### fatalism.

Suppose it’s true that

(EM) (p ∨ ~p)

Now suppose that

(B) (Tp ∨ Fp)

Let’s also suppose EM and B are necessarily equivalent. Symbolically:

`

(EM/B) [(p ∨~p) ^ (Tp ∨ Fp) ^ (p ↔Tp) ^ (~p ↔Fp)]

Okay now for fatalism. Fatalism (as I understand it) is the thesis that the future is fixed—

Some have argued that from EM/B fatalism follows. Here’s the argument:

Consider the proposition

(1) There will be sea battle tomorrow.

By EM/B it follows that (1) is either true or false It should be noted that this argument relies on a very weak and nearly uncontroversial principle of

(LE) (Tp ⊃ Tp) ^ (Fp ⊃ Fp)

(LE) is equivalent to

(LE’) (Tp ⊃ ~◊Fp) ^ (Ftp ⊃ ~◊Tp)

Here’s a way of symbolizing the argument for fatalism from EM/B and LE:

(EM/B) [(p ∨~p) ^ (Tp ∨ Fp) ^ (p ↔Tp) ^ (~p ↔Fp)]

(2) Any future-tensed proposition p

(3) ∴ [(p

(LE’) (Tp ⊃ ~◊Fp) ^ (Ftp ⊃ ~◊Tp)

(4) (Tp

(5) ∴ ~◊Fp

*excluded middle*(EM) holds—*viz*., that any proposition p, it’s*necessary*that p or not-p. Symbolically:(EM) (p ∨ ~p)

Now suppose that

*bivalence*holds—*viz.*, that for any proposition p, it’s*necessary*that either p is true or p is false. Symbolically:(B) (Tp ∨ Fp)

Let’s also suppose EM and B are necessarily equivalent. Symbolically:

`

(EM/B) [(p ∨~p) ^ (Tp ∨ Fp) ^ (p ↔Tp) ^ (~p ↔Fp)]

Okay now for fatalism. Fatalism (as I understand it) is the thesis that the future is fixed—

*viz*., that anything that might happen in the future, what will happen must happen such that there is only one possible future.Some have argued that from EM/B fatalism follows. Here’s the argument:

Consider the proposition

(1) There will be sea battle tomorrow.

By EM/B it follows that (1) is either true or false

**right now**. Furthermore, if (1) is true**right now**, then no one can prevent tomorrow’s sea battle, for it*impossible*for anyone to make a*true*time-indexed proposition false. And vice-versa. If (1) is false**right now**, then no one can prevent the non-occurrence of tomorrow’s sea battle, for it is*impossible*for anyone to make a*false*time-indexed proposition true. Since (1) was arbitrarily chosen, this argument can be generalized for any future-tensed proposition. That is, let p_{f}pick out any future-tensed proposition. It follows from EM/B that p_{f}is either true or false**right now**. Furthermore, if p_{f}is true**right now**, then no one can prevent it, for it is*impossible*for anyone to make a*true*time-indexed proposition false. And the same goes if p_{f}is false. If p_{f}is false**right now**, then no one can prevent it, for it is*impossible*for anyone to make a*false*time-indexed proposition true. And this is just the thesis of fatalism, which said that the future is fixed in such a way that there is only one possible way the future can be.*logical entailment*that says if p is true then it necessarily follows that p is true. Symbolically:(LE) (Tp ⊃ Tp) ^ (Fp ⊃ Fp)

(LE) is equivalent to

(LE’) (Tp ⊃ ~◊Fp) ^ (Ftp ⊃ ~◊Tp)

Here’s a way of symbolizing the argument for fatalism from EM/B and LE:

(EM/B) [(p ∨~p) ^ (Tp ∨ Fp) ^ (p ↔Tp) ^ (~p ↔Fp)]

(2) Any future-tensed proposition p

_{f}is a proposition.(3) ∴ [(p

_{f}∨~p_{f}) ^ (Tp_{f}∨ Fp_{f}) ^ (Tp_{f}↔ p_{f}) ^ (Fp_{f}↔ ~p_{f})](LE’) (Tp ⊃ ~◊Fp) ^ (Ftp ⊃ ~◊Tp)

(4) (Tp

_{f}⊃ ~◊Fp_{f}) ∨ (Fp_{f}⊃ ~◊Tp_{f})(5) ∴ ~◊Fp

_{f}∨ ~◊Tp_{f}Labels: it's written in the stars.

## 1 Comments:

I'm guessing you, like me, would deny the conditional "if is true right now, then no one can prevent tomorrow’s sea battle" for lack of respecting modes of "can"?

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