I have always presumed that logical causation - such as logical rules like the formation of a valid syllogism, or the law of the excluded middle - operate independently of physical causation. That is, such expressions are not dependent on the laws which govern motion, mass, etc. 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).

So the question is, what is the link between logical necessity (e.g. if A > B and C > A, then C >B) and physical laws? How does physicalism propose to demonstrate that logical laws supervene on physical principles?

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    There is no causation in logic. Some formulas are equivalent to others, and common language confuses the issue with formulations like "this circle has circumference Pi because its diameter is 1", when in fact saying one proposition is the same as saying the other. It is not analogous to physical causation (I.e. The observation that some events often happen in succession). – armand Feb 21 at 12:38
  • Good distinction. I think however the relation between ‘cause’ and ‘reason’ as mentioned in the entry below captures the sense of ‘cause’ that I am interested in. – Wayfarer Feb 21 at 21:39
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    In that case, also consider that the "reason of knowing" says more about you as a thinker than about the logic at hand, namely, in what order you discovered the operands of the logical operators. Maybe you found out the circle has diameter 1, prompting you to understand it has circumference Pi. Or maybe you measured the circumference first. Anyway, this temporarily exists only for you and is irrelevant to the logic of the deduction. That's why I think your question either makes no sense or requires a thorough reformulation. – armand Feb 21 at 22:01
  • That’s fair - it’s why I posed the question in the first place. I think the reformulation would be along the lines, what kind of relationship obtains between physical causation and reason? When we ask in respect of some physical fact ‘what caused this to happen’, we are looking for a causal relation. But in so doing, we invariably employ the rules of rational inference, which are not physical. – Wayfarer Feb 21 at 23:02
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    The relation is simple: causation is in the "things themselves", reason is in the talk (or thinking) that describes them. To do physics, we have to reflect it in our talk, but it does not mean that all rules in our talk reflect physics. Some of them service our need to understand ourselves and each other when talking. Logic is part of talk design, just like grammar. On physicalism, it is still derivative from physics and biology, of our brain function mostly, but not in the way that what it is used to express reflects physics by describing it. – Conifold Feb 22 at 6:43

I would start by saying, just to clarify slightly, that I think that speaking of logical causation is misleading, as (it is explained by other answers) "because" is not a truth operator. (Hence logical necessity works better.)

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."

Later (Propositions 6.37, 6.371 and 6.362) "A necessity for one thing to happen because another has happened does not exist. There is only logical necessity. At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena. So people stop short at natural laws as at something unassailable, as did the ancients at God and Fate. And they both are right and wrong. But the ancients were clearer, in so far as they recognized one clear conclusion, whereas in the modern system it should appear as though everything were explained."

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.

I would also like to add what I perceive to be a flaw in the positivist approach of science and philosophy, which is the one which seems to lead most physicalists to their position and its implications, about causation, determinism, etc... When the positivist declares that all valuable knowledge comes from science (or broadly, some application of the scientific method), this assertion is scientifically unjustifiable. There is no "science of the sciences" from which to draw conclusions, and we can see that the justifications of the positivist position rest on other types of affirmations, notably such as priori intuitions, but also beliefs, values, etc...

Despite the rhetorical appeal of Carnap's (one of the historical spearheads of positivism) claim that "Metaphysicians are musicians without musical talent", one would resolutely qualify it of unscientific.


As to your question regarding the dependence of logical laws upon physical laws, you may have a look at

Personnaly I can imagne a scenario in which logical laws could be derived from physical laws :

(1) logical laws describe the way we reason

(2) the way we reason is part of our psychology

(3) psychology is part of physics [ the mind is part of "nature"]

(4) therefore, logic is a province of physics

This would be , I think, a form of psychologism; but standardly, it s said that premise (1) is false; logic is not about the way we reason in fact, but about the way we ought to reason ; it is a normative science, not a descriptive one.

  • Elementary logic books often empasize the fact that " because" is not a logical operator. The reason is that logical operators are truth functional ( i.e. are " truth functions") , meaning that the truth value ( true/ false) of any statement " ___ Operator ____ " is totally determined by the truth values of the sentences that are used to fill in the blancks.

  • For example , knowing that "The Moon is made of green cheese" is false and that "2+2=4" is true , you can " compute" ( without any further information) the truth value of the molecular" If ... then" sentence " if The moon is made ... then 2+2=4"

  • The connective "Because" is not truth functional. It is not enough to know the truth value of P and of Q in order to determine the truth value of "Q because P". Knowing that " Mary has left Peter" and that " Peter has lost his job" , I cannot tell whether it is true that " Mary has left Peter because Peter has lost his job".

  • Note : using the notion of causation in logic is not absurd, but is somewhat outdated; Aristotle said that, in a syllogism, the middle term is the " cause" of the conclusion ( it explains why the predicate of the conclusion is attributed to its subject).

  • A broader notion could be substituted for the notion of cause, namely, the notion of " reason". The premises of a reasoning can be consdered as the " ratio(nes) cognoscendi" ( reason of knowing) of the conclusion, that is, as the grounds on which rests the assent to the conclusion.

  • Reference: Gary Hardegree ( Umass) : https://courses.umass.edu/phil110-gmh/text/c02.pdf

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    Thanks, that is helpful. The note about ‘reason’ is especially relevant. – Wayfarer Feb 21 at 21:37

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. Since the behind ontological "substance" is not known, they have to be both metaphorical reflections of the same ontological substance if it exists...


I recommend you review Hume’s Fork.

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.

  • Whereas I tend to side with Kant over Hume. – Wayfarer yesterday

What's the relationship between physical and logical causation?

Consider a physical apparatus, such as a computer. Although a quantum physicist may argue that the behavior of all material objects is probabilistic, without a great loss of accuracy, we may consider (some) computers to behave deterministically. That is, we may consider the computer as composed of much smaller devices called "gates". The inputs to a gate determine the outputs of that gate. One can track a cause and effect relationship between the inputs to the computer to its outputs by tracking what happens at each gate.

Now, suppose we program a computer to calculate whether or not a certain number, call it x, and to either display "x is prime" or "x is not prime", based upon whether the computer can find a whole number which divides x, other than 1 and x itself. Now, suppose we input 99999989. Again, we can follow the low level behavior of each of the gates in turn, and determine a chain of cause an effect that eventually results in the computer displaying "99999989 is prime".

However, we can also provide another explanation for the same behavior. The computer displayed "99999989 is prime" because in fact 99999989 is prime.

In my opinion, it is just as valid to say that 99999989 being prime is the reason why the computer displayed "99999989 is prime". After all, if a non-prime number were given as input, say 100000000, it would have responded with differently.

We all have choices in how we use words, but I would not object to the following language: "The fact that the number input, i.e. 99999989, was prime, caused the computer to ultimately output '99999989 is prime'". Others may object that the use of the word "caused" here is "incorrect usage of language". However, I think they are claiming a monopoly on semantics that they cannot enforce.

  • "Monopoly on semantics" is a nice phrase, I have to remember that... After all natural languages belong to everyone and every individual can express his/her context within... So you've drawn a picture of reality being accurately described by FOL predicates here. After all, every (classical) science is based on some logic. But I'd still argue about your "causation", I think it's unjustified to say "logic A causes the chain of events B" and I'd translate it to: "the chain of events B can be meaningfully interpreted within logic A". – k-wasilewski Feb 21 at 15:59
  • @k-wasilewski. Some semantic claims are "enforceable", in the following sense. If one were to assert 2=3, without some adjoining explanation or context, one will be driven from polite society. Not so with mixing logical truths with causation. If I should ask on a forum "why did my computer program never terminate?", and someone should respond with "because the square root of 2 is not a rational number, dummy!", their comment could be, and probably would be, understood without encountering backlash, other than for the use of the word "dummy". – Math Keeps Me Busy Feb 21 at 16:15
  • Alright, philosophy aside. You're still using a very "formal logic friendly" example (I, myself, am a programmer), but the question was about the "physical laws". I understand that computer science obides all of them, but still think you're selecting your examples not very arbitrarily... Just saying :) I think "all sciences are founded on math and logic and therefore their definitions of 'causal laws' are, more or less, constructed using logic" would be more of an answer. – k-wasilewski Feb 21 at 16:37
  • OK, it's clear that the thread title should have been: Physical causation and logical necessity. – Wayfarer Feb 23 at 23:21

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