Logic and maths set out the ways in which things can be said. Then we choose, from amongst these ways, those that suit us. SO it should not be a surprise that the logic and maths we choose is effective.

Recall Logical Pluralism.

If causality isn't deduction-apt, explain how we land robotic rovers on Mars and how Russian missiles are laying waste to Ukrainian cities.

The issue is perhaps whether modus ponens - and hence necessity - is the correct way of understanding, say, physics.

The issue is perhaps whether modus ponens - and hence necessity - is the correct way of understanding, say, physics — Banno

I believe Wayfarer and unenlightened are on the right track, as suggested by them bringing up mathmematics (The Unreasonable Effectiveness of Mathematics in the Natural Sciences). This is an old trick in the rationalist's playbook: I believe Descartes was one of the first to employ it. He tried to reduce or translate the empirical into math. Physical entities, for example, were to be only meaningful in terms of geometry and arithmetic; this is the current trend in science I believe). Once that was accomplished, necessity, mathematically speaking, is a natural corollary.

SO it should not be a surprise that the logic and maths we choose is effective. — Banno

That's too easy. Through mathematics, a great many things have been discovered which could otherwise never have been known. It's not just a matter of making a nicely-fitted suit.

I believe Descartes was one of the first to employ it. — Agent Smith

Descartes was nevertheless solidly located in the Western philosophical tradition. It was Platonic epistemology which accorded a high status to dianoia and mathematical analysis.

It's one aspect of it, but I feel there's a lot more to be said. — Wayfarer

I don't see that there is more at least with regard to making the distinction between causal and logical necessity. In the case of physical causation, we press P and we get P. We see that it must be so, given the configuration of the computer. We discount all the possible coutervailing factors, faults, power failures etc. We now see that the consequence is in some sense necessary. It simply must happen. No 'but-what-about?' questions, please, because we've already dealt with those. All good. But the necessity in question is not the same necessity as the necessity of logical inference. The difference is simply that there is no self-contradiction in supposing that we press P and all other factors are taken into account and we still don't get P. All that is just Hume with an up to date example.

On the one hand, we press P and we get P by causal necessity.
On the other hand, we press P and it's not the case that we get P by logical necessity.

Two kinds of necessity. Or, if we prefer, let's discard the expression 'causal necessity' precisely because we know we will get confused if we use the same word for two different things.

So what more is there?

Perhaps this. What makes or tempts us to say that the appearance of P after the pressing of P must be so?

more broadly, the link between logical necessity and physical causation seems fundamental to science generally, and even to navigating everday life — Wayfarer

I think we can establish that the link is an ambiguity in the idea of necessity, as above. Useful, but not profoundly interesting. The deeper question is - what, if anything, is causal 'necessity'?

That's too easy. — Wayfarer

So much the better.

Every time we observe an electron shot through two slits we see a flash of light on a screen placed behind it. Can we logically conclude that if we observe an electron going through two sliths implies a flash on a screen? If we have observed this happening before then yes. It's not guaranteed, but it's plausible. It's logical to plausibly assume there is a causal connection. But only in a physical context and assuming time runs forward. If time ran backwards it would have been retro causation. The mechanism of the causal effect isn't clear a priori. There could reside tiny creatures in the screen flashing a tiny flashlight every time they are hit on the head with an electron. It could also be that causation is teleological in nature.

For the empirical sciences ‘causality’ is a ‘logical necessity’. If not experimentation would be pointless.

What am I missing coming late to this discussion?

This seems to remind me of Penrose’s view that there are three main realms, mathematical, consciousness, and physical (physics). They all relate, but all have distinctive features.

Let's fill the kettle and put it over the flame. Physical cause says that the water will heat. But there is nothing logically contradictory in the water not heating up.

Physical cause and logical necessity are distinct, and different.

But the necessity in question is not the same necessity as the necessity of logical inference. — Cuthbert

Because, I suppose the argument is, it cannot be determined a priori, in principle - that is, as a matter of definition.

The deeper question is - what, if anything, is causal 'necessity'? — Cuthbert

I think that is what interests me about the subject.

One of the responses posted on Stack Exchange was another quote from Wittgenstein, to wit:

Wittgenstein famously states that (Tractatus Logico Philosophicus, proposition 5.1361) : "The events of the future cannot be inferred from those of the present." and "Superstition is the belief in the causal nexus."

That seems a far more radical statement of scepticism than what you have posed, does it not?

I'm going to press on with 'Kant's answer to Hume'. I've just found, for anyone interested, that the Prolegomena to any Future Metaphysics is very nicely formatted for Kindle on this page. (You can find an app on Amazon to upload it to your Kindle.)

What am I missing coming late to this discussion? — I like sushi

The distinction that Cuthbert makes above, between logical necessity and physical causation. But the implications are mainly philosophical, not practical - like, they're not going to be of interest to a bench scientist, I imagine.

But there is nothing logically contradictory in the kettle not heating up. — Banno

But if it were quite so simple as this, then why does it have so many entries in philosophical textbooks, and why did Kant say that it was Hume's attack on causality that woke him from his dogmatic slumbers?

Our appreciation of change (‘time’) is a logical necessity for causal experience. That is a vague connection I guess?

The apple can fall to the right or to the left. But it can also stay in balance at the apex of Norton's dome. — Haglund

The ball on Norton’s dome is either resting as it was left or it has fallen off. It is kind of binary like that - and hence why it is used as good test of Newtonian metaphysics. It shouldn’t roll off, but then counterfactually, it always does.

So the question becomes who nudged it? What explains spontaneous symmetry breaking in nature?

That being said, a gas in vacuum expands (forward causation, forward time) or it implodes (reversed causation, backward time). — Haglund

Does time ever run in fact backwards? You are coming up with some pretty random comments.

But if it were quite so simple as this, then why does it have so many entries in philosophical textbooks, and why did Kant say that it was Hume's attack on causality that woke him from his dogmatic slumbers? — Wayfarer

Because philosophy.

We can understand the kettle not heating up while over the flame. Such an occurrence would be problematic for physics, but not for logic. But the kettle not being a kettle - that's a problem for logic.

So back to modus ponens. Modus ponens and other such theorems are logically necessary. If modus ponens is mistaken as showing the structure underpinning physical causation, it makes physical cause look necessary. It's a part of the mistaken picture of the world as necessary and deterministic.

It seems to me that modus ponens is not a good representation of physical causation.

I believe Descartes was one of the first to employ it.
— Agent Smith

Descartes was nevertheless solidly located in the Western philosophical tradition. It was Platonic epistemology which accorded a high status to dianoia and mathematical analysis. — Wayfarer

Nevertheless, a nifty move! Of course the problem doesn't go away. Even if F = ma, why should it it be that and not F = $\frac{m}{a}$? I suppose I'm seeing things in a manner of speaking. At the end of the day, the exact relationship is beside the point; that there is one is what's mind-blowing.

Coming to logical necessity, as Banno asserted, and I suppose this is the nub of the controversy, why should a billiard ball struck with a certain force, move with a certain velocity (speed + direction)?

Two important metaphysical topics converge in this OP: causality + necessity/possibility.

Questions that seem apposite (The bottom line: Causation is a pattern, synonymous with laws/rules)

1. Why should there be laws?

2. Why are the laws as they are?

Mayhaps, the multiverse is important to the question. There could be universes where causality is nonexistent (chaos or something else) or different (we have equations but they look different).

:up:

Physical cause and logical necessity are distinct, and different. — Banno

So much for material implication then.

It is a thought worth pursuing. Actually even though it's very sketchy, it's suggestive of Kant's response to Hume's problem.

Apropos of which, there are a couple of passages in the Prolegomena which lay out the problem posed by Hume in pretty succinct terms.

Hume started from a single but important concept in Metaphysics, viz., that of Cause and Effect (including its derivatives force and action, etc.). He challenges reason, which pretends to have given birth to this idea from herself, to answer him by what right she thinks anything to be so constituted, that if that thing be posited, something else also must necessarily be posited; for this is the meaning of the concept of cause. He demonstrated irrefutably that it was perfectly impossible for reason to think a priori and by means of concepts a combination involving necessity. We cannot at all see why, in consequence of the existence of one thing, another must necessarily exist, or how the concept of such a combination can arise a priori. Hence he inferred, that reason was altogether deluded with reference to this concept, which she erroneously considered as one of her children, whereas in reality it was nothing but a bastard of imagination, impregnated by experience, which subsumed certain representations under the Law of Association, and mistook the subjective necessity of habit for an objective necessity arising from insight. Hence he inferred that reason had no power to think such combinations, even generally, because her concepts would then be purely fictitious, and all her pretended a priori cognitions nothing but common experiences marked with a false stamp. — Kant, Prolegomena

(I love the colorful turn of phrase.)

After mentioning the fact that Hume's 'common-sense' critics comprehensively failed to see Hume's point, he then says:

The question was not whether the concept of cause was right, useful, and even indispensable for our knowledge of nature, for this Hume had never doubted; but whether that concept could be thought by reason a priori, and consequently whether it possessed an inner truth, independent of all experience, implying a wider application than merely to the objects of experience. This was Hume's problem. It was a question concerning the origin, not concerning the indispensable need of the concept. — Kant, Prolegomena

That last qualification, part of which I have bolded, is of the utmost importance in understanding what is at issue. Remember, Hume's Treatise was on 'human understanding', and Kant's a 'Critique of Pure Reason'. They're considering the elements of knowledge. Hume is demonstrating that, even though the relation between cause and effect is everywhere assumed to be self-evident, in fact we have no logically necessary (or a priori) grounds to think that it is so. And note that Kant says that Hume is engaged in metaphysics, as he himself is: because metaphysics must rest on apprehension of 'inner truths' directly apprehended by reason.

Kant then goes on to answer this challenge from Hume. I'll come back to that, after I've got a bit more of a handle on it.

Mayhaps, the multiverse is important to the question — Agent Smith

https://www.theatlantic.com/science/archive/2016/08/the-multiverse-as-imagination-killer/497417/

The Norton dome shows there is no cause of the rolling down.

The gas example shows that cause and effect are dependent on the direction of time. It either runs forward or backwards. It's either cause preceding effect or effect preceding cause.

I still don’t get what is going on here?

Logical Necessity is not Physical Necessity. One deals in the abstract (where causality is of no consequence) and the other deals with, well, physical stuff (ie. Physics). In physics it is quite plain to see that causation plays a part … I am clearly missing something.

I will just read instead

The Norton dome shows there is no cause of the rolling down. — Haglund

Nope. It shows that Newtonian idealism fails the reality test. The model doesn’t take into account the fact that the world of material objects also has irreducible thermal jitter.

The gas example shows that cause and effect are dependent on the direction of time. It either runs forward or backwards. It's either cause preceding effect or effect preceding cause. — Haglund

But time doesn’t run backwards. So there is a lack of evidence for your counterfactual of the effect preceding the cause.

Nope. It shows that Newtonian idealism fails the reality test. The model doesn’t take into account the fact that the world of material objects also has irreducible thermal jitter. — apokrisis

The object is a point particle laying at rest in a vacuum on the apex. What thermal jitter?

Time is not a thing anyway. It is just our poor human way of measuring something we don’t understand much about (something called entropy).

That doesn’t exist. It is an abstraction.

But time doesn’t run backwards. So there is a lack of evidence for your counterfactual of the effect preceding the cause. — apokrisis

I just mean time could have run backwards. Effects could have come first.

That doesn’t exist. It is an abstraction. — I like sushi

So is quantum field theory. Abstractions have a point. The Norton dome shows cause and effect aren't that straightforward.

I suggest reading about Linear Logic, that greatly clarifies and narrows the distinction between logical, causal and modal necessity, even if causality isn't directly discussed in the majority of articles on the topic.

Modern philosophical confusions about the relationship of logic and causality are largely due to the fallacy of 'material implication' - a classically valid mathematical rule of inference adopted by Frege and Russell that is inadmissible for casual reasoning.

According to 'material implication', the hypothesis, rule or law A --> B is equivalent to a data-set of the form NOT A OR B:

A --> B <---> (NOT A OR B) ,

where (NOT A OR B) refers to elements of the set {( A = FALSE, B = FALSE), (A = FALSE, B = TRUE), (A = TRUE, B = TRUE))

Common sense should instantly recognise this rule as unreasonable, made worse by the the fact that (NOT A OR B) OR (NOT B OR A) is a tautology, which if material implication is accepted implies that
A --> B OR B --> A is true, i.e. that for any event types A or B, either A must cause B OR B must cause A.

In Classical logic, material implication is true as a result accepting the law of excluded middle. On the other hand, intuitionistic logic that rejects LOM thereby rejects material implication, whereby only the inference (NOT A OR B) --> (A --> B) is intuitionistically valid.

But if causal theories are supposed to summarise and describe our experimental interventions in the course of nature, then even the intuitionistically valid latter inference rule is inadmissible , considering the fact that even if (NOT A OR B) is observed, this doesn't necessarily imply that manipulating events of type A influences events of type B, since A type events might not be relevant to B type events. This leads us to so-called 'Relevance Logics', which includes linear logic, in which A --> B is interpreted to mean 'One A-type resource transforms into one B-type resource'.

Cause and effect is quite distinct from logical necessity. One deals with physical reality (space-time), whilst the other cares not a jot for it.

Anyway, thanks for making your points. I think I am getting some idea what this thread is about now.

There seems to be a conflation of physics and mathematics mixed in with conscious experience. Messy, as it appears the OP is driving at a mixed question - conflating mathematics and physical reality - and trying to tackle it philosophically.

I might be wrong. If I am right it is going nowhere fast.

The object is a point particle laying at rest in a vacuum on the apex. What thermal jitter? — Haglund

Even if you cooled such a system to near absolute zero, you could only constrain the thermal jitter.

Just as if you could polish the dome to be near frictionless, you wouldn’t actually make it frictionless.

So I’m lost as to what point you are trying to make in making strong causal claims based on over simplified representations of reality.

Time is not a thing anyway. — I like sushi

:up:

Let's fill the kettle and put it over the flame. Physical cause says that the water will heat. But there is nothing logically contradictory in the water not heating up. — Banno

That would just mean the flame died or the gas was obstructed. But indeed, water not boiling in a kettle on a flame is no logical impossibility. Logic doesn't contain physics.