it's been a good discussion. — Andrew M

Agreed. And thank you as well. This has been educational for me, and I think my point of view on these topics has become more sophisticated as a result.

That seems right to me. Or, in alternative language, that the potential is grounded in the actual. — Andrew M

I like that. It sounds very Aristotelian.

Note that I haven't argued that what exists depends on what does not exist (or exists indefinitely). I don't think that is true. I've only argued that part of the universe can be indefinite, or lack definite form, for a particular observer. It takes an interaction or measurement to actualize that potential, so to speak. — Andrew M

Then I think we may have reached a satisfactory point of agreement. I still think that certain logical principles must be regarded as necessarily and universally valid, but I've gained a greater appreciation for how QM forces us to modify how we apply and qualify these principles. A universe which contains indefinite portions is significantly different from the universe Aristotle conceived of, so it makes sense that we've had to develop new methods of logic to describe it. I just don't think this amounts to a revolution in logic and an overthrow of the old paradigm (and it doesn't sound like you do either). Methodologically, logic has had to adapt and innovate to keep pace with the natural sciences, but I think the deepest truths of logic have remained the same. The natural sciences have inspired us to develop a more nuanced understanding of the principles of logic and reject certain false conclusions which follow from a lack of nuance (e.g. that superpositions are impossible). But the underlying, conceptual structure of logic does not depend on how we conceive the natural world.

If we accept "consciousness causes collapse" but reject the many minds interpretation, then wouldn't we conclude that whatever is definitely the case for Wigner's friend is also definitely the case for Wigner? Once Wigner's friend performs a measurement and collapse occurs, the result he observes becomes definite for all potential observers even if they do not observe it themselves. Wigner doesn't know what his friend observed, but once his friend observes it, it is no longer in a superposition. We could also reject both the many-worlds interpretation and "consciousness causes collapse" and hold that unattended measuring devices can also cause collapses which become definite for all potential observers, conscious and mechanical alike. Does that not work?

If it does work, then the physical world can be divided into observed (consciously or mechanically) parts, which are definite, and unobserved parts, which are indefinite. If it doesn't work, then perhaps we must adopt a many-worlds or many-minds interpretation. Either way, definite parts of the universe (whether it's only one observer's universe or the universe for all observers) exist definitely and indefinite parts exist indefinitely. I think we must posit that the indefinite parts are grounded in the definite parts. And I think we must do so regardless of what portion of the physical universe is indefinite. Here's an argument:

Firstly, it seems impossible for the definite parts to be grounded in the indefinite parts. For if what exists most fundamentally exists indefinitely, then it does not definitely exist. But we exist definitely, and our existence can't be grounded in things which don't definitely exist. Our existence might be grounded in things with some indefinite properties, but these grounding things must at least definitely exist and possess some properties definitely.

Secondly, it seems necessary that the indefinite is grounded in the definite. For if a thing exists indefinitely, it does not definitely exist, hence it does not definitely have any properties, hence nothing definitely true can be said about it. Perhaps we can only make probabilistic claims about the indefinite, but even these claims are definite insofar as the probabilities we predicate of something indefinite are definitely its probabilities. So unless we want to treat indefinite things like Kantian noumena about which nothing can be meaningfully asserted, we must posit that what exists indefinitely is grounded in what exists definitely, even if what exists definitely has no other definite properties than set of definite probabilities.

The superposition can extend to the electron's existence as well. Consider Schrodinger's Cat where there can conceivably be lengthy alternative histories in superposition (and exhibiting interference). This also plays out in the Wigner's Friend thought experiment which describes a scenario where a system's state is definite for one observer (the friend) but indefinite for another observer (Wigner, for whom the friend is in superposition). — Andrew M

This is the first I've heard of Wigner's friend, but I just read that the purpose of the thought experiment is to support the theory that consciousness causes collapse i.e. that everything is in a superposition until a conscious being observes it. But maybe I misunderstood what I read. Theoretically, it is possible that nothing exists definitely until it is observed. In that case, consciousness is necessary for existence. I'll call this theory quantum idealism. If something could be definite for one observer but indefinite for another, then perhaps a many worlds interpretation of quantum idealism would follow. Each consciousness exists in its own world. Where two conscious beings observe the same thing, their worlds converge and where they observe contrary things (e.g. I observe the cat is alive and you observe it's dead) their worlds diverge. Since Wigner's friend observes something definitely which remains indefinite for Wigner, the consciousness of Wigner's friend has diverged into two separate worlds, each with its own version of Wigner's friend. Until Wigner contacts his friend, it is undetermined which of the two divergent worlds Wigner's world will converge with.

I don't necessarily endorse either a many worlds or a single world version of quantum idealism, but I think this is one possible way to account for lengthy alternative histories existing in superposition without contradicting LEM. As long as reality bottoms out in definite facts, such as being x observes y, LEM remains in tact. Whatever is indefinite exists only relation to what is definite. The cat is only indefinitely alive or dead in relation to the definite fact that it is in the box.

Dickson would agree that you can define logical connectives either way. But he argues that only (non-distributive) quantum logic has empirical significance, and thus relates to correct reasoning, since it derives from quantum theory. He discusses this further under "The Motivation" on p3. — Andrew M

All the math in this stuff goes over my head, especially given the limited amount of time I have to peruse it. It seems to me like the main difference between quantum and classical logic is that "a or b" in quantum logic means "a or b or it is indefinite whether a or b". So is the reason he sees quantum logic as more empirically significant that physical states of affairs can be indefinite? I see how this would make quantum disjunctions more useful to apply in certain contexts, but I don't think it makes the classical disjunction false. And if the classical disjunction is not inherently false, then neither is the principle of distributivity. And if I am right that reality bottoms out in something definite, then the classical disjunction applies to what is most fundamental.

Indefiniteness can apply to existence as well. An electron could be in a superposition of an excited state and ground state (having emitted a photon). In this case the number of photons (0 or 1) is in superposition. That is, what exists or not can be in superposition. — Andrew M

Couldn't we say that the electron exists but no definite state of the electron exists and no definite number of photons exists? Saying no definite state exists just means that the state is indefinite. I see why it seems problematic that we can neither affirm nor deny that a photon exists. Could we perhaps resolve this problem by thinking of the photon's indefinite existence as a property of the electron. Existence is only existence as such when it is definite. If something exists indefinitely, it only exists as a property of something which exists definitely. For instance, the position of a particle in superposition exists indefinitely as a property of the particle, which exists definitely.

QM upends that intuitive picture. You can have a quantum coin which, when flipped twice and then observed, will always be found in the same state it started in (e.g., always heads). There is no straight-forward way to visualize that process without giving up counterfactual-definiteness. And so the LEM is no longer applicable in the obvious way. — Andrew M

I'm not sure I understand this argument. Are you saying that giving up counterfactual definiteness also forces us to give up LEM? I've argued that this isn't the case because you can't meaningfully predicate something of a non-existent subject. LEM even applies to indefinite states of affairs because all states of affairs are either definite or indefinite. It just doesn't apply to particular determinations of indefinite states of affairs because no such determinations exist.

If the unobserved universe exists in an indefinite state at both the micro and the macro level, and the only parts of the universe that are definite are the parts we observe, I see how this could be problematic. If indefinite existence is a property of definite existence, and the unobserved universe exists indefinitely, then the unobserved universe is a property of the observed universe. This would imply that the existence of the universe is dependent upon our observation of it. I think it would be better to avoid this conclusion if possible, but it's still preferable to allowing things which don't definitely exist to have properties. You said, "what exists or not can be in a superposition". This strikes me as not only counterintuitive but inconceivable. If something does not exist, then it is nothing, and it can have no properties. Therefore, a thing can only have properties insofar as it exists. If it is indefinite whether a thing exists or not, then it is indefinite whether it has properties.

So there are at least two broad options available. One option is that there is a more fundamental logic (say, quantum logic) that applies universally with classical logic emerging as a special (or approximate) case that applies in decohered environments. A second option is that classical logic is universal, with indefiniteness being just a placeholder for what has not yet been satisfactorily explained in definite terms. — Andrew M

I won't speak to the second option, but if the first option entails that things are fundamentally indefinite, then I think we should reject it. It seems to me that, although we can allow some things to be indefinite, our description of the world must bottom out in something definite. For instance, the particle can only have an indefinite position if it definitely exists. If the particle exists indefinitely, then I argue that we should think of its indefinite existence not as an independent entity but as a property of something definite. For only things which exist can have properties, so if a thing doesn't definitely exist, it doesn't definitely have any properties, so nothing we can say about it is definitely true.

Hence the distributive law is wrong. — Quantum logic is alive ∧ (it is true ∨ it is false) - Michael Dickson

If the disjunction symbol means what it means in classical logic, the distributive principle is correct. If it means what it means in quantum logic, it is incorrect. The disjunction symbol can mean whatever we want it to mean, so I don't think either application is fundamentally right or wrong.

Oddly, one can say the same about i - the root of negative one. Despite this, we make use of them. — Banno

True, but there's reason we say i is imaginary. It's not real in the same way as other numbers are. that being said, I'd love to hear a mathematician's insight into why i is so useful and why it can contribute to the generation of fractal patterns like the Mandelbrot set.

Hence, despite the vigorous protestations of modern logicians, they have not done away with Aristotle's logic, but rely on it whenever they apply the rules of manipulation they have developed. — Dfpolis

Agreed.

there is no law preventing us from thinking "square circle," or "triangles have four sides." It is only if we want our thought to apply to reality, to what is, that we should not think these kinds of thoughts. — Dfpolis

There's no law preventing us from thinking the words square circle, but we can't form a concept corresponding to these words. We can form some coherent concepts which don't seem to apply to reality e.g. wizards and unicorns. So I think it's correct to call the laws of logic laws of thought, since they constrain not only what is possible in reality but what is possible for us to conceive in our own minds.

So, let me suggest that we abstract from our experience an understanding of what it means to be -- an understanding of the nature of existence. And, implicit in this a posteriori understanding are laws of being that must be reflected in our thought, if our thought is to apply to what is. — Dfpolis

I think that you are correct if we understand a posteriori to mean learned through experience and a priori to mean known without having been learned. A child is not born with a developed understanding of the laws of logic. We must hone our intellects in order to comprehend the truth of a proposition like "a proposition cannot be both true and false". However, if a posteriori means contingent upon experience and a priori means knowable as true or false regardless of particular experiences, then I think you are incorrect. For as long as we possess an intellect capable of abstracting and experiences capable of being abstracted from, we should be able to deduce the same laws of logic. Even if I had no experiences to abstract from but the consciousness of my own existence, I should be able to deduce that I exist, therefore I don't not exist, and since not not existing is the same as existing, my only options are to exist or not exist. Moreover, I should see that these principles must be the same for all existing things due to the nature of existence. Given the weakness of the human mind and its dependence on sensation, a human solely conscious of his own existence would probably not being to perform this sort of deduction. But in principle, I think it is possible for a being capable of ideation and understanding to perform this deduction regardless of his particular experiences. As you say, the laws of logic are implicit in the nature of being, so even if the human intellect, due to its weakness, depends on many particular experiences to become conscious of the laws, the laws are contained implicitly within every possible experience. Perhaps you have reasons for objecting to the word a priori, but I think that if anything is a priori, it is logic.

Yes, one approach here is to say that classical logic applies when things are definite, e.g., when a measurement has been performed, or the subject being predicated exists, or the contingent event has occurred. But it does not apply outside that context. So it's not that classical logic is violated by indeterminacy, it's that the preconditions for its use have not been met. Garbage in, garbage out. — Andrew M

If classical logic doesn't apply to indefinite scenarios, then this would seem to be due to a limitation of the applicability of the law of excluded middle. A statement is indefinite if neither it nor its negation is true. For instance, it is neither true nor false that the photon passed through A1.

But the purpose of the present king of France analogy was to expose what I think may be a confusion on the part of some (perhaps not Putnam) who assert that quantum mechanics proves that the laws of classical logic are limited in their application and open to empirically informed revision. The reason the law of excluded middle doesn't apply to the photon's position is the same as the reason it doesn't apply to the present king of France. Neither the photon's (definite) position nor the present king of France exist, and the absence or presence of a property can only be meaningfully predicated of something which exists. No empirically motivated insight is required to grasp this principle. As you brought up, it was grasped at least to some extent by Aristotle. The empirically motivated insights of quantum theories have certainly led us to revise our understanding of physics. Whereas it was previously believed that all spatial entities had definite positions, it is now widely held that subatomic particles exist in superpositions. This notion, although well supported, is highly counterintuitive. I think the confusion occurs when people make something along the lines of this argument:

(1) QM has led us to revise our intuitive understanding of space.
(2) QM has led us to develop new logical languages (with different connectives).
(3) Therefore, QM has led us to revise our intuitive understanding of logic.

This syllogism is obviously unsophisticated and invalid, so it might be fair to call it a straw man, but I think it illustrates the way people often think about this topic. "If quantum mechanics can defy our intuitions about space, then why not our intuitions about logic," the reasoning goes. I think the conclusion is false because the idea that excluded middle doesn't always apply didn't originate with quantum logic. The fact that quantum logic is non-distributive, as I far as I can tell, follows directly from the fact that excluded middle doesn't apply to quantum superpositions i.e. we can neither say that the photon passes through A1 nor that it does not pass through A1 because it doesn't have a definite position.

Although the law of excluded middle may not be universal in as obvious a sense as the law of non-contradiction, I still think we can truthfully call it universal. Reality consists of things which exist, and as long as excluded middle applies to all things which exist, it applies to all things in reality. Therefore, it is universal. Since no definite position of the photon exists, the law of excluded middle does not apply to it. But the photon itself exists, so the law applies to the photon. For instance, it is either true or false that the photon has a definite position.

I'm not sure if we have a substantial disagreement at this point. I agree that the law of excluded middle cannot be carelessly applied to all propositions, and you've shown that quantum disjunctions can describe superposition in a way which classical disjunctions can't. But I don't see this as evidence that the law of excluded middle is contingent or that logic is open to empirical revision (I'm not sure if you ever intended to make that argument, but my original purpose in this post was to argue against it). We develop new logical languages to more effectively describe new facets of reality which we discover. But the fundamental logical laws of reality, or at leasts the laws of our capacity to think about reality, remain the same regardless of what we observe. One point I will concede is that quantum disjunctions are no less valid than classical disjunctions. They are equally applicable to reality, or at least to the parts of reality for which they are intended.

With this general sense of logic, it is indeed possible to have a logic in which conjunction and disjunction mean something different than what they mean in classical logic, but play broadly similar roles. — SophistiCat

Honestly, sometimes I feel all this is just a game. Anyway, the point is there are logics that can handle contradictions pretty well or so some tell me. — TheMadFool

It seems that we are free to invent logics of many different kinds. Some may be useful and others may be invented as games. But it seems to me that principles such as identity, non-contradiction and excluded middle must hold within any logic whose theorems are conceivable to us.

So based on this state space geometry, quantum logic is the general case and classical logic is the special case (where states are definite and have unique complements). — Andrew M

It seems that disjunction in quantum logic has a different meaning than in classical logic. In classical logic, A or B means either A is true or B is true. In quantum logic, A or B means either A is true or B is true or it is indefinite whether A or B is true. You pointed out that this indefiniteness is not merely epistemic (at least according to the Copenhagen interpretation). It might be epistemically indefinite i.e. uncertain, whether a coin landed on heads or tails, but we know that it actually did land on one or the other side. But in the case of the photon, it is metaphysically indeterminate whether it went through slit A1 or A2. Disjunction in quantum logic can express this state of metaphysical indeterminacy.

But I don't think that metaphysical indeterminacy proves that there are exceptions to the laws of classical logic. We can discuss indeterminacy using a classical disjunction. For instance, suppose that process P has two possible outcomes, A or B. P is either indeterminate or determinate. This is a classical disjunction. If P is determinate, then either A obtains or B obtains. If P is indeterminate, then it is undetermined whether A obtains or B obtains.

If P is indeterminate, then the proposition "A or not A" does not make sense, for the same reason that the proposition "the present king of France is bald or not bald" does not make sense. There is no present king of France, so it's neither quite correct to say he is bald nor that he is not bald. Likewise, there is no determinate outcome of P, so it is neither quite correct to say A obtains nor not A obtains. Neither example proves that the law of excluded middle has exceptions. All existing subjects either have or lack a given predicate, but if the subject does not exist, then it does not make sense to assert that the subject lacks the predicate. It does not make sense to assert that the present king of France lacks baldness because this implies that he has hair, which he does not because he doesn't exist. Likewise, it does not make sense to assert that the outcome of P is not A, because this implies that P has a determinate outcome. For a more concrete example of indeterminacy, take the statement "Bob will leave his house tomorrow". Assuming that Bob has free will and the future does not yet exist, it is undetermined whether he will leave his house tomorrow. So it is neither quite true to say that he will leave his house nor that he won't leave his house because both statements falsely imply that his future is already determined.

Just because classical disjunctions don't express indeterminacy doesn't mean that indeterminacy defies the laws of classical logic. We can still reason about indeterminate states of affairs using classical logic. For instance, we can conclude that, if A obtains, then P is not indeterminate.

So I don't think that we should think of quantum logic as a deeper form of logic and classical logic as merely a special case. It may be true that the physical world is fundamentally indeterminate, meaning that determinate processes such as coin flips are a special case in relation to the indeterminate subatomic processes which underlie them. And it does seem to be true that quantum logic is often more useful than classical logic when it comes to describing quantum phenomena. But this is only because quantum logic is specifically designed to express indeterminacy, not because classical logic is violated by indeterminacy.

Logic without distributivity is not as problematic as you think. You may find this recent article interesting: Non-distributive logics: from semantics to meaning. — SophistiCat

I read the paper's introduction, and two pieces jumped out at me:
1) "For instance, a natural question is whether relational semantics of (some) non-distributive logics can provide an intuitive explanation of why, or under which circumstances, the failure of distributivity is a reasonable and desirable feature; i.e. whether a given relational semantics supports one or more intuitive interpretations under which the failure of distributivity is an essential part of what ‘correct reasoning patterns’ are in certain specific contexts. Perhaps even more interestingly, whether relational semantics can be used to unambiguously identify those contexts. Such an intuitive explanation also requires a different interpretation of the connectives ∨ and ∧ which coherently fits with the interpretation of the other logical connectives, and which coherently extends to the meaning of axioms in various signatures."

If conjunction and disjunction (∨ and ∧) are interpreted differently than in classical logic, then it does not seem so surprising that the principle of distributivity might fail. But this does not entail that the principle does not hold universally. The principle does hold universally (it seems to me) so long as we interpret the conjunction and and disjunction symbols (and whatever other symbols might also be relevant) to mean what they mean in classical logic. If we change their meanings, then it makes (classically) logical sense that we'd get a different set of theorems.

2)
"the graph-based semantics supports a view of LE-logics as hyper-constructivist logics, i.e. logics in which the principle of excluded middle fails at the meta-linguistic level (in the sense that, at states in graph-based models, formulas can be satisfied, refuted or neither)"

So it seems like the law of excluded middle might also be rejected in these logics. There's nothing strictly illogical about operating within a system where true and false aren't the only possible values a statement can have. It might sometimes be useful make 'unknown' a third option, and maybe other logics can incorporate probability such that a statement can have any value between 0 and 1. But I still think it is true that, in reality, every meaningful proposition must be either true or false. The proposition either corresponds to reality (e.g. the Eiffel Tower is in France) or it does not correspond to reality (e.g. the Eiffel Tower is not in France). There is no third option.

But I admit that much of what I read in the introduction went over my head. So perhaps I'm misinterpreting the quotes I pulled out.

But this is if you look at quantum logic as making an absolute metaphysical statement about quantum mechanics, rather than simply treating the logic instrumentally, or as usefully capturing some aspect of the phenomenon without pretending to the ultimate truth. — SophistiCat

I agree that if we look at logic as an instrument, then it does not matter whether its axioms and theorems correspond to objective truths about reality. But I think that we should look at the principles of classical logic as being objectively true.

Did God create the universe for us or were we created for the universe? If the former then logic isn't empirical and if the latter it is. — TheMadFool

To be clear, I think that, phenomenologically, logic is at least somewhat empirical. We come to understand logical truths, like the principle of non-contradiction, by abstracting from various experiences, and all experience involves sensory phenomena, whether it's directly received from the senses or reproduced in the imagination. And we communicate logic using words and symbols, which we process via our senses. But we should distinguish the cause of our coming to understand logical principles from the cause of the certainty of logical principles. Once we understand logical principles, it becomes apparent that their certainty does not depend on the specific experiences whereby we came to understand them. I may have realized that non-contradiction is true by considering that a triangle cannot be a square, but I could have just as easily realized it by considering that a bachelor cannot be married or by considering any other contradiction. If the principle were empirical, then I'd have to admit the possibility that non-contradiction may only apply to my specific set of experiences. But once I admit this possibility, the entire structure of thought is undermined. If contradictions are possible, then perhaps experiential evidence against contradictions (e.g. I've never observed a square triangle) might really be evidence for contradictions. I don't have empirical evidence to tell me how I ought to interpret empirical evidence, so if contradictions are possible, perhaps I should interpret my experiences to signify the opposite of what they seem to signify. We arrive at our knowledge of logic through a combination of sensory experience and intuition. But once we grasp logic adequately, it becomes a necessary and indispensable foundation for our understanding of the world. So when I say that logic is not empirical, what I mean is that we should not seek to adjust the fundamental principles of logic in order to accommodate empirical evidence. We need logic to make sense of empirical evidence, so, as long as we are committed to the search for truth, we must regard logical axioms and theorems as a priori and self-evident.

The only reason for you to think that our capacity for logic is a product of evolution or intelligent design is that these explanations are (or seem) reasonable. But if the implication of these explanations is that logical principles are mere tools for interpreting the world or contingent structures of thought that might have been created otherwise, then the foundation of reasonable thought is undermined. In that case, you would have no rational justification for believing in either evolution or intelligent design. I think the best explanation for why we use logic is that logical axioms correspond to basic features of all existence: things are what they are, they are not what they are not, and for any given property, a thing either has or does not have that property.

But otherwise, yes, it comes down to the measurement problem. — Andrew M

I just refreshed my memory on the double slit experiment, and it seems practically certain that setting up a device to determine which slit the particle goes through will affect where it lands. So if you place a detector on A1 or A2, then it is certain that the particle will not hit R. If you turn off the detector, then the particle will hit R, but you won't know whether it went through A1 or A2. The particle behaves like a wave if you don't track its motion and like a particle if you do. So since the detector clearly affects the conditions of the experiment, then I think it makes sense to assert that the principle of distributivity holds when the detector is off. The statement "(A1 and R) or (A2 and R)" is true, we just don't know which disjunct is true and which disjunct is false. When we turn the detector on, both disjuncts are false because tracking the particle changes the way it moves. It seems arbitrary to me that we should make the realist assumption that (A1 or A2) is true, even though this assumptions can't be empirically verified, but not also assume that the principle of distributivity holds just because we can't empirically verify either (A1 and R) or (A2 and R). In fact, I think rejecting the realist assumption would be preferable. I can conceive of a particle teleporting straight onto R without passing through either slit. This would only violates the nomological law of continuous motion. But I can't conceive of the principle of distributivity as being false because it is a logical tautology. Like I said before, distributivity follows necessarily from more primitive logical axioms, so the principle's universality can't be denied without also undermining the universality of some of the most basic laws of thought.

If one of the disjuncts were true in reality, it would be a hidden variable. But that would require a non-local interpretation, per Bell's Theorem. — Andrew M

I think I see how this could be problematic. Suppose you did a double slit experiment with two entangled particles separated by a significant distance. Then turning on the detector for one of them would communicate an effect to the motion of the other which would travel faster than the speed of light. Is that what you have mind? So is Putnam's argument that we ought to sacrifice the universality of classical logic in order to preserve realism and locality? If so, I don't think that's advisable. I don't think there's anything wrong with using quantum logic as tool, but I think we should still maintain that the principles of classical logic are always true. Maybe in the future, there will be something to explain how localism and realism are compatible with classical logic. Maybe future experiments will deliver definitive evidence against localism and or realism. I know that some very strange paradoxes would seem to follow if localism were false, but this seems like nothing in comparison with the confusion that would follow if we relativize logic, which is the foundation of all rational thought.

OK, so it's interesting to consider Putnam's argument here. He notes that you could says exactly the same thing about Euclidean geometry. It might be considered necessarily and universally true, but it nonetheless fails to describe the world we live in. — Andrew M

I don't think Euclidian geometry is necessarily universally true in the same way that classical logic is. A principle like "there is exactly one straight line passing through any two points" is always true with regard to our perception of space. We can't imagine a non-Euclidian realm in which the principle does not hold. But just because non-Euclidian space is unimaginable does not mean it's inconceivable. Non-Euclidian space violates the principles of sensory perception but not the principles of rational thought. My claim is that a logic in which the principle of distributivity is false does violate the laws of thought such that any claim made in such a logic, regardless of its usefulness, amounts to nonsense if we actually try to conceive of its meaning. It is impossible to think the proposition "((A1 or A2) and R) and not ((A1 and R) or (A2 and R))". You can write it out in symbols and claim that it is true, but you don't actually have a concept of what you are affirming any more than you have a concept of a married bachelor. The only reason that we are even capable of working out the principles of non-Euclidian geometries and non-classical logics is that we are capable of using classical logic. The principles of classical logic underlie everything rational we think and do in science, philosophy and daily life.

Is there some specific axiom of classical logic that you think we can afford to relativize? Distributivity is a theorem, not an axiom, so to reject the theorem would require rejecting an axiom. I know some people point to the law of excluded middle (which allows for double negation) as possibly dubious, but I don't think so.

Which goes to show that "laws of thought" - including the principle of distributivity - don't have to be as rigid and universal as people often assume. We can adopt different logics for different uses. — SophistiCat

There might be certain contexts (although I can't think of any) in which it might be useful to assign certain contradictions as true. But I still think there is a law of though which makes contradictions inconceivable. It seems to me that a violation of the principle of distributivity is likewise inconceivable. If I turned on my blinker and turned either left or right, then does it not necessarily follow that I turned on my blinker and turned left or turned on my blinker and turned right? Can you conceive of the former as true and latter as false? Would that not violate the laws of thought?

I think I understand, but please tell me if I am missing something. So when the photon hits R, as long we hold to a realist interpretation, we must assume that it passes through either A1 or A2. So R is true, and (A1 or A2) is true. The former is verified by observation and the latter by realist assumptions. Therefore, their conjunction is true. But neither (A1 and R) nor (A2 and R) can be verified as true, since we don't observe the photon to pass through either A1 or A2. So the statement "(A1 and R) or (A2 and R)" is evaluated as false, because neither disjuncts can be verified. (Or can they in fact be verified as false? When we measure A1 and A2 individually, do we never or only sometimes detect a photon passing through them?)

I don't think that this proves that the principle of distributivity fails. It may be useful to not apply distributivity when dealing with quantum phenomena, but that doesn't mean that the principle is false. It is inconceivable for the principle to be actually false. If R is true and A1 or A2 is true, then either R and A1 is true or R and A2 is true. That's a simple tautology. Just because we can discover more in quantum mechanics by not applying a principle does not necessarily mean that the principle is false. And if we have reason to believe that the principle is necessarily and universally true, as I think we do in the case of distributivity, then its usefulness in quantum mechanics should make no difference. Even if we treat it as false in quantum mechanics, I don't think we must interpret this as invalidating the principle's universality. Perhaps it is true that either (A1 and R) or (A2 and R), but since we can verify neither disjunct, we treat it as false, not because it is false in reality because our measurements fail to demonstrate it. (Or, if our measurements in fact demonstrate the contrary, that the photon passed through neither, then we would have to interpret the act of measurement as affecting the photon).

However I will maintain that there is a sense in which we choose, amongst possible logical systems, that which best fits what it is we are trying to explain.

SO what might very loosely be described as the empirical component of logic is no more than choosing a logic that fits our purpose, when our purpose is describing how things are — Banno

Although we may have to modify the way we apply logic depending on what purpose we are employing it for, it seems to me that the most basic principles of logic, as well as the principles which can be derived from them, such as distributivity, must always remain the same. Isn't a proposition or inference which violates a basic principle (e.g. identity, non-contradiction, excluded middle) nonsensical and impossible for us to conceptualize. What purpose could a logic which deals in incomprehensible nonsense possibly serve?

Putnam is saying that the photon going through (slit A1 or slit A2) and hitting region R describes an interference experiment. That is, you don't know which slit the photon went through but, on conventional realist assumptions, it went through one slit or the other. However the photon need not hit region R if you do measure which slit it went through. Now we know this already since this is just what QM predicts. But Putnam's claim is that those two experimental observations are the left-hand-side and right-hand-side of the principle of distributivity, and so violate it. — Andrew M

I don't think this necessarily contradicts the principle of distributivity. It seems that measuring which slit the photon goes through affects the conditions of the experiment. So if you don't measure, then both ((A1 or A2) and R) and ((A1 and R) or (A2 and R)) are true. If you do measure, then both are at least potentially false because not-R can be true. Am I still missing something?


Also, here's a derivation of one side of the principle of distributivity. The principle follows from more basic logical principles, so if you reject distributivity, you must also reject at least one of the other principles used in this derivation.
1. Show (A and (B or C)) implies ((A and B) or (A and C))
2. A and (B or C) - assumed conditional derivation
3. Show (A and B) or (A and C)
4. not-((A and B) or (A and C)) - assumed indirect derivation
5. not-(A and B) and not-(A and C) - 4 De Morgan's Law
6. not-A or not-B - 5 simplification and De Morgan's Law
7. not-not-A - 2 simplification and double negation
8. not-B - 6 7 disjunctive syllogism
9. B or C - 2 right side simplification
10. C - 8 9 disjunctive syllogism
11. not-not-C - 10 double negation
12. not-A or not-C - 5 simplification and De Morgan's Law
12. not-A - 11 12 disjunctive syllogism
13. 7 and 12 contradict one another, so the indirect derivation is complete
14. Line 3 is proven, so the conditional derivation is complete

Putnam gives an example of the double-slit experiment on pp180-181. On his view, the photon goes through (slit A1 or slit A2) and hits region R, yet it is not the case that the photon (goes through slit A1 and hits region R) or (goes through slit A2 and hits region R). — Andrew M

I don't see how that's possible. "The photon goes through A1 and hits R, or the photon goes through A2 and hits R" is just a less efficient way of saying "the photon goes through A1 or A2 and hits R". Just like "you will eat eggs for breakfast and chicken for lunch, or you will eat pancakes for breakfast and chicken for lunch" is a less efficient way of saying "you will eat eggs or pancakes for breakfast and chicken for lunch". I can't conceive how an observation which violates principle of distributivity could be possible. What would that even look like? Putnam is an accomplished and respected philosopher, so I'm sure there's something I'm missing. I'll try to read the paper again at some point and hope I have better luck with it. But if you think you understand what he's saying, please try to explain.

Addendum: after glancing at the equations on pp180-181, I see that he's using probability. I don't have a good grasp of probabilistic logic, but my understanding is that it adds a number of layers of complexity and uncertainty to classical logic. I may be wrong, but I think that the principles of probabilistic logic are quite contentious among logicians. Perhaps quantum mechanics only violates ordinary principles of probabilistic logic, not classical logic.

As long as you accept that the external world is real, there is no difficulty in understanding that a moving billiard ball has kinetic energy. — Ron Cram

So it may be true that we don't see causality, but it is false to say we don't experience causality. — Janus

Have either of you heard of Malebranche? He believed that the external world was real. However, he also believed that all events in the external world were caused by God. All events in our consciousness, such as feeling the impact of tennis balls, in his view, were also caused by God. God lines up the events in the external world and the events in human consciousness so that they correspond to one another. I think Liebniz believed something similar. How would you prove that they are wrong, that it's the first ball and not God which causes the second ball to move?

Yes, we can. When we see a billiard ball moving, we can understand that the billiard ball has kinetic energy. When the first ball strikes the second ball, the first ball has less kinetic energy (it may slow or stop) and the second ball begins to roll. The second ball now has the kinetic energy. You can watch the transfer of kinetic energy as it happens. There is no question about this. And it can be confirmed by mathematics. — Ron Cram

What do you mean when you say we can observe kinetic energy being transferred? We can observe the first ball strike the second ball followed by the second ball moving. But you'd observe the same thing if you were watching an animation of pool balls. We can only observe phenomena, but not the reasons behind phenomena. Reasons are not available to our senses, only to our intellects. So I think proving that one pool ball causes the second to move would require a logical proof and not just an appeal to experience.

Take a small child to see his first pool table and the child instantly understands that one pool ball has caused the second ball to move. — Ron Cram

This is true. Humans intuitively understand events in the world as being causal. But the fact that we intuitively understand the world to be this way doesn't mean that our understanding is correct. We can observe the pool balls striking each other and then moving as a succession of events. But we can't observe the reason why this happens. So it isn't obvious that the first pool ball caused the second to move, only that the second ball moved after the first one struck it. Personally, I do believe that the first ball caused the second to move, so I'm open to the idea that it could be proved logically. I just don't think it's obvious from a philosophical point of view.

It would be fucking hypocritcal of me to do that an call you out for the bottom part... I genuinely thought that was funny... it made me smile. — thedeadidea

Then I'm sorry I didn't take your comment at face value. I guess arguing with people on the internet is making me overly defensive.

Okay lets say there are more relativist strained, (postmodernist, marxist, Rorty fans etc etc...) then what there are not. Let's assume you are a not is it fair for me to use a rehashed dumb dumb media impression of a categorical norm to assume this is your position ? — thedeadidea

No, it would not be at all fair of me or anyone else to do that.

If it is okay for philosophy to demand specificity and just shrug such nonsense right off... why wouldn't scientists, materialists and so on do it... — thedeadidea

I think that if a certain idea is prevalent in a culture, people within that culture who disagree with that idea will be eager to express their disagreement. The idea that the sciences are "better" than other academic subjects is quite common. However, you'd be right to point out that that's a crude position to take, and it's probably more common among ignorant lay people than actual scientists. But a lot of very smart people also have beliefs which (whether or not they're true) incline people who disagree with them to want to point out the limits of science. Quine, for example, thought that philosophy should strive to become an extension of the natural scientists. For another example, look at how psychology since the days of Freud and Jung has become so much more integrated into the sciences. Whether or not these are positive developments, it's easy to see how they (and many others) would lead to people pointing out the limits of science.

That is funny.... — thedeadidea

Just because I believe something doesn't I'm currently arguing for it.

I don't believe in free interpretation to the specific geography of idiots to one particular village or another is a meaningful place to start.... Such a position is either physicalism wherein they want to play a semantic distinction of existence being 'something physical' as distinct from a conscious imputation OR they are categorically a moron... I don't know what to tell you other than euphemistic generalizations are not helpful to the project of philosophy. — thedeadidea

I don't quite understand. Are you saying that I shouldn't argue based on what some idiots believe? I'm only saying that the reason I think that people like to point out the limits of science as opposed to the limits of history is that a lot of people think science can explain everything and other subjects are inferior e.g. Rick from Rick and Morty. That's all.

If you want the philosopher game conforming to Science look up basically anything by Quine. As probably one of the most influential but non-canonical philosophers... — thedeadidea

Quine is a good suggestion. How about his book Word and Object? Also, the reason I made those claims was not to present a well formed argument. I'm genuinely only looking for book recommendations. But I do want to address one point you made that stuck out to me.

I think History has certain limits I don't criticize History itself for one particular historians interpretation of it... But Science for some reason is held to a different standard.... I think it is because Science is useful in ways philosophers wish their discipline was.... But that is just me... — thedeadidea

I think the reason science is held to this different standard is that so many people, most of whom are not scientists, like to claim that nothing exists that isn't captured by the sciences. No one claims (except maybe Foucault) that scientific truths are a product of history. But many people claim that historical events and all other events as well (even subjective ones) are a product of the laws of physics and chemistry and biology. Famous scientists like Steven Hawking and Neil Degrasse Tyson have made statements to the effect that science has made philosophy obsolete, whereas no one every says the opposite. Just look at popular scientist fictional characters like Rick from Rick and Morty or Sheldon from Big Bang Theory. They're arrogant and they think anyone who doesn't understand science is an idiot. Obviously, most scientists aren't like that, but there's a reason that these characters are scientists and not art historians or linguists. And I haven't even mentioned religion. How many times have you heard the phrase "science disproves god" or something similar.

Keep in mind, my point is not that scientists are wrong to think that the scientific method is best if not the only way for humans to attain knowledge (although I do think they're wrong). I'm just trying to show why people are more eager to point out the limits of science rather than the limits of history. And I hope I'm not coming off as anti-science. I love modern medicine and airplanes, and I am fully aware that it was not philosophers who gave me these things.

I would recommend Gilbert Ryle's influential book The Concept of Mind. — Andrew M

I'll definitely put it on my list.

Produce the quote. We can take it from there. — StreetlightX

"We can never demonstrate the necessity of a cause to every new existence, without shewing at the same time the impossibility there is, that anything can ever begin to exist without some productive principle" (Treatise of Human Nature, Book1, Part 3, Section 3)

I was trying to prove him wrong on this point in the OP. You are right about epistemology vs. ontology. He is talking about what we can prove and not what exists. But I think that if we can prove something to exist, then it does exist.

Isn't causation alike? — BrianW

Agreed. Almost every event has a multitude of causes, some of which it's unlikely we're even aware of.

I think this is a case of non-overlapping magesteria. Deduction is distinct from induction. Necessity is a feature of the former but not the latter and causality is an inductive inference.

Perhaps Hume means to say that causation isn't a necessary relationship but wouldn't that be repeating the obvious, afterall isn't causality induction? — TheMadFool

I think you need induction to determine which causal relations exist and how they occur, but the fact that all events have causes is deductive.

The existence of natural law does not imply uncaused, contingent things can't exist. Adolf Grünbaum makes the case here. — Relativist

Grunbaum's argument against the principle of sufficient reason only works if we take PSR to mean that every event has an explanation that not only suffices explain it but also precludes the possibility that any other event could have occurred in its place. I think this version of PSR goes too far. We can claim that everything needs an explanation without being determinists.

But when it comes to knowing the relationship between a cause and its effect, no such logical necessity applies, as what we really observe is only the habitual or recurring conjunction of cause and effect. We customarily call that 'causal' but it doesn't have the same binding necessity as deductive proofs. So how can we claim to know that there is such a relationship? That is his challenge. — Wayfarer

It's true that we don't perceive causal necessitation directly through our senses. But if we observe that various types of events are constantly conjoined, can't we use a priori mathematical and modal concepts to demonstrate that it is extremely improbable that these constant conjunctions occur by random chance?

Kant thought that causation was an a priori concept through which all sensuous experience had to be filtered. I think he believed that without the concept of cause, we'd be unable to perceive time, as there would be no order to its moments. For instance, you wouldn't be able to process a basic phenomena like walking if you didn't understand that each step caused you to move forward and your position one second ago was therefore ahead of your position two seconds ago. Thus, by his logic, the only reason we understand the world as ordered by causality is that if we didn't, intelligible experience would be impossible. But I think the causal order we observe goes above and beyond what would be necessary just to allow us to differentiate between moments in time. We've discovered highly intricate principles of cause and effect both at the microscopic and macroscopic level. These principles aren't prerequisites of experience. We've been experiencing things for thousands of years without knowing about microbiology or general relativity. So why are we capable of making scientific discoveries and using them to great effect (e.g. modern technology)? To me, it seems like the best answer is that causal relations we infer into our observations actually exist in reality.

Correct me if I'm wrong but I don't believe Hume said that it was possible that events can be uncaused. — StreetlightX

I'm pretty sure you are wrong, although most of what you said is correct. You're right that Hume's main point was to show that we cannot establish that necessary causal relations exist. But in order to make this point, he argued that there's no reason to believe that events couldn't occur without causes.

Which is, to your point, a conflation of ontology with epistemology. — Maw

Yes, Hume was trying to show that we can't have knowledge of causes. But if he's correct, then it follows that causes don't necessarily exist in reality, at least as far as we know.

If no one has ever observed causation, then what is it that we're missing? What would proof of causation look like? — Harry Hindu

I'm not denying that causation is real. But I do think it's difficult to observe it directly. Even when we participate in it by making decisions, we can't always trace those decisions back to their ultimate causal source.

Also, are you saying that all existing things have causal power (perhaps even necessarily), or are you saying that causal powers are the only real properties existing things have? I agree with the former point, but not the latter.

Because what does not make logical sense to you may not be so illusive to others. If I could put a banner at the top of this site it would be "Your incredulity is not an argument". — Isaac

In most of your arguments, it seems like you're trying to push the entire burden of proof onto me. I guess that's fair, since I'm the one making claims about the way the universe necessarily has to be. But if you're just gonna be a complete skeptic, then I can't think of any rational argument to convince you to change your mind. It seems like you're saying "maybe the universe is fundamentally inconceivable, so therefore there's no point in trying to use reason to understand it." If you're right, then I can't use reason to prove you wrong. Maybe reason is just a useful tool for building rocket-ships and laptops. I can't imagine how reason could be so useful without being capable of deducing authentic truths about reality. But maybe the only reason I can't imagine that is that I'm relying on my faulty powers of reasoning. So all I can think to do at this point is make an emotional appeal. Don't you want to understand the world you live in? The only reason that reason is such a useful tool is that we presume that it communicates truth about the way things really are. If we just treat it like an arbitrary construct of human subjectivity, then I suspect it will behave like one. Newton and Einstein didn't make their great discoveries because they thought they were merely using a tool. They believed themselves to be uncovering the secrets of existence.

But perhaps I'm misinterpreting you, and you're no really a skeptic and or pragmatist.

Assuming an external law wouldn't move us closer to an explanation. It would just raise the question of why there happens to be one particular law in effect rather than another. — Andrew M

I agree. And unless you think that there's an infinite regress of laws, you have to eventually ask why law A is in effect rather than law B or C. And regardless of what your answer is, I don't think you can attribute it to physical objects or their features. Laws are unchanging and exert control over all activity throughout the entire universe, whereas physical objects and their features change and they are limited to particular regions of space time.

It is stupid. Again, I have to ask, do you have any idea about the context and the history of the phrase? Any idea at all? If you don't then the obvious thing would be to find out before attempting to philosophize. Post the question in Questions if you don't know how to use Google. — SophistiCat

Maybe it was misleading of me to use the phrase from the Declaration of Independence. I wasn't trying to start a historical discussion about the intentions of the Founding Fathers and their use of language. I was interested in whether we should view people as equals, specifically with regard to their inherent value.

And you seem to be confusing the terms all people, individuals, and people, and ignoring the term "fundamental." And then you're opposing a belief against a proposition. When it comes to beliefs and feelings, there is no accounting for either, and you get to have either in any way you want. But do you act on the basis of them? To date if yes, it would seem just ignorance on your part, your actions based on your feelings and beliefs, a state of innocence. But now you're been told, so your innocence is disappearing faster than an ice cube in hot tea on a hot day. I do not really flatter myself or this site that this is the first you've ever heard of the fundamental equality of people, so I doubt you're very innocent. But this is serious business. If you have wrong beliefs you now know and likely have known that they're wrong. Act on them and indeed it is immoral, and maybe also whatever your action(s) are, are illegal. — tim wood

Yes, we are all equal in that we're people, in that we're made of atoms, and in that we're located on the planet earth. We are equal in that (to put it Platonically) we participate in many of the same universals. But we're never equal with regard to particulars. Each of our particular features is unique. But uniqueness is not necessarily a good thing. We might be uniquely bad in some respects. We might be bad in most respects. And I don't see how a person who's bad in most respects can be seen as equal in any meaningful sense to a person who's good in most respects.

...

But what does it mean that we should be equal?

Are you suggesting that we genetically engineer all humans to be equally attractive with equal IQs? What about the inequality of value that arises from the fact that some humans are just morally superior to others? Should we try to genetically engineer all people to be equally morally principled? Is that even possible? If it is possible, it sounds terrifying.

Or are you saying that even though we should be equal (in some ideal world, perhaps), we also shouldn't pursue total equality as a goal?

Or are you only referring to particular kinds of inequalities?

For example, the fundamental equality of all persons is established. It is therefore wrong to prejudiciously discriminate against persons or groups of persons. — tim wood

How can you prove a statement like that? I don't believe that all people are equal in any way. Is that immoral?

That you see logic as a law without which the universe seems absurd, tells us about you, your beliefs and your limits of sense. It doesn't say anything about the universe. That you think you can imagine a universe without gravity tells us about your imagination (or your confidence in it), not the universe. — Isaac

A universe that disobeys logic is absurd by definition. It would be circular reasoning to try to use logic to prove itself, and I don't have any other way to prove that it's valid. But if we can't use logic to decide what can and can't be true about the universe, then we can't use anything. Empirical observations are only useful because we can pair them with logic in order to draw conclusions. So what's the point in saying that universe might not actually make any logical sense? I guess it's good to be humble, but I think we need to assume that it makes logical sense if we're going to seek knowledge.

No. That's exactly the question of the thread. Why would you presume something must be governed externally in order to not be random. Have you seen Lagton's Ant? — Isaac

If something happens over and over again in the exact same way, I assume there's a reason for it. And if something happens for a reason, it's not random. If something happens for no reason, it is random. And the ant is governed by laws. They're in his programming. He is determined to move in a certain way, and being determined is the opposite of being random. I take random, undetermined and for no reason to all be synonymous. Whether laws have to be external is a separate issue.

We don't know in advance how we would expect objects of mass to behave, so we can make no probabilistic statements whatsoever about the fact that they all act the way gravity describes. — Isaac

If there is any consistent pattern in the behavior of objects of mass, then I think it's safe to assume that those patterns did not just show up coincidentally. Objects of mass will probably continue to behave as we've observed them to behave in the past, and there's probably a reason for that. Do you even disagree? If you don't think that gravity is a result of an external law, then what is it a result of? A lot of people here seem to think it's the result of the inherent properties of objects of mass.

No. Coin flips appear random because we don't have the data to determine their path. If we did, their resting face would be entirely predictable. — Isaac

I don't think we disagree on this point. Perhaps the statement I made that you were responding to was unclear.

No. A state of affairs is not "relations between abstract entities." Abstract entities do not exist (that would be inconsistent with physicalism). Abstractions are just tools of the mind, they do not actually exist. — Relativist

The very phrase "state of affairs" seems to imply that there are multiple affairs in a single state. I'm not claiming that particulars, properties and relations can exist independently. But in order to explain what a state of affairs is, don't you need to appeal to the existence of its abstract constituents? Just because the abstractions are codependent doesn't mean they don't exist. And I don't think it would be helpful to define existence as being exclusive to things which can (hypothetically) exist independently. Because independent SOAs consist of their codependent parts and therefore depend on them.

I can't think of any effect that isn't also a cause. The effect exists and therefore is capable of forming new causal relationships. Everything that exists has the potential to interact causally. — Harry Hindu

My main problem the idea that existence is causal power is that causal power can't be observed. So different philosophers have different approaches to explaining what it is and how it works. For instance, some think causal power resides in particular entities, whereas others (including Russel, I think) believe it comes from universal laws which govern the behavior of entities.

But I think we can directly observe that things exist. For instance, if I hear a noise, I can conclude that the noise exists. I don't need to know what causal power is behind the noise appearing in my experience.

The fundamental thing to keep in mind is that (according to Armstrong), everything that exists is a state of affairs (a particular with its properties and relations). The properties and relations do not exist independent of the state of affairs in which they are instantiated. We can still think abstractly about properties and relations (through the "way of abstraction"), but these are just mental exercises. — Relativist

Interesting, and good to know. But if Armstrong takes the most basic objects in the universe to be states of affairs, then I don't see how he can call himself a physicalist in the traditional sense. States of affairs, as I understand them, consist of relations between abstract ideas like properties and particulars. These are not objects we can empirically observe. They are concepts by which we make sense of our observations.

Sure. But every refusal you make, means you choose something over the refused object.
So every time you refuse to believe something, you also choose to believe something else.
You don't refuse without a choice; so you have some responsibility in the matter. — Shamshir

I think choice plays a role in our more complex and uncertain beliefs. But if a belief just seems obvious to us (e.g. the world is round), how can we choose to reject it?

Speech can't be causal as in physical forcing anyone to do anything. — Terrapin Station

Not directly. But there's definitely some truth in the saying that the pen has more power than the sword. The Crusades were inspired partly by Christian preaching. Revolutions are usually inspired by political dissidents. Darth Sideous used language to turn Anakin to the dark side. So language can definitely have disastrous consequences.

What exists is what causal power. Fairies exist as ideas and ideas have causal power. Square trianges are impossible to even imagine and therefore only exist as a string of visual symbols, or words. Contradictions are ideas that exist and have causal power too. — Harry Hindu

So is existence a property with the same definition as causal power? And does causal power mean the potential to cause events or actual interaction in causal phenomena? If an effect is caused but is not itself capable of causing anything, does that effect exist? If it doesn't, then how do you deal with the problem on non-existent entities?

Even if I am publicly advocating for violence in a compelling and charismatic way that causes people to commit terrorist attacks?