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Thesis The sea battle argument is a scope mistake, and Aristotle half saw it

Giulia Ferrante Fellow
· 4 replies · 110 views
Modal & non-classical logicAnalyticGreek & RomanAristotelianismAristotle#fatalism#future-contingents#scope-distinction#sea-battle
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Where it stands

Every year I teach chapter 9 of De Interpretatione to seventeen-year-olds, and every year somebody leaves the room a fatalist. So here is the case I make to them, and I would like it attacked by people who know more logic than my students.

The argument: if "there will be a sea battle tomorrow" is already true today, the battle is settled and nothing anyone does can prevent it. If it is false today, the battle is ruled out. Either way the future is fixed by present truth, and deliberation is theatre.

My thesis is that the argument trades on moving "necessarily". This is true:

Necessarily, either there will be a battle or there will not.

This does not follow from it:

Either necessarily there will be a battle, or necessarily there will not.

The first puts necessity over the whole disjunction; the second distributes it onto each half. Once you write the two out, the fatalist's step is plainly invalid. Aristotle comes close to saying exactly this near the end of the chapter, where he says it is necessary that there will or will not be a battle, but not necessary that there will be one, nor that there will not.

Whether he also denied that "there will be a battle tomorrow" has a truth value today is a separate question, and readers have argued about it for a very long time. I am not taking a side on that here. My claim is narrower: once the scope is fixed, fatalism has lost its logical support, and it needs some other premise to survive.

Where does this go wrong?

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4 replies

For the thesis 1

  1. Fr. Ikechukwu Anyanwu

    For Fellow

    I'd side with Giulia, with a medieval reinforcement. Boethius distinguishes simple from conditional necessity, and the scholastics after him talk of necessity "in the composite sense" versus "in the divided sense". Both are really scope distinctions. In the stock classroom example, "someone seen sitting is necessarily sitting" is true read as a whole (necessarily, if someone is seen sitting, they sit) and false read as a claim about the person (he cannot stand up). Aquinas uses this kind of distinction to reconcile God's knowledge of future contingents with their contingency. So the scope diagnosis isn't a modern trick that notation smuggled in; it's an old tool that notation made easier to see.

    Helpful · 2

Against the thesis 2

  1. Tomasz Wójcik

    Against Fellow

    It goes wrong, I think, in "that's all it is". The scope point kills the crude version. But there's a sharper version that doesn't need the bad step.

    Suppose that yesterday it was true that there would be a battle today. That is now a fact about the past, and most of us think the past is fixed: whatever was the case is now unchangeably so. Then "it was true yesterday that there would be a battle" is necessary, and from that, it seems, so is the battle. No scope slip anywhere. That's very close to the shape of Diodorus's argument, and it's why the medievals, Ockham especially, ended up distinguishing propositions that are genuinely about the past from ones that are only past in their grammar.

  2. Pieter de Jong

    Against Fellow

    I'd diagnose it differently again, and I say this as someone who thinks determinism is probably true. On a block picture the sentence is just tenselessly true or false, and nobody thinks that makes anything happen. Truth depends on the battle, not the other way round. The fatalist's mistake is thinking the truth of a statement constrains events. So I agree there's a fallacy, I just don't think scope is the whole of it.

    Helpful · 1

Other replies

  1. Giulia Ferrante

    Fellow

    Tomasz, that's fair and I'll concede it. The scope point disposes of the argument as Aristotle's fatalist states it, but it doesn't touch the version that runs through the fixity of the past. So I'll revise: the scope mistake is the first move, and the honest second move requires a view about which past truths are really fixed.

    Father Ikechukwu, I'm stealing the sitting example for class.

    Helpful · 3