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G. E. M. Anscombe writes the following (page 80):

...[Wittgenstein's] view, expressed at 6.37, that 'there is only logical necessity', and at 5.525, that the possibility of a state of affairs is simply expressed by an expression's being a significant proposition, appears to be a pure exigency of the picture theory of the proposition. It is a very common dogma at the present day that there is no sense of 'necessity' and 'possibility' except 'logical necessity' and 'logical possibility'. It is possible that this dogma, which is in part an effect of the influence of Hume, is also a hangover from the time of the overwhelming influence of the Tractatus.

This made me think that there must be some example of necessity besides logical necessity that has been recognized in the past. However, I could not think of one.

Hence the question: Are there examples of necessity other than logical necessity?


Anscombe, G. E. M. Introduction to Wittgenstein's Tractatus. (1971) St. Augustine's Press.

  • By "logical" she probably means analytic necessity, which was the most common conception in the first half of the 20th century (before Kripke). It was developed by Carnap et al. But Quine talked about "physical" necessity, Leibniz's was close to Kripke's "metaphysical" necessity, and the Aristotelian "necessity" that Aquinas used in the third way bears little resemblance to any modern conception, see What do necessity and possibility mean in Aquinas' Third Way argument for the existence of God? – Conifold Sep 17 at 20:55
  • Does moral necessity count? – curiousdannii Sep 17 at 23:04
  • @curiousdannii I assume moral necessity would count. – Frank Hubeny Sep 17 at 23:20
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    The modal language of necessity is quite common in ordinary usage and it has many sources. In addition to those already mentioned, there is practical necessity, legal necessity, various kinds of fiat necessity ("all applicants must complete form B2") and epistemic necessity (this must be true given what we already know or believe to be true). – Bumble Sep 18 at 0:08
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A great deal of science is expressed as a form of necessity. But none of it really is, or science itself could not move forward. Is it necessary that when I drop things they fall? Well, yes, but only in a gravity well. In most of the universe, not really. Is it necessary that there is only one line parallel to another through a point? Well, yes, but only at low speeds where geometry is basically Euclidean. And even then, only as an approximation. We may already have found signals that quantum-tunnel faster than the speed of light, at the cost of a certain degree of degradation. Etc.

Such a necessity involves choosing the theories in which one has faith. This is typical of modalities in general.

Basically, modes are always relative. They express that there is an attached context that is presumed to be shared, and therefore is not being expressed. From there you can look at what features a context must have in order to act according to the rules of, say necessity rather than obligation. They do take different forms.

For instance necessary modes allow one to assume their assertions are so seldom violated that they can be ignored. You do not have to plan for their failing. One does not punish violations of one's physics, one marvels at them and starts over with slightly different physics. When we are less certain of the physics we are using, we actually back off and use the mode of obligation in a backhanded way. This should work... If it fails, there is likely some punishment, but may just be shame on the part of the person who picked the wrong theory or got the computations wrong.

Any time you rule out failure of a given type from explicit consideration, you add contents to the reigning local modality of necessity. Such considerations can range from what is proven mathematically down to what character defects one cannot impute to a judge making a court opinion, or what someone can do and say and still really love you.

From a classical grammatical point of view, this is all metaphorical and there is an underlying real necessity, obligation, desirability, etc. which these continually-changing criteria only mimic in form. But very few people would consider this applicable any more. To think of any kind of absolute meaningful necessity is as big an unjustified leap as imagining an absolute moral law or an absolute standard for what is desirable.

In a universe with absolute necessity, that necessity is logical necessity. But there is then no need for the notion of necessity. What is logically necessary is simply true, and there is no need for this modality at all.

I think that Wittgenstein's point is exactly that -- that modality itself is really just a kind of sloppiness that does not actually contribute meaning, In reality, there is only really the one modality that is not any way modal, where the 'attached context' is 'truth' and there is exactly one possible world, the world.

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Well, take the claim that nothing travels faster than light. This is clearly physically necessary in the sense of being true in any possibility, where our actual laws of physics hold. But it is not logically necessary, since its denial is compatible with 'the laws of logic'.

Of course this formulation is a bit imprecise, since it's not really clear what the laws of logic are. Maybe one should drop talk of laws in favour of talk of consequence relations characterizing logics and relativize logical necessity to logics. So, let for some logic L a claim p be L-logically necessary, if p is true in any possibility closed under L's consequence relation. Then we can say that nothing travelling faster than light is not classical-logically necessary, since in some possibilities closed under classical consequence some things travel faster than light.

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Physical necessity. Metaphysical necessity.

More broadly, every kripke frame of worlds you define for your purposes of analysis has it's own notion of "necessity".

Physical necessity would be what holds on every class of worlds that has our laws of physics, for example. This has obvious utility if we want to discuss, eg, "are philosophical zombies possible or merely conceivable".

In the most basic, general way of putting it, necessity means "what is true in every possible world that has this restriction "X" is "X-necessary".

Logical necessity is merely the broadest possible restriction of X: it makes X "is true on every possible world".

I might add details to this later.

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