Aristotle's Point


This is the man himelf the morning after. As Monty Python have it, 'Aristotle, Aristotle was a bugger for the bottle



It is possible that you came here directly from Salamis. If so, read on. But if not, I suggest you go there first. For those pages lay out the historical background which makes sense of the point of logic laid out below.

To appreciate Aristotle's point, I suggest you put yourself in Themistocles' shoes over those three days.


DATELINE 19 SEPTEMBER: THE NIGHT BEFORE THE BATTLE       

The night before the battle you are keenly aware of what the morning likely holds. There will be a sea-battle, you are sure. And one in which you will probably meet your end. So you assent to

[19A]    There will be a sea-battle tomorrow

No doubt you will pray to the Gods for deliverance: perhaps they could send Boreas, The North Wind, to drive the Persian fleet a hundred miles out to sea. If that miracle were to come about, it would take days for the Persians to return. You are also sure of that. So you will certainly not assent to

[19B]    There will be a sea-battle tomorrow even if a storm drives the Persians out to sea tonight.


DATELINE 20 SEPTEMBER: THE DAY OF THE BATTLE       

Not much doubt concerning what is happening now, right before your eyes. Whether or not Boreas came to your aid overnight, the Persian fleet is there before you, and you are in the thick of a bloody hand-to-hand struggle. So you definitely assent to

[20A]    There is a sea-battle going on (now).

And for exactly the same reason you also assent to

[20B]    There is a sea-battle going on (now), even if a storm drove the Persians out to sea last night.


DATELINE 21 SEPTEMBER: THE DAY AFTER THE BATTLE       

And similarly, since you have not forgotten the battle, you affirm

[21A]    There was a sea-battle yesterday.

And again, on exactly the same grounds, you will affirm

[21B]    There was a sea-battle yesterday, even if a storm drove the Persians out to sea the night before.

I suggest that you pause to make sure you have all of this clear before the mind before you read on. For the upshot of this tiny point of logic has enormous revolutionary significance.

For it now follows that

[1] The Future is different from the Present and the Past

There is a marked logical difference between messages about the Future, on the one hand, and messages about the Present or the Past on the other. They differ sharply in their entailments.

The message encoded by [20A] entails the message encoded by [20B], and the message encoded by [21A] entails the message encoded by [21B]. But the message encoded by [19A] does not entail the message encoded by [19B].

Two further things now follow:-

[2] Messages concerning the Future do not have Truth Values.

For if [19A] were True, it would entail [19B], just as [20A] and [20B] entail their counterparts.

 

[3] 'will' and 'will not' are not related as contradictories.

(Two messages are contradictory iff one is true whenever the other is false, and vice-versa). Indeed, we can say more. The opposite of

[19A]    There will be a sea-battle tomorrow

is not

[19N]    There will not be a sea-battle tomorrow

but

[19A]    There might not be a sea-battle tomorrow

All three of these theses are prefigured in the masterly opening paragraph of De Interpretatione 9:

"With regard to what is and what has been it is necessary for the affirmation or the negation to be true or false ................ .....But with particulars that are going to be it is different."

-oOo-

And now, to pursue the further ramifications of this point, to search for its explanation, and to appreciate its revolutionary significance, I suggest you visit The Sea-Battle Hub, and select your next move.