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Extra resources for Logical Explorations in the Philosophy of Mind
In other words, if the common part does not perceive, no basic part (and hence no sense organ whatever) perceives. If it ceases functioning, there is no perception at all. It is the sine qua non of perception. As Aristotle says in the DS passage, the common part is the koin¯e dunamis (“common power”) underlying all perception. , in De insomniis 461a6), it is the arch¯e t¯es aisth¯ese¯ os, the basis of all perception. It is clear that (T4) is attractive in the context of a theory of sleep: it allows us to identify the common part as the “sleep centre”, the part whose inactivity causes a total shutdown of the whole perceptual apparatus.
56 It does not make a difference whether one adopts (A1) or ∀x(xAp → ∃yy ∗ AxAp). 7. 1. The first argument. The argument at (b) goes as follows. Suppose that we add (*) to P1 and call the resulting system P1∗ ; 1∗ p means that p is derivable in P1∗ . We may then prove: (1) 1∗ hACt → ∃xxAhACt, by (Ekh) and (A1); (2) 1∗ (Es ∧ sAhACt) → sACt, by (Ekh) and (Tr); (3) 1∗ (Es ∧ Et ∧ sACt) → (s = k ∨ s = h), by (C1); (4) 1∗ (Es ∧ Et ∧ sAhACt) → (kAhACt ∨ hAhACt), by (2), (3) and (=2); (5) 1∗ (kAhACt ∨ hAhACt) → ∃xx∗ AxACt, by (Ekh) and (∀1); (6) 1∗ (Es ∧ Et) → ¬sAhACt, by (4)–(5) and (*); (7) 1∗ Et → ¬∃xxAhACt, by (6) and (∀2); (8) 1∗ Et → ¬hACt, by (1) and (7); (9) 1∗ ¬∃xhACx, by (8) and (∀2).
A “property”) to each predicate P ∈ PRED. In addition, V satisfies the following conditions: V(k) = k, V(h) = h, and V(C) = C. Definition: Type 1, type 2 and type 3 models are type 0 models which satisfy the additional conditions [A1], [A1] and [A2], [A1] and [A3], respectively, for all w ∈ W, d, e, f ∈ Ew : [A1] – If dw ∈ Aw then for some g ∈ Ew : gw ∈ Aw and for all v ∈ W, if Rgw wv then dv ∈ Av ; furthermore, – if dw ∈ Aw , Rdw wv, ev ∈ Av , Rev vu, and f w ∈ Aw , then Rf w wu. 67 The 68 “Iff” term “dissective” comes from Goodman 1951, p.