ∈ 1ϕ(x, f x) ↔ α(f 0) and ∃x ∈ 1∀yϕ(x, y) ↔ ∀yα(y). DAC∗ 1 then gives ∃f ∈ Fun(1)[α(f 0) → ∀yα(y)], from which Un follows easily.

The conclusion, so far, is that the externalist can maintain the KK-thesis by arguing—or just asserting—that the external conditions Ce (Φ) for knowledge are knowable by default. Either Karl needs no warrant for Ce (Φ) at all, or else he just needs the negative warrant that he knows of no reason to doubt Ce (Φ). I see no other route to the KK-thesis for the externalist. Like the above case of naive internalism, the foregoing treatment assumes that since Karl knows Φ if and only if Φ ∧ BΦ ∧ Ci (Φ) ∧ Ce (Φ), then KKΦ if and only if K[Φ ∧ BΦ ∧ Ci (Φ) ∧ Ce (Φ)].

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