The laws of thought are three:
1. The law of non-contradiction (LNC), which states that the statements p and not-p cannot both be true. In symbolic notation: ~ (p • ~p)
2. The law of identity, which says that everything is identical with itself. In symbolic notation, a = a
3. The law of excluded middle (LEM), which states that either p or not-p is true. In symbolic notation: p V ~p
As philosophers often point out, the laws can be stated either in logical terms (i.e. in terms of propositions and their logical relationships) or in ontological terms (i.e. in terms of the things that propositions are about and their metaphysical relationships). But the difference is irrelevant to the points I will be making, so I’ll ignore it for present purposes.
The reason these are characterized as laws of thought is that reason, it is claimed, would not be possible at all if they were not true. They are first principles of rationality in the sense that they are so basic to it that they are more obviously correct than any argument that could be given either for or against them. Hence, it is claimed, even someone who claims to have reason to doubt or deny any of them must implicitly presuppose them in the very effort to question them.
Take LNC, which is commonly taken to be the most fundamental of the laws. The traditional defense against would-be skeptics is that it simply cannot coherently be denied. As Aristotle points out in the Metaphysics, to assert anything at all is to put it forward as true, and therefore not false. But that includes the skeptic’s own statement that LNC is false. In making this assertion, the skeptic is claiming that it is true, and therefore not false, that LNC is false. If he weren’t, there’d be no disagreement between him and the defender of LNC. But this itself presupposes LNC, so that the assertion is self-undermining.
Note that it misses the point to allege that the defender is begging the question by presupposing what is at issue. For the point isn’t that the defender is presupposing what is at issue. The point is that the critic himself is presupposing what is at issue. It isn’t that the critic can coherently deny LNC even though the defender affirms it. It is rather than the critic himself, no less than the defender, cannot avoid commitment to LNC.
Another way to see the incoherence of denying LNC is via the principle that from a contradiction, anything follows. Here’s a common way to explain how. Suppose that LNC is false, so that two propositions p and ~p are both true. Then, by the rule of addition in propositional logic, we can infer from p that either p or q (i.e. p V q), where q can be any proposition at all (including the proposition that the denial of LNC is false). By the rule of disjunctive syllogism, p V q and ~p will then together give us q. Hence, from the denial of LNC, you can derive the falsity of the denial of LNC. You will thereby have shown that the skeptic can be refuted from his own premise. Again, skepticism about LNC is incoherent.
Things are a bit trickier with LEM, and there are also technical arguments by which some have nevertheless tried to challenge LNC. I’m not going to get into all of that here. Having given a sense of the traditional approach to defending the laws of thought, I’ll focus just on the objections from quantum mechanics, specifically.
Consider the wave-particle duality phenomena exhibited in the famous double-slit experiment. The same particles, the experiment shows, behave in both a wave-like manner and a particle-like manner. But doesn’t this violate LNC? In particular, doesn’t it show that something can be both a particle and at the same time a non-particle (because it’s also a wave)? Or doesn’t it violate LEM, insofar as it shows that it is not true that something is either a particle or not a particle? Or consider the famous thought experiment involving Schrödinger’s cat. Doesn’t it violate LNC insofar as it shows that a cat can be both alive and dead at the same time? Or doesn’t it violate LEM insofar as it implies that it is false to maintain that either the cat is alive or it is not alive?
Thus, it is claimed, modern physics shows that we need to revise classical logic, insofar as quantum mechanics has refuted these laws of thought. Mind-blowing!
Well, not so fast. The first point to make in response is that, here as in other contexts, people speak quite sloppily when they assert that “Quantum mechanics shows that...” As philosopher of physics Peter Lewis notes in his book Quantum Ontology, when discussing quantum mechanics and its implications, we need to distinguish between (1) quantum phenomena, (2) quantum theory, and (3) alternative possible interpretations of quantum theory. The phenomena observed in the two-slit experiment would be an example of quantum phenomena. The mathematical representation of the physical systems central to quantum phenomena together with the laws said to govern those systems and the way their states are measured comprise quantum theory. And Bohr’s Copenhagen interpretation, Bohm’s pilot wave interpretation, Everett’s many worlds interpretation, etc. would be alternative possible interpretations of quantum theory and quantum phenomena.
Now, if we’re talking about what quantum mechanics can actually be said to have shown, that is confined to categories (1) and (2). We know that there are these odd phenomena, and the mathematical representation quantum theory gives us is the best description we have of the systems associated with those phenomena. But the breathless pop philosophy claims made in the name of quantum mechanics typically appeal instead to ideas in category (3) – all of which are controversial at best. None of them can be said to have been shown, or proved, or established by physics.
That includes claims to the effect that quantum mechanics has refuted the laws of thought. It has done no such thing. There is nothing in either quantum phenomena or quantum theory that entails that. Rather, what has happened is that some people have proposed interpreting quantum phenomena and quantum theory in a way that gives up one or more of the laws of thought. That’s all. And even then, the interpretation is not a purely “scientific” interpretation of quantum mechanics, because none of the competing interpretations in category (3) is purely scientific. All of them involve bringing certain philosophical assumptions to bear on the interpretation of quantum mechanics. (For example, Bohr’s interpretation famously takes for granted an instrumentalist philosophy of science.)
The upshot of this is that revisions to the laws of thought can be read out of quantum mechanics only if they are first read into it. And thus quantum mechanics itself does nothing at all to establish the plausibility of such a revision. For any proposed interpretation in category (3), we need to ask: What philosophical assumptions are independently known to be the most plausible, and thus suitable to guide us in deciding how to interpret quantum mechanics? The traditional metaphysician would answer that the laws of thought are among these assumptions. Those who would reject one or more of these laws would disagree, but the point is that they cannot appeal to quantum mechanics as a reason for doing so without begging the question. Hence arguments from quantum mechanics for rejecting the laws of thought are ultimately circular.
To address the specific examples cited, consider first Schrödinger’s famous thought experiment. The first thing to say is that it is only a thought experiment, intended to call attention to some puzzling questions raised by the notion of a quantum superposition. That’s it. Anyone who says “Quantum mechanics shows that a cat can be alive and dead at the same time!” doesn’t know what he’s talking about. You could try to argue that the cat would be both alive and dead at the same time. Or you could try to argue that it would be neither alive nor dead. But you could instead, with no less justification (indeed, I would say with far greater justification), argue that neither of these interpretations makes any sense. And that is exactly what the traditional metaphysician argues, on the grounds that LNC and LEM cannot coherently be denied. Absolutely nothing in “the science” itself shows otherwise.
Same with the two-slit experiment. What we can say with confidence is simply that there are some weird phenomena here. But how to interpret them is another story. Yes, there is something here that in some respects behaves in a wavelike way and in other respects in a particle-like way. But by no means does that entail that it is, say, both a particle and not a particle at the same time, or that it is neither a particle nor a non-particle. Here too, you could try to make the case that we should interpret what is going on in a way that rejects either LNC or LEM. But you could with no less justification (indeed, I would say with far greater justification) hold instead that any such oddball interpretation is just a non-starter. And once again, “the science” itself gives no reason whatsoever to doubt the soundness of this traditional metaphysical judgment. (I discuss the philosophy of quantum mechanics in more detail in chapter 5 of Aristotle’s Revenge.)
Koons on Aristotle and quantum mechanics
Schrödinger, Democritus, and the paradox of materialism
Color holds and quantum theory
Causality and radioactive decay
Another way to see the incoherence of denying LNC is via the principle that from a contradiction, anything follows.ReplyDelete
For someone who claims that LNC does not hold, presumably (if he is at least trying), he would be PERFECTLY FINE with "anything follows". That is, once someone has been willing to assert that LNC does not hold, he should be willing to accept that "LNC holds" and "LNC does not hold" are both true at the same time. This is, in fact, the very meaning of denying LNC. But of course, he isn't willing to say that. Which is (of course) incoherent.
Then, by the rule of addition in propositional logic, ...
If (by supposition) LNC does not hold, there is no particular reason to allow that the rule of addition in propositional logic holds, either. One might think that assuming the rule of addition holds is just carrying in LNC by the backdoor. In reality, one cannot THINK coherently while denying LNC, so it is not particularly worthwhile to "show" that denying LNC results in some other absurdity: denying LNC is itself as absurd as any other absurdity that "follows".
denying LNC is itself as absurd as any other absurdity that "follows".Delete
and yet, is it not (equally) absurd to claim that anything (in particular) follows from the denial of LNC? (and why shouldn't the denier willingly accept that "LNC holds" and "LNC does not hold"? his intelligent denial will just be rooted in the claim that context is everything, and this fact/claim is borne out by an unwavering commitment/advertence to Quinean indeterminacy of translation.)
I would go further and say that rejecting LNC is not only absurd but unintelligible. The phrase "x is not a" becomes meaningless gibberish if x is also a. At best, such statements can be vacuous placeholders in a boutique non-standard logic. I think this is even stronger than LNC being a precondition for coherent thought, because what we'd be trying to accept (a true contradiction) isn't even something that can be articulated properly.Delete
"once someone has been willing to assert that LNC does not hold, he should be willing to accept that "LNC holds" and "LNC does not hold" are both true at the same time."Delete
I'm sorry, what? What would that even mean exactly? If you're saying that someone can at times hold that LNC is true but also acknowledge when there are exceptions than I suppose that's one thing (absurd as it is). All you're saying is that LNC is sometimes true and at other times not true. But if on the contrary someone suggests that it is both true and false at the same time and in the same sense then we're left wth absolute absurdity. Really, if you were take that to its logical conclusion you'd have to deny having any knowledge whatsoever, even the fact of one's own existence, on the basis that, given contradictions could be true, it could be said that despite your belief in your own existence, you could still not exist because after all contradictions could be true. Just because belief seems to negate the possibility of your non-existence doesn't mean you actually exist, because given LNC is both true and not true (again, whatever that even means) the evidence could irrefutably point one direction while reality is simultaneously in the opposite (or in both states, or only in one. How could you know). In the end, how could we say we know one way or the other if the very foundation of knowledge is evidence and when the necessary correlation between evidence and reality is severed by rejecting the absolute primacy of LNC? What principle of reason could be prior to it?
@ SomeGuy: Exactly: speech and thought break down as being senseless if you deny LNC. It's not only that you can no longer communicate well, you can no longer even THINK well. You tie up in knots of absurdity that defy all meaning.Delete
and this fact/claim is borne out by an unwavering commitment/advertence toDelete
David, without LNC, the "unwavering" commitment can be equated to wavering that turns direction at every moment. "Indeterminacy" will become complete gibberish that is profoundly meaningless even to the individual who utters the words, much less to someone else. See Professors Frost and Withers at N.I.C.E.
I don’t really see that these areas of logic apply here, even in your category 3. If for example we assume one of the relational interpretations (RQM or QBISM), then there is a sense in which there are no physical properties at all ‘outside’ of an entanglement, or more specifically, outside an entanglement that shares information (eg. a measurement). So in this case, you could say that all physical properties are ultimately a relational representation. What is it that is being represented? Someone like Rovelli would say that there is nothing, everything is purely relational. I would argue that there is something more fundamental ‘underneath’, a substructure in which the ‘wholes’ of corporeal reality exist. The underlying forms unfold towards other forms as representation, which gives reality it’s consistent nature at a macro level.ReplyDelete
However it doesn’t really matter which view you take, because the physical properties (the particle) are like an image of a process, and maybe of something deeper. Before the image is taken, it’s only a potential image. You can’t say it violates LNC any more than you could take a photo of Elvis, and say that Elvis is therefore both a person and a photo.
Or am I missing something?
I read this a couple times and I still don't understand what you are saying.
This is and example:
"The underlying forms unfold towards other forms as representation, which gives reality it’s consistent nature at a macro level."
Then you say that "the physical properties (the particle) are like an image of a process"
Are you saying the physical properties of a particle just are "the particle"? Or both are either are an image (particle detectors take pictures?) of a process (aren't processes actions that things undergo?).
Regarding Elvis. Some people have the impression that QM implies that Elvis does not exist until someone takes his picture.
@bmiller: “ Are you saying the physical properties of a particle just are "the particle"? Or both are either are an image (particle detectors take pictures?) of a process (aren't processes actions that things undergo?).”Delete
The physical properties we associate with the particle are only ever seen as part of an observation or measurement, There is no reason to think that photons are little balls flying through space. It’s only when the wave interacts with an electron in an atom (whether a detector or the absorbing material in the photoelectric effect) that the ‘discrete particle’ properties appear. The electron itself is of course a wave, in this case constrained by it’s position in the atom (and by mass) . There are no local, physical properties of a photon except in these interactions. The wave function is always spread out across space, with certain constraints that determine the probability it will interact at any particular opportunity.
It may help (or not!) to consider that from the perspective of the photon, there is no space or time. Light does however have entanglements in space and time, and the only time these entanglements result in any physical signs is a specific type of entanglement that we call a measurement, or what is sometimes called the ‘collapse of the wave function’. In some ways you could say that it’s mass and time and space that are the really weird things, but of course we tend to start from the position that these are the obvious things we take for granted.
“Regarding Elvis. Some people have the impression that QM implies that Elvis does not exist until someone takes his picture.”
Yes and this is the natural conclusion if your ontology is that physical properties are the foundation of reality, aka materialism. If you only have the ontological horizontal, then the foundations of local reality tend to fall apart with QM. You’ve reduced the wholeness of being to it’s parts, and then those parts don’t really have any stand-alone substance. You get desperate attempts to save it such as inventing trillions of new universes every millisecond, but few step back and look at the big picture that has a hierarchy of whole things, and other aspects of a vertical ontology such as free will.
"There are no local, physical properties of a photon except in these interactions."Delete
Rather: Our discrete measurements of local physical properties of a photon depend on these interactions.
"The wave function is always spread out across space, with certain constraints that determine the probability it will interact at any particular opportunity."
Rather: The wave function is conceptual, non-spatial, and describes a probabilistic distribution across space...
"It may help (or not!) to consider that from the perspective of the photon, there is no space or time."
I would suggest rather: It may help to consider that from the perspective of the photon, there is no perspective of the photon.
Rather: The wave function is conceptual, non-spatial, and describes a probabilistic distribution across space...Delete
“Rather: Our discrete measurements of local physical properties of a photon depend on these interactions.”Delete
Instead: We have no evidence that physical properties exist beyond these interactions. Whatever causes the physical properties observed is non local, and all the physical properties are in superposition up to that point, and are therefore only potential properties.
“Rather: The wave function is conceptual, non-spatial, and describes a probabilistic distribution across space...”
Instead: The epistemic and ontic nature of the wave function is a mystery. Whatever it describes is a critical aspect of the infolding of the very real seeming world we inhabit.
“I would suggest rather: It may help to consider that from the perspective of the photon, there is no perspective of the photon.”
Instead: We gave good reason to believe that time and space are emergent phenomena. We know very little at all about the more fundamental substrate from which they emerge.
Indeed, in the double-slit experiments, a quantum entity (eg an electron) exists as a particle under certain conditions (eg when there is a detector to detect which slit the quantum entity passes through) and exists as a wave under different conditions. The quantum entity does not exists both as a particle and a non-particle under the same set of conditions at the same time.ReplyDelete
johannes y k hui
johannes y k hui,Delete
Are you saying you have been taught that a single electron will be detected as coming through a single slit when there is a detector at one slit but if you put detectors at both slits then you will detect it at both slits?
Wouldn't that violate conservation of momentum in that one electron would have double the momentum of a single electron depending where you measure it?
No, I wasn’t saying (or implying) what you said. - johannes y k huiDelete
johannes y k hui,Delete
Thanks for the clarification.
My favorite interpretation of quantum mechanics is "Shut up and calculate!"ReplyDelete
Schrödinger’s Cat works chiefly as a reductio ad absurdum of the naively narrow interpretation of what it means to be an ‘observer’ in the quantum-theory sense. Unfortunately, it is generally cited by people who hold the very interpretation that it discredits; and being unable to see that it is discredited, they base all their further thoughts on this subject upon the same falsehood.ReplyDelete
Look: At the level of elementary particles, human beings do not observe quantum phenomena. In the thought experiment, the cat is killed by an apparatus that goes off when a Geiger counter detects the decay of an atom. As Bohr pointed out, the Geiger counter itself is the observer of the quantum event, and everything after that point is accounted for by plain old classical mechanics. None of the events on the macro scale are dependent upon single quantum-scale interactions. You could just as well set up the apparatus to kill the cat when a human being throws a switch, and it would make no difference in the operation either of the apparatus or of the cat. Similarly, you could rig a sensor circuit that would show immediately when the Geiger counter sends its signal, and so anticipate with certainty (by a fraction of a second) what is going to happen to the cat.
The idea that a human observer is required to collapse a waveform, in fact, is nothing more than a silly bit of anthropocentrism.
Hey, Dr. Feser. I have seen some people say something like this: the LNC holds, but not everywhere and at all times. And they usually point to some kind of pseudo-mystical, esoteric thing. So it does no good to say that they are presupposing the LNC to disprove LNC, because they do in believe in the LNC, just not absolutelyReplyDelete
Since they commit to the LNC, they are obligated to demonstrate valid exceptions to it. As Feser has shown, the appeal to QM doesn't work. So, where in the universe is the exception and why?
The force of Schrödinger's cat is this: we accept that a particle is in a superposition of two spin states, and we accept that the cat's life, by means of a detector and Geiger counter, is causally connected to the article's superimposed state. That means that the scholar must choose one of the following:ReplyDelete
1. Superposition isn't truly superposition: there's a local hidden parameter that determines whether the particle is spin up or spin down. But local hidden parameters are ruled out by many experiments.
2. Causal connection between the microscopic world and the macroscopic world breaks down. But there is no evidence that QM stops working past a certain scale.
3. The superposition of the particle's spin state transfers to the life of the cat. But there's no way to give a coherent, macroscopic interpretation of this.
Which option does the scholar pick? It's basically the "Liar, Lunatic, Lord" trilemma of C.S. Lewis, but applied to physics.
Have you taken a Modern Physics course at the College level?
Could be none of the above.Delete
It could be that the cat is either alive or is dead but we don't know.
Just like we don't know if and when you will respond to this response.
"It could be that the cat is either alive or is dead but we don't know." <- This is Option #1. It's an assertion that superposition isn't really superposition. You didn't understand my comment.Delete
Trouble is, we do not ‘accept that the cat’s life is causally connected to the particle’s superimposed state’. At any given moment the cat, which is not in any meaningful way a quantum phenomenon, is either alive or dead. If we don’t observe the Geiger counter and don’t look in the box, we don’t know which it is – but that is true of any experiment where we don’t observe the outcome, and has nothing to do with quantum mechanics.Delete
Which brings us back to this: The actual ‘observer’ of the quantum event is the Geiger counter, and whatever Rube Goldberg contraption you rig up to be activated by that observation is not relevant to quantum theory. I reiterate that human beings do not themselves observe quantum events; they only observe instruments which are designed to detect such events. The events are known to occur whether an instrument measures them or not. Nuclear fusion, for instance, consists of an enormous number of quantum events taking place (typically) in the core of a star. No human or manmade instrument has ever directly observed such an event, but we know, by the fact that stars shine and exhibit the properties observed by astronomers, that the events are taking place. And they are taking place in our absence. If you look at a remote galaxy, you are seeing light generated by quantum events that occurred long before there was any human being to see them. And you would be very silly indeed to suppose that those galaxies exist only because a human astronomer came along and pointed his telescope at them to cause the waveforms to collapse.
At any given moment the cat, which is not in any meaningful way a quantum phenomenonDelete
This statement, according to physicists, is like saying that a cat is not in any meaningful way an atomic phenomenon. If you accept atomic theory, then you accept that everything made up of atoms--including cats--obeys the laws of atoms and the periodic table.
And you would be very silly indeed to suppose that those galaxies exist only because a human astronomer came along and pointed his telescope at them to cause the waveforms to collapse.
This was Einstein's retort to Niels Bohr: "Do you really believe that the Moon disappears when you're not looking at it?" during his famous series of debates with Niels Bohr. But it did not save Einstein and it will not save you!
Classic physics are used for almost all cases in everyday life where we are concerned about physics. It's only when things are very small (on the order of 1nm) or moving very fast (approaching the speed of light) where we have to take into account QM (in the first case) and relativity (in the second case) or both when small things are moving very fast.Delete
Cats in boxes are not quantum phenomenon as Tom says.
Cat’s are not quantum phenomena only because of the high number of interactions with the wider world. These cause the superposition of the experiment to be very quickly lost as the state of the cat becomes actual to it’s wider environment. In Einstein’s terms, you could say that God has chosen, and so it is.Delete
Of course it’s just a thought experiment, but if you want to use the thought experiment more effectively, consider the “Wigners friend” version of it…
Here is the link to Wigner's friend from Wikipedia and his final conclusion:
According to physicist Leslie Ballentine, by 1987 Wigner had decided that consciousness does not cause a physical collapse of the wavefunction, although he still believed that his chain of inferences leading up to that conclusion were correct. As Ballentine recounts, Wigner regarded his 1961 argument as a reductio ad absurdum, indicating that the postulates of quantum mechanics need to be revised in some way.
So it seems that he thought that he had followed quantum theory to it's logical conclusion and found that it didn't make sense, at least as far as consciousness being involved was part of it.
Hi Bmiller. I wasn’t referring to Wigner’s ideas about consciousness. I don’t think consciousness is required, only corporeal entities (or agents as QBISM calls them). I was referring to the recent experiments of Wigners friends that seem to show that different observers witness different realities. For one the cat is alive, for the other the cat is dead.Delete
"Classic physics are used for almost all cases in everyday life where we are concerned about physics. It's only when things are very small (on the order of 1nm) or moving very fast (approaching the speed of light) where we have to take into account QM (in the first case) and relativity (in the second case) or both when small things are moving very fast."
I do not think you are claiming otherwise, but for the record QM is a universal theory; and there do exist macroscopic quantum phenomena -- superconductivity, Bose-Einstein condensates, etc.
Perhaps the Schrödinger's cat should by default be alive (instead of being dead or alive at the same time) until the POTENTIALITY of the relevant decay of the atom became actualised, since that cat was an alive cat in the first place.ReplyDelete
johannes y k hui
As I understand matters, a pile of lumber is in potency toward many states. It could actualize as a house, a scaffold, a grandstand, et al. Or it could remain a pile of lumber. When the builder ['observer'] decides on a design, these potentials 'collapse' into a single 'actual potential.'Delete
Potentiality is a poor man's counterfactual definiteness.Delete
The logic that underpins quantum physics is consistent with Aristotle's principles, specifically, the principle of non-contradiction as well as the principle of the excluded middle.ReplyDelete
In physics, the application of the first principle is always satisfied as it states that, when a system evolves from one state to another, it gains new properties which were just potential, while it loses others simultaneously (this is what motion is all about, not the poetic license of a “flow” of time and space but, much simply, just a change of state of the considered physical system).
The application of the second Aristotelian principle in physics asserts that for every physical property, there is an opposing property.
The use of orthonormal Hilbert spaces in quantum physics mathematically represents these Aristotelian physical properties.
An article by D. Aerts in 1993 effectively illustrates these framework structures, and even provides an example of a macroscopic quantum structure that is based on non-Boolean logic and isomorphic to the logical framework of spin 1/2 physics.
Notably, it was D. Aerts himself who in 1981, in his doctoral dissertation "The One and the Many," rigorously demonstrated the formal contradiction between stating (a) a system is divided into two subsystems and (b) the properties of that system correspond perfectly with pure quantum states (for the specialists in quantum logic, this is because the logical relationship called weak modularity, which is always valid in a Hilbert space, is not valid in a system composed of two separated subsystems).
This elegantly resolves the intrinsic contradiction in the formulation of the famous cat paradox (or pseudo-paradox E.P.R.).
In order to help clarify this discussion about quantum mechanics, I would like to stress the fact that in physics, when we consider an equation of motion, we explicitly describe the value of a measurement, M, if it were to occur at a specific space and time measurement (x,t). Mathematically, this is represented as M(x,t). However, it's important to note that a priori, M(x,t) is not a property of the measured system, but rather a property of the measuring tool. If the system is out of the spatial and temporal range of the measuring tool, there would be no result at all.ReplyDelete
In Newtonian physics, it is postulated that M(x,t) is a property of the measured system, independently of the measuring tool. However, this goes against our common sense, Aristotelian physics, and quantum physics.
In reality, M(x,t) encompasses the notions of actuality, potentiality, and contextuality. Interpreting it as a simple description of the actuality of the system to be measured is a simplification of its true meaning and can only be justified for relatively gross engineering purposes. A physical system's form, its "whatness," includes its actuality (i.e. what can be measured in the here and now of the instrument of measure), its potentiality (which, by definition, is not measurable by any instrument as it is not in any (x,t), but needs a motion that would cause it to become actual and then measurable), and its contextuality (which is the relationship of the said system with the whole measurement environment). M(x,t) expresses all of this.
A quantum wave of probability P(x,t) is not the property of the considered physical system, but rather a description of the probability of getting a specific result by a contextual measurement instrument operating in principle in its (x,t).
As a result, the famous wave packet reduction, is simply the result of the physical system interacting with the measurement instrument in its (x,t) and does not require any consciousness to happen.
"...As a result, the famous wave packet reduction, is simply the result of the physical system interacting with the measurement instrument in its (x,t) and does not require any consciousness to happen..."Delete
You miss the entire gist of quantum mechanics. The wave function is the agents best guess (in terms of probabilities) about what the experimental results will be. The "collapse" occurs when the agent becomes aware of the result.
"...A measurement does not, as the term unfortunately suggests, reveal a pre-existing state of affairs. It is an action on the world by an agent that results in the creation of an outcome— a new experience for that agent..."
An Introduction to QBism with an Application to the Locality of Quantum Mechanics
Christopher A. Fuchs, N. David Mermin, Ruediger Schack
"In Newtonian physics, it is postulated that M(x,t) is a property of the measured system, independently of the measuring tool. However, this goes against our common sense, Aristotelian physics, and quantum physics."Delete
Interesting. So this would be an instance of the principle that whatever is received is received according to the mode of the receiver. (Also, whatever is conceived is conceived according to the mode of the conceiver.) But the question seems to be not so much about the independence of the measurement from the measuring tool (that would be nonsense), but the independence of that which is measured (received, conceived) from the measuring tool. (Compare: we know reality by means of real concepts, but concepts are not the (primary) object of our knowledge.)
On your hand, you missed the point I explained in my post on January 28th at 11:39 PM, namely that it has been rigorously demonstrated, already since 1981 by D.Aerts, that there is a formal contradiction between stating (a) a system is divided into two subsystems and (b) the properties of that system correspond perfectly with pure quantum states. To make that point even more understandable for people with little knowledge of quantum mechanics, if you have a quantum system hitting a cat, the quantum system and the cat together are NOT a quantum system. This means that wondering if the cat is both (or neither) dead and alive is a nonsensical question: the cat does not become "quantic", period. This has nothing to do with a consciousness, which would open the box. By the time the quantum state has hit the cat, it has reduced its wave of potentiality to only one pure state, hence killing or not killing the cat, regardless of whether the box has been opened or not. I hope this helps.
"The independence of that which is measured (received, conceived) from the measuring tool": you are completely correct, this is what Newtonian physics posits as an axiom. This is what determinism actually is: a system is defined in and of itself independently from whether it is measured or not. It is a very engineering-oriented approach, where things are built up with pre-existing elements. This Newtonian approach to experience is meaningful if we limit our measurements to realities that are already in act, i.e., in existence. As soon as we consider potentialities, this assumption becomes too stringent and has been falsified by quantum mechanics in the same way it is falsified in our ordinary common sense world.
It is actually possible to empirically test one of the various interpretations of QM - specifically the 'many worlds' one - albeit in a manner that would only impart information to the tester ( others would be in the position of having to take their claims on trust , but why should they? ). The necessary experiment is unlikely to appeal to many, but there may be some atheistic takers, suffering from a terminal condition and interested to know how things would turn out.ReplyDelete
Basically, suppose that one sets up a 'suicide machine', in which, when a button is pressed, there is a 50% chance of some quantum event- an atomic decay say - causing effectively instantaneous death, so the subject would have no conscious indication should the decay occur. Following the 'many worlds' interpretation, when the subject presses the button the world will bifurcate into a 'region' where the decay has occurred and the subject is dead, and another where it did not and the subject is alive and well. Now the point is of course that there will be continuity of consciousness between worlds where the subject remains alive, so the subject will find that the suicide machine just will not work, no matter how many times the button is pressed or how many such machines or variations thereof are employed. Over many such attempts this would be enormously improbable outside of the many worlds interpretation.
@freethinker. However we can predict from the formalism that the result of the experiment will be that 50% of the time the subject dies. So it’s not testing anything other than the formalism.Delete
I'm not tracking with this. Whether or not the Many Worlds interpretation is true, the probability breakdown of an observed outcome would remain the same, namely 1/(2^x) in your given scenario, where x is the number of button presses. The math itself doesn't seem to answer the question "Am I alive because a "single-world" suicide machine improbably failed to kill me or because I improbably ended up in the single branching world which ensured my survival?" The math in both cases is the same, but the fact that the observer is still alive doesn't, so far as I can tell, answer the above question.Delete
P hacking won't prove any particular interpretation of quantum mechanics any more than it proves any other hypothesis .Delete
In reply to the points made above, by pressing the button on the suicide machine n times, the subject can make the probability of his survival being due to pure luck ( the probability ofa 'killing' decay being 50% in the scenario described ) arbitrarily small, including fantastically small. One half to the power of n becomes vanishingly small very quickly as n increases. So surely , the failure of any suicide machine of the kind described to work as far as the subject is concerned could not be reasonably ascribed to luck. But it would be consistant with the many worlds interpretation, in which conciousness ( and so memories etc ) would be continuous along bifurcations in which the subject survived. This ( for him ) would be an experimental confirmation of MWH.Delete
The problem with the experiment is that it must be more likely for him to be alive given MWH than it would be otherwise. If there’s a 1/10000 chance he survives, it’s both a 1/10000 chance the machine never kills him AND a 1/10000 chance his consciousness makes it through the bifurcations. So, although there’s is a 100% chance he makes it through on MWH, and a 50% chance without MWH, it’s only because MWH makes every potency into actuality. So there’s also a 100% chance he DOESNT make it through too.Delete
Apologies if this has been discussed to death, but it seems quantum mechanics has all the ingredients necessary to create a new religion.ReplyDelete
The phenomena here mentioned are so far removed from every day experience that they might as well be miracles for people who do not have access to the experiments -- that is, most people.
It has a priesthood, a collection of learned men, who are closely associated with the phenomenon: Bohr, Einstein, Schrodinger, etc., who can properly interpret and communicate the miracles.
Its findings have vast implications, since it is proposed to underlie every material process.
It promises that a proper understanding of its findings (Schrodinger's cat, double-slit) should dramatically overturn our existing worldview (the laws of thought).
It has its own proselytizers, in the form of the pop sci press.
Maybe this is the Church of Microphysicalism?
I may miss the point you are making but LNC and say the wave-particle duality live in two different realms. This duality has nothing to do with contraddiction: particles are not the opposity of waves. They are two states of the matter and yes they can be present at the same time.ReplyDelete
I think the fundamental problem is thinking univocally about particles and waves in the quantum context rather than analogically.ReplyDelete
"...The present article reports on the finding of the principle behind quantum mechanics. The principle, referred to as genuine fortuitousness, implies that the basic
event, a click in a counter, comes without any cause and thus as a discontinuity in
spacetime. From this principle, the formalism of quantum mechanics emerges with
a radically new content, no longer dealing with things (atoms, particles, or fields)
to be measured. Instead, quantum mechanics is recognized as the theory of distributions of uncaused clicks that form patterns laid down by spacetime symmetry
and is thereby revealed as a subject of unexpected simplicity and beauty..."
Aage Bohr, Ben R. Mottelson, and Ole Ulfbeck
The break with causality described in the above paper must be understood as a break with causa efficiens as described by Heisenberg.
“…Thus scholasticism, following Aristotle, spoke of four kinds of ‘causes’: the causa formalis which might be considered as the form or the spiritual essence of a thing, the causa materialis which referred to the matter of which the thing consisted, the cause finalis or the purpose for which the thing was created, and finally, the causa efficiens. Only the causa efficiens corresponds to what is meant by the word ‘cause’ today…As material processes became more prominent in man’s conception of reality, the word causa was used increasingly to refer to the particular material event which preceded, and had in some way caused, the event to be explained…”
The Physicist’s Conception of Nature
I think that ontologically this supose contradiction does not hold even if logically they could hold.ReplyDelete
The problem is in the nature of what a particle is. The particle is not a wave nor a litle ball. As Wolfgang Smith point's out, this elements of quantum theory are not in the corporeal world, they are in a substractum under the corporeal world, ontologically speaking.
This ontological laws work in the corporeal world, but they did not need to work in the domain of all possible mathematical realizations of matter, where "things" are just possibilities and not realities in the corporeal sense.
Even if someone uses a paraconsistent logic to describe QM, this would not mean that the PNC does not hold in the world, even if logically this could be possible.
As Willhemsen points out though the fact such principles are referred to as "laws of thought" is a testament to the extent that idealism has slipped into our speech. They are first laws of things and only secondly laws of thought. As the great Austin Woodbury would say "think follows thing."ReplyDelete
The scientific description of light as an appearance characterized by both particles and waves is further explained and unified if light is understood and observed to be always in a spiral or helix form - like the material form of DNA, which is, itself, a direct materialization of the structure of light.ReplyDelete
If a spiral-form is seen at its point of rotation, or its crossover point, it is observable as a "particle". And if the same spiral-form is seen with reference to its limbs of rotation, before or after its point of rotation, or its crossover point, it is observable as a "wave".
So, also, light is observable as both "particle" or "wave", depending on which phase of its process is observed by attention, or point of view in time and space.
A vibrating string can be seen to demonstrate the same spiraliform gait as any mode of observable light. And, so, as a kind of poetic inspiration, modern scientists have produced numerous string theories, in their search for the presumed knowledge that will supposedly explain everything.
Nevertheless, whether light is observed and, thus understood as a "particle" or a "wave" or as a string, that observation or understanding is, itself an act of perspectival objectification, wherein and whereby Reality Itself is reduced, by the very act of observation, or understanding or mental fabrication, to a relation and, thus, a subordinate of attention, or point of view of the presumed separate ego-"I".
An "object" is, or appears as an "object" only because it is being perceived of conceived from a point of view in space and time.
Therefore,what is the nature, condition, or state of an "object" when "it" is not being viewed from any point of view in space and time.
Apart from point of view, are there any "objects" (as such), or any differences at all?
Or, rather, if all possible "objects" or "differences" are simultaneously existing, as they must be, unless and until point of view differentiates and particularizes them, then what is the nature, condition, or state of that simultaneous totality?
Apart from the defining and categorizing done by the presumed separate ego-"I", What IS that totality beyond perspective, and thoughts, and every now of time, and every place of space-locatedness?
That What is the only universe that Really IS.
And no brain-made mind of body-self, can say That Universe is seen by any ego-"I" at any time or place.
The following article may be of interest to some readers:
"What Quantum Mechanics Doesn’t Show" by Justin P. McBrayer and Dugald Owen, in Teaching Philosophy 39:2, June 2016
Nice paper. The only objection I have to it is with respect to the last point about the PSR. It seems like the authors have in mind a contrastive PSR when they say that QM plausibly contradicts it, but it's hard to say since they don't actually provide a definition for the kind of PSR they have in mind.Delete
The following article may be of interest to you (since you've gone to Schmid for help in the past):Delete
An Appraisal of Aquinas' First Way: Quantum Mechanics Contra the Causal Principle
Thanks for the link to Joe Schmid's article. It was very fair-minded and well worth reading. Cheers.
I noticed in this discussion that many dystopian physical and logical concepts are used, which is a common occurrence among those who lack an understanding of quantum physics, Aristotelian logic, and philosophy. To improve understanding, at his point, it is warmly recommended to grasp the difference between mixed states and pure quantum states. In quantum mechanics, a mixed state is a probabilistic mixture of pure states and is not a pure state itself. Thus, it does not conform to the requirements of being a vector in a Hilbert space, which is necessary for describing pure quantum states. Mixed states cannot be represented by a wavefunction and require the use of density matrices for their mathematical description. Having a clear understanding of these concepts will aid in discussions about the EPR paradox, contextuality, and entanglement. Ultimately, a sound understanding of the underlying logical structure is necessary for sensible discussions in these topics. The rest can be disregarded and best left to those seeking to disrupt the conversation but which do not really seek to deepen the topic.ReplyDelete
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We can solve your "self-amending" counterexamples by being more precise in our predication. "X can't be a and not a in precisely the same respect and at precisely the same time" -- this isn't violated by a constitution that changes over time.Delete
In the monograph I linked to a few comments down, Peter Suber analyzes the "time" resolution to the self-amending document paradox. Basically, what you're saying is that the first iteration of a constitution is like a lit candle, the self-amending process is like the lit candle creating a second candle with a slightly different scent, and the finalization of the self-amending process is the old candle igniting the new candle and extinguishing itself in the process. However, he concludes that this is not a sufficient resolution, and that there is still something self-contradictory about this process.
Interesting post, but the arguments against LNC are not convincing. If we are speaking about the "laws of thought", then, as I'm sure you know, the principle that anything follows from a contradiction is debatable (independently of one's stance on LNC). Many philosophers deny that one can infer anything from a contradiction.
For example, let A be the (material) conditional proposition/sentence whose antecedent is the conjunction of the ZFC axioms and whose consequent is the negation of a difficult mathematical theorem (say, Fermat's last theorem). Then, A is a contradiction (there are no models in which the ZFC axioms are true and Fermat's last theorem is false, so A is logically equivalent to a proposition of the form "B and ~B"). But, arguably, we can't infer just anything from A. For example, the inference "A, therefore it is raining" does not look like a good inference. The laws of thought don't license that inference (arguably).
So, anyway, I think you're much to quick to dismiss non-classical logics as incoherent, self-undermining, etc. These are fascinating topics that deserve to be treated seriously! (I do agree with your general point that a lot of QM hype is overblown, by the way.)
@Michael N, you write:Delete
Interesting post, but the arguments against LNC are not convincing.
Where did Feser say that the arguments against the LNC are convincing?
Your statements above make no sense.
If you're having trouble understanding, try reading Peter Suber's monograph on the paradox of self-amending documents. His conclusion is that self-amending documents violate the law of non-contradiction but yet are not self-refuting or subject to retortion. Peter Suber is a professional philosopher of the same caliber as Ed.
Not very eminant then.Delete
The link doesn't work for me. Tried Googling Suber's monograph but couldn't access it that way either. I found a snippet which isn't much, but for the sake of discussion:Delete
"A constitution can contain a clause that provides for its amendment. But can this clause be used to amend itself?
Article V of the U.S. Constitution requires that an amendment be ratified by three-fourths of the states. Could they change this requirement to 90 percent? Or declare that the president can amend the constitution at his whim? Or abolish amendments altogether?
“If legal rules that authorize change can be used to change themselves, then we have paradox and contradiction; but if they cannot be used to change themselves (and if there is no higher rule that could authorize their change), then we have immutable rules,” writes Earlham College philosopher Peter Suber." -from https://www.futilitycloset.com/2011/01/10/the-paradox-of-amendment/
I don’t see how this violates LNC, because you have one distinct time period where you are allowed to amend the document, but if you use that right to amend the document and say that you can no longer amend the document, then only after that the document cannot be amended. There is no time where the document simultaneously is amend-able and not amend-able. It goes from amend-able to not amendable.
Ed, what will you tell a dialetheist since dialetheists believe that some true propositions have true denials, that some contradictions are true?ReplyDelete
Maybe it's best to treat the LNC as a metaphysical principle instead of a semantic one since Aristotle's metaphysical LNC avoids the liar's paradox.
Re the presumed "laws of thought" it seems to me that Hamlet had something to say about this, with my addition in bracketsReplyDelete
"There are more things in heaven and earth (and in the intrinsically paradoxical nature of Quantum Reality) Horatio than are dreamt in your philosophy"
Rather unusually, I think this post doesn't go nearly far enough. For reference, I'm a mathematician who has taken quite an interest in QM and its interpretations.ReplyDelete
I would take issue with the following: "Here too, you could try to make the case that we should interpret what is going on in a way that rejects either LNC or LEM."
I actually don't think there are any coherent interpretations of QM (or even any popular incoherent ones) that really reject either LNC or LEM.
Let's say that one decides, for example, that in the Schrodinger cat experiment, the cat is in a superposition of alive and dead. Then it is the case that "the cat is in a superposition of alive and dead." It is therefore NOT the case that "the cat is NOT in a superposition of alive and dead." And so it turns out that we need the LNC just as much as before (and similarly with LEM). Of course, physical reality turns out to have some unexpected properties, and observables we thought of as definite aren't always definite. But that's quite another thing from denying the laws of thought.
I wish Dr. Feser would criticize Dr. Graham Priest's arguments for dialetheim because dialetheists believe some contradictions are true,ReplyDelete
I think there is no point in spending more than a sentence arguing with dialetheists, as to prove they are right, they must also prove and accept that their dialetheistic construct is intrinsically wrong, which, we must honestly admit, is a no-brainer.Delete
I can be wrong, but i believe that dialetheists only aim to show that some propositions dont fit the binary true or false division or something.Delete
I dont remember seeing these guys trying to show more that language has a few tricks, not that the world is like that.