## Logical Necessity and Physical Causation

• 15.8k
I recently posted a thread on Stack Exchange on the relation between physical and logical causation.

The responses I received on Stack Exchange were generally sceptical of there being a direct relationship between these. One was as follows:

A Wittgensteinian answer to this question would that there is no such thing as physical causation as is generally understood in modern science, but that physical causation is an a priori intuition, which is useful for hypotheses, but which tells us nothing about the world in-itself or its meaning.

another:

Hume recognized that there are two categories of knowledge: empirical and mathematical/logical. He called the former “Matters of Fact” and the latter “Relations of Ideas.”

They are independent. Cause and effect in science is really a constant juxtaposition of events. We observe A followed by B. If this happens uniformly through Custom we infer causation, but we have no reason to justify this.

That is all we have in the sciences. Kant tried to save metaphysics from Hume but modern science has largely sided with Hume over Kant.

and....

Logic generally belongs to maths department founded upon axiomatic set-theory and symbolic algebra/category theories. Physics has a narrower and more concrete focus on phenomena experienced of this world. Thus their relation is same as math and physics in general. You may define and invent your own logical system, it may not be restricted by any physical laws, but still cannot be arbitrary and shall be self-consistent and useful to other applied areas ultimately. However, this by no means imply that there's no relationship between logic and physics.

It seems to me that the widespread scepticism about this issue all goes back to David Hume's questioning of inductive reason. As one of the comments above notes, Kant attempted to 'save metaphysics from Hume' - I think this is a reference to Kant's Answer to Hume. Me, I'm inclined to side with Kant.

The problem this scepticism presents to me is its glaring inconsistency with scientific practice and technology. Consider how we interact with the world through computers, such as the one you're reading this on. These devices are built around microelectronics, devices comprising millions (even billions) of minute components, unfathomably complex to the untrained (including myself). These generally operate with quite astonishing degrees of precision and predictability through the mediation of sequences of billions of separate logical steps carried out at lightning speed and providing instantaneous results - I touch particular keys and lo! the corresponding character appears on the screen (to take only the most simple of examples). It appears seamless but in reality the appearance of those characters is the result of predictable causal chain which generally operates with extremely high degrees of consistency; I don't press P and get Q, not unless there's a fault or configuration error. And the same can be said for computerised processes across an enormous range of applications nowadays where practically everything we do is mediated by computers, from the James Webb Telescope to you calling your friends on smartphones.

So, I have a deep confusion about why philosophy sees this disconnection between logical necessity and physical causation. It seems to me computer science relies on the connection between the two - microprocessors basically comprise chains of logic gates to effect physical outputs. And more broadly, the link between logical necessity and physical causation seems fundamental to science generally, and even to navigating everday life.

Here's a discussion of this issue by G.E.M. Anscombe: Causality and Determination

The Philosophy Stack Exchange discussion is here.
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Hey man. Nice to be able to talk about something fascinating.

I haven't read the OP in detail, will do so later, but I'd like to see what you make of my argument.

I've been reading the actual Hume and some very, very good commentary on him. He's intoxicated me, can't believe it took me so long to read. Obviously he has errors that cannot be fixed given the theory he works with.

But I've been thinking a bit about Kant's response to Hume. I mean, I think Kant takes the logical step in creating all these categories. But I don't think they solve the issue of causation, nor do I think they solve the issue of the perceived consistency of external object.

In other words, Kant created a space in which to do metaphysics, I agree. But I do think that many of the problems Hume's point out are really, really hard. Maybe insoluble.
• 15.8k
I'd like to see what you make of my argument.

Well, you'd better present one! :wink:
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Ah.

I argue that Kant does not solve the problem of causation, nor that of object constancy. I think it makes sense to say that causation is something we bring to the world, but we cannot be sure future experience will be the same as past experience. Nor do we know if causation applies to the object themselves, absent us.

You think he does?
• 5.9k
So, I have a deep confusion about why philosophy sees this disconnection between logical necessity and physical causation.

I've always seen the two as connected. But also, it is hard to frame that connection precisely.

However, focus on counterfactuality. The laws of thought are organised to arrive at the counterfactuality of the Law of the Excluded Middle. And the idea of physical causation is organised by the principle of sufficient reason.

The LEM states that it is necessarily true that that A is not not-A, and thus that counterfactuality applies.

And the PSR states that an event is by necessity caused by X if the absence of that X results in the non-occurrence of the event. So again, it is the counterfactual that proves the case.

The problem then is that this is a very mechanical view of nature - indeed a reductionist one - where all causality is understood in terms of some countable set of efficient causes. Little atomistic pushes and pulls, or individual happenings, that either do or don't occur within a global Newtonian void - a spacetime frame that is itself a-causal and just a passive place for stuff to happen.

So it seems clear that conventional ideas about logical necessity and physical causality are indeed very alike, but this is also because they come from a shared reductionist perspective which itself needs questioning.

Physical causation has a problem dealing with the contingency and spontaneity found in the world. Logical necessity likewise has a problem dealing with the vagueness of predicates.

In both cases, counterfactuality is only achieved in the ideal limit ... so never in reality achieved, only approximated with some arbitrary precision.
• 15.8k
Thanks for your response, but I think it needs elaboration. Kant's 'answer to Hume' involves some pretty dense reasoning. I'm going to spend some time on the SEP entry on that topic before I come back to you.

Physical causation has a problem dealing with the contingency and spontaneity found in the world.

thanks for chipping in.

Yes - but physical causation doesn't have to be all powerful, does it? I'm the last person who would argue that it is - I accept the reality of karma, for instance, which overflows the horizons of physicalism - but within its range of applicability, physical causation and logical necessity seem to coincide, don't they?

Take a high-school physics example, the second law of motion - f=ma. Given that you know any two of those values, then the third can be deduced because f and m (for example) are such-and-such. So the cause of the acceleration is the result of the force multiplied by the mass. That, I suppose, is a deductive, as opposed to inductive, result. But it also suggests an invariable and causal relationship between cause and effect. And actually I think this is getting close to Kant's answer to Hume. There's a very knotty problem here which I'm getting close to, but haven't quite understood yet.

(Also found the reference to the Bertrand Russell essay on Cause which Anscombe refers to.)
• 9.1k

I don't see the connection between the so-called problem of induction and what you are calling logical causation. I don't really know what that means.
In this syllogism:

• If A then B
• A
• Therefore B

There is no causation involved. Or did you mean something else?

To me, induction provides the meat that is ground in the machine of deduction.

Beyond that, as we discussed in a recent thread, I think causation is a metaphysical property that is not particularly useful. I assume that is not what you want to talk about and I won't bring it up again.
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There is no causation involved.

But what about when it is applied to (for example) computing? Then there is plainly causation involved, as it produces a physical outcome. The fact that such-and-such is the case causes a particular result. I can't see how causation is not involved.
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• 9.1k
But what about when it is applied to (for example) computing? Then there is plainly causation involved, as it produces a physical outcome. The fact that such-and-such is the case causes a particular result. I can't see how causation is not involved.

Maybe I misunderstood. If I push on the keyboard and a P shows up on the screen, I can see saying that my finger caused the P to show up. But isn't that what you are calling physical causation. Whereas my syllogism is what I assumed you are calling logical causation. That's the situation where I said no causation is involved.
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I touch particular keys and lo! the corresponding character appears on the screen (to take only the most simple of examples). It appears seamless but in reality the appearance of those characters is the result of predictable causal chain which generally operates with extremely high degrees of consistency; I don't press P and get Q, not unless there's a fault or configuration error.
Just a side note, since I am perhaps personally involved in that P getting to the screen. The engineering of those tiny computer components needs to go to substantial lengths to get that P consistently on the screen. It takes what is essentially a random process (say electrons tunneling across a barrier) and walks the tight wire between sufficient dice rolling to get a consistent behavior, and reducing the number of dice rolled to get sufficient performance. It has to work all the time, but not more than that. This is sort of an effort to hammer out hard predictable causal behavior from randomness.
Just saying that the seemingly causal behavior of your machine is not necessarily the result of any fundamental causality, but rather a lot of effort to make it so. Per Wittgenstein quoted in your OP, it is useful for hypothesis.

I can see saying that my finger caused the P to show up
It's arguably one of the many causes. I mean, the thing probably wouldn't have shown up there just then had your finger not pressed that spot just then. But per my comment above, fundamentally the two are not directly connected. It's just really useful to make that connection.
• 12.2k
Kant was not a realist about causation. As I understand it Hume claims that on account of "constant conjunctions" of events we come to habitually assume that the preceding event causes the constantly observed attending subsequent event. It certainly seems that events are intelligible to us only on account of positing causation, almost the whole of the natural sciences are based on this, and I think this is Kant's answer, which Hume would probably have agreed with.

Kant's position, as I understand it, is that, notwithstanding the intelligibility of the empirical being reliant on causation and the obvious fact that the comprehensibility of the relations between events is couched in terms of causation, these epistemological facts by no means show that causation is a property of "events in themselves" (if this latter term is even coherent).
• 15.8k
Just saying that the seemingly causal behavior of your machine is not necessarily the result of any fundamental causality, but rather a lot of effort to make it so. Per Wittgenstein quoted in your OP, it is useful for hypothesis.

The effort would be to no avail were there not causal connections there to be made.

If I push on the keyboard and a P shows up on the screen, I can see saying that my finger caused the P to show up. But isn't that what you are calling physical causation.

Isn't it? Didn't I? It's your intentional action, plus a lot of work by the likes of NoAxioms that has been done in the background, to ensure that it works this way.

As I understand it Hume claims that on account of "constant conjunctions" of events we come to habitually assume that the preceding event causes the constantly observed attending subsequent event

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.

https://www.gutenberg.org/files/52821/52821-0.txt

He goes on:

But to satisfy the conditions of the problem, the opponents of the
great thinker should have penetrated very deeply into the nature of
reason, so far as it is concerned with pure thinking,—a task which
did not suit them. They found a more convenient method of being
defiant without any insight, viz., the appeal to common sense.

That's what I think I can be accused of having done - I'm appealing to common sense realism. But at least I'm making progress to understanding what it is I don't understand.
• 12.2k
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.

Right, but all that seems to be saying is that intelligible experience itself, and not merely rightness, usefulness and even indispensability for our knowledge of nature, is impossible without thinking in terms of causation, and again I think that Hume might have agreed.

I'm not sure what Kant could mean by "implying a wider application than merely to the objects of experience" unless he is just referring to any possible object of experience as opposed to actual objects of experience.
• 5.9k
Yes - but physical causation doesn't have to be all powerful, does it? I'm the last person who would argue that it is - I accept the reality of karma, for instance,

That's fine for you. But what if one thinks karma is illogical and unphysical? Some other answer is going to have to be found.

But it also suggests an invariable and causal relationship between cause and effect.

Sure, Newtonian mechanics encodes an efficient cause-based metaphysics. That's how it starts. A reduction of nature to atomistic construction.

But then Newtonian mechanics became useful when it was rewritten in Lagrangian form and so came to slyly incorporate the holism, the entropic finality, of the Least Action principle.

Somehow nature - when faced with every possibility - "knows" how to follow the particular path that minimises the overall action.

So holism rules in the bigger picture. And no one wants to talk about.

Yet if you are seeking necessity in Newtonian mechanics - or any physics - it is the principle of Least Action that is the global constraint which is in charge of the show.

And actually I think this is getting close to Kant's answer to Hume.

Kant's answer was that you have to be a holist about causality. But he saw that as an epistemic necessity rather than necessarily the ontic reality.

But since Kant, we've had the quantum and relativity revolutions, not to mention thermodynamics. And in all these, the Least Action principle has proven itself to be more part of physical reality, less simply some epistemic "sense-making" tactic.

Quantum mechanics is rooted in the contextual and non-local. The path integral is the sum over all possible histories.

In relativity, action travels in straight lines by following the curve of a geodesic.

In thermodynamics, the Second Law entrains all action to the finality of entropy maximisation.

So physics relies on holism even to be reductionist. The trick is push that holism into the background so that the reductionism is what is left as the bright-lit foreground.

The holism gets encoded as physical laws that then are placed "in the mind of the creating god" or somewhere equally transcendent. Maybe even "just in the scientist's imagination". It makes no real difference. The point is just to dump the hardest bit of the metaphysical puzzle in some dark corner that no one any longer wants to talk about.

That leaves the simple bit - the application of the mechanical formulae, the differential equations, to a world that is presumed only to operate as a logical, cause-and-effect style, machine.

Bringing Hume and Kant into this is just turning the ontological issue into an epistemic debate.

All society has to know about reductionism is that it works. Only a metaphysician would have to remain concerned with the question: "but is it true?". :grin:
• 5.9k
It takes what is essentially a random process (say electrons tunneling across a barrier) and walks the tight wire between sufficient dice rolling to get a consistent behavior, and reducing the number of dice rolled to get sufficient performance. It has to work all the time, but not more than that. This is sort of an effort to hammer out hard predictable causal behavior from randomness.

Classical certainty is quantum uncertainty suitably constrained. :up:

The quantum state is described by its exact symmetry. The PNC fails to apply and thus it physically represents a logical vagueness.

Then the classical state describes the exactly broken asymmetry - the counterfactuality that the PNC enshrines as a conception of either a physical state, or a logical state.

So we produce two incompatible conceptions of physical reality, but then find that to be a supremely useful trick, as both are just the descriptions of the limits on being, and thus a suitable basis for describing all the actual states of being which are to be found in-between.

In one direction lies "complete indeterminism". In the other lies "complete determinism". Then in the metaphysical space thus created we find ... the cosmos as a unity of these opposites.
• 750
So, I have a deep confusion about why philosophy sees this disconnection between logical necessity and physical causation.

In the case of logical necessity, a set of premisses can necessitate some conclusion. The conclusion will be a 'necessary' consequence in the sense that it would be self-contradictory to assert the premisses and to deny the conclusion. In the case of physical causation, no description of prior states is sufficient to generate a similar self-contradiction. We know the sun will rise tomorrow. But we can never deduce that it will do so from any description of the universe today. That is the 'disconnection.' Why it is considered an important or troublesome disconnection is another very interesting question.

But it seems to me that materialism or physicalism must presume that logical laws are dependent on physical principles, because, in the physicalist view, everything is dependent on those laws (even if only by supervenience) — Stack X link

If the above distinction is coherent, and physicalism cannot accommodate it, then so much the worse for physicalism. That is, the validity of logical inference does not depend upon any particular state of the physical universe. The physical universe works in one kind of a way and logical inference in another. We can say things that are true about the universe and false about logical inference and vice versa. So different things work in different ways as we might expect.
• 15.8k
Bringing Hume and Kant into this is just turning the ontological issue into an epistemic debate.

This is a philosophy forum, so it is apt. It's not a physics forum - and if I introduced this thread to Physicsforum it would be deleted because they don't generally much like philosophical threads.

But since Kant, we've had the quantum and relativity revolutions,

You may be interested in Kelly Ross' analysis Kantian Quantum Physics. Michel Bitbol has also undertaken similar analyses e.g. here.

The point is just to dump the hardest bit of the metaphysical puzzle in some dark corner that no one any longer wants to talk about.

:lol: Swept under the rug, you might say. That's what gives rise to the endless arguments about interpretations of physics.

We know the sun will rise tomorrow. But we can never deduce that it will do so from any description of the universe today.

I understand the distinction between inductive and deductive reasoning. Nevertheless scientific principles such as the second law of thermodynamics are presumed to entail necessary consequences, i.e. we will expect them never to be contradicted. If such is to occur, we would seek a further natural causal explanation as to why this could occur.
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This is a philosophy forum, so it is apt.

But it is still confusing epistemology with ontology,

Kant and Hume were talking about what we could know. And that clarified that we only model reality.

Having got that sorted, we can get back to asking the big question. What is reality? And knowing how the modelling works helps us figure that out.

We can see for example that we tend to grant too much concrete reality to the material and efficient causes of being, but also then not enough concrete reality to the formal and final causes of being.

Or at least this is what Peirce and other systems thinkers realised.
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A minor point, but when a mathematician explores a possible theorem, searching for a hypothesis that will guarantee a certain outcome, he does so over a period of time. But when he finds such a starting point, the conclusion instantly exists. A implies B involves no time component. Is this true of cause and effect in the physical world? Hitting the ball with your bat is certainly cause and effect, possible only during an interval of time.
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Interesting point - but then, we don't expect scientific laws to change over time, although there's some dispute over that (Peirce for instance calling them 'habits of nature' and questioning whether they are truly invariant.) Mathematical proofs and the like are also not contingent on circumstances or conditions, they are derived by pure intuition. Whereas empirical facts consist of a concatenation of circumstances and observation. But, that is why mathematical platonists insist that maths concerns a transcendent realm, which empiricists will always deny (see the indispensability argument in the philosophy of mathematics.)

Kant and Hume were talking about what we could know.

Rather, what are the foundations of knowledge. Kant credits Hume with establishing that causal relationships could not be simply assumed (or known a priori). He says most of Hume's critics failed to understand the cogency of Hume's argument (as I said, that criticism might also apply to my argument.) But nobody here yet (myself included) as really indicated the import of Kant's 'answer to Hume' (I'll try and find time to properly read that SEP article I referred to and then have a shot at it.)
• 750
I understand the distinction between inductive and deductive reasoning.

Doesn't that resolve the deep confusion you mentioned?

Nevertheless scientific principles such as the second law of thermodynamics are presumed to entail necessary consequences, i.e. we will expect them never to be contradicted.

'Presumed' and 'expect', true. That is, when we get some awkward experimental result we have a policy of not explaining it by saying the second law has broken down. That is because without such a policy we would keep leaping to easy but unjustified conclusions. But sometimes the presumed fundamental laws do break down. There was a policy of not explaining planetary motion by discarding the geocentric universe which was taken as a fundamental and necessary tenet. Every other avenue was tried. Ultimately that 'law' had to be discarded, despite its apparent necessity.
• 4.4k
Hume only points out that one can't come up with an a priori deductive argument for causality.

However, a posteriori deductive arguments for causality are the stock-in-trade of science (re the laws of nature and induction).

So, if your PC does something weird, it could mean

1. Your a posteriori deductive argument for causality is an epic fail.

OR

2. The PC is acting up, it's kaput, it's malfunctioning (saving the phenomena)
• 16.9k
However, a posteriori deductive arguments for causality are the stock-in-trade of science (re the laws of nature and induction).

What woudl such a thing be like? Can you show us one?
• 4.4k
What woudl such a thing be like? Can you show us one?

Well, from classic definition of induction as an argument from particulars to generalities and back.
• 16.9k
But that uses induction - what would a deductive argument for cause look like?
• 4.4k
But that uses induction - what would a deductive argument for cause look like?

Well, if what I said doesn't do the trick, I don't know what will. Maybe if we take induction in a mathematical sense (deductive), it'll help.
• 802
The laws of thought are organised to arrive at the counterfactuality of the Law of the Excluded Middle.

Don't think so. 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.

That being said, a gas in vacuum expands (forward causation, forward time) or it implodes (reversed causation, backward time).
• 16.9k
I'm guessing the link between logic and causation is to do with modus ponens:

$p\\p \supset q\\\vdash q$

If $p$ is taken as the circumstances preceding an event, $p \supset q$ as a causal law and $q$ as the consequence caused, this might be understood as presenting the general form of physical causation. This presumably implies that the causal law, like modus ponens, is necessary.

So, is $p \supset q$ an accurate parsing of a causal law? I'll go with Anscombe and say that it isn't.
• 6.5k
Logic is timeless - present tense eternal. Socrates is mortal, always has been and always will be for ever and ever. Whereas in time and cause, Socrates was alive and became dead and being dead and alive contradicts logic. No one has a problem with this though, because we have tenses to keep them separate. Cause keeps them separate Socrates was alive and is now dead, because he drank hemlock. In this way cause saves logic from time.

These devices are built around microelectronics, devices comprising millions (even billions) of minute components, unfathomably complex to the untrained (including myself). These generally operate with quite astonishing degrees of precision and predictability through the mediation of sequences of billions of separate logical steps carried out at lightning speed and providing instantaneous results

The point is just to dump the hardest bit of the metaphysical puzzle in some dark corner that no one any longer wants to talk about.

In the dark corners of computers are hidden the variable, unpredictable analog signals that are 'treated as' 0s and 1s.

I think the Unreasonable Effectiveness of Mathematics is the same problem restated more clearly. And I don't think it is all that intractable. Mathematics is the study of abstract structure of every kind : symmetry and asymmetry, order and chaos, temporal and timeless, etc. So it doesn't actually seem surprising that mathematics can be applied effectively to both electronics and pebbles on a beach There is a pattern in the pebbles but it is statistical; there is randomness as well. Logic had better just shut up here about the law of non-contradiction for a moment. We come to understand the cause of the pattern in terms of prevailing wind and wave angle moving pebbles of different sizes at different speeds along the beach - "on average" over centuries. A simple explanation using 'cause' with a very broad brush indeed and a deal of handwaving at the forces of chaotic waves that no one is going to calculate individually.

Edit: Note that mathematics aways begins with a biblical style commandment of creation: Let there be light. Let x be a number.
• 15.8k
I understand the distinction between inductive and deductive reasoning.
— Wayfarer

Doesn't that resolve the deep confusion you mentioned?

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

I think the Unreasonable Effectiveness of Mathematics is the same problem restated more clearly.

So do I! I was going to include it as one of the refs in the OP. He says

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

Why isn't it understood? And what is it that isn't understood? Isn't it just the convergence between mathematical logic and physical necessity that he's talking about?
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