There is no "collapse" into an infinite number of universes. — Rich

There is no wave function collapse in the Everettian Interpretation.

I have no idea what he's talking about. Maybe it's overlooked because it doesn't exist. The guiding wave and the wave perturbation are real and do not branch because there is no collapse of the wave function. The wave function in Bohmian Mechanics becomes a quantum potential so it really isn't a wave function any more. — Rich

In Bohmian Mechanics the wave function describes quantum potential at both slits - which are the "potential" worlds or branches that are in superposition. Zeh describes them as "empty" wave components since they don't specify where the actual particle is (this is instead specified by the Bohmian guiding function).

The problem of direct realism is that even an optical illusion can be used as a strong argument against it. — boundless

I would disagree. Opponents take a distinction that arises naturally in everyday experience and then their conclusion generally involves denying that same distinction. For example, "How do you know everything isn't an illusion?" or "We don't perceive things as they really are, because illusions".

So I see Locke as an Aristotelean trying to defend Aristotelism (in some forms) from Platonic attacks. — boundless

Perhaps so, but his "primary qualities" and "secondary qualities" isn't a natural distinction. Trying to draw a line regarding which qualities the apple "primarily" has is to misunderstand the nature of language abstraction.

CI seems to imply really anti-realism, which I find very problematical. — boundless

Agreed.

Rovelli's take is very intriguing but it seems to go towards a sort of "solipsism". — boundless

I find Rovelli's RQM very intriguing as well, but it is a realism of sorts. Its difference to MWI is that only interactions of other systems with the system in question define what is real for that system. So you can't compare accounts between systems until they interact, in which case their respective accounts will always be found to be consistent.

MWI has too many "worlds". — boundless

It seems only as many as is necessary. Note that the vast size of Hilbert space is the same under all interpretations. If it is not interpreted physically, then where do the unitary transformations happen?

Regarding Bohm there is the explicit "non-locality" and the ambiguity when it comes to define "real". Even the "nomological" variant which asserts that the "wavefunction" is nominal seems to go against the tendency to see reality in a way free from our "pre-conceptions" (I find the "point particles" an outdated concept). — boundless

Agreed.

So, in my opinion this shows that "beneath" QM there might be a "subquantum" theory. Maybe even weirder! — boundless

In my view the universe just is quantum mechanical at base. If decoherence emerges from QM, then perhaps gravity does as well. For a possible explanation along these lines, see Sean Carroll's recent talk entitled "Extracting the Universe From the Wavefunction". The main idea starts at 29:49.

Bohmian mechanics avoids this entirely by positing a real quantum potential and wave perturbation. — Rich

The "real quantum potential" just is the branching wave function, so it's just Everettian worlds by another name. The additional postulate is that the quantum potential guides (non-locally) the particle that is observed.

As H. D. Zeh (the discoverer of decoherence) puts it:

It is usually overlooked that Bohm’s theory contains the same "many worlds" of dynamically separate branches as the Everett interpretation (now regarded as "empty" wave components), since it is based on precisely the same ("absolutely real") global wave function. — Why Bohm’s Quantum Theory? - H. D. Zeh

Is invisible, unmeasurable, unknowable stuff the new paradigm of science? — Rich

Fair enough, let's see what the theory of quantum mechanics says. There are two postulates that are shared by all the different interpretations. They are:

[1] The world is described by a quantum state, which is an element of a kind of vector space known as Hilbert space.
[2] The quantum state evolves through time in accordance with the Schrödinger equation, with some particular Hamiltonian.

Note that there are no invisible worlds postulated there.

Now here's the evolution of the wave function for the double-slit experiment with a detector at the slits and an observer that reads the result. The first quantum state is the particle being emitted. The second quantum state is the resulting superposition when the particle is detected.

[1] (A particle is emitted; detector says "ready"; observer sees "ready")
[2] (A particle travels through the left slit; detector says "left"; observer sees "left") + (A particle travels through the right slit; detector says "right"; observer sees "right")

You can see that there are two worlds described by the wave function. How do you interpret that as one world without adding a postulate to make one of the worlds disappear? Or, if you do add a postulate, what is the principled motivation for doing so?

Of course Aristotle, as far as I know, was a direct realist and therefore he thought that we see reality as it is. The problem is that when epistemological concerns are appreciated, then there is another level of "accidents", i.e. how things appear to us in contrast to how things are in themselves. — boundless

Yes, though this is a perfectly natural and ordinary distinction. For example, the straight stick appears bent when partially submerged in water. But it's something else entirely to say that the straight stick is itself merely an appearance. This kind of "Plato's Cave" conclusion was just what Aristotle rejected.

IMO Aristotle disinction between "substance" and "accidents" was the foundation of the distincion between "primary qualities" and "secundary qualities" of Galileo (and Descartes, Locke...). This introduced the "indirect realism" which then influenced Kant etc. For Plato the "changing world" was without substance, a world of accidents, so to speak. The epistemological concerns that began in the 17th centrury were due to Aristotle, rather than Plato (of course Aristotelism can be considered a "form" of Platonism, hence the saying of Whitehead "western philosophy is a series of footnote of Plato's philosophy"). — boundless

So I read it in the other direction. I see these philosophical innovations as a rejection of Aristotle's natural empiricism (where distinctions arise naturally in one's ordinary experience of the world) and instead as a reintroduction of Plato's dualism in different forms.

I also see the ordinary language philosophers as a corrective to that kind of thinking. For example, Wittgenstein's private language argument and Ryle's regress argument against indirect realism.

Of course this is a "metaphysical/interpretative" reason. But it is the same reason why before the introduction of GR, SR was to be preferred over LET. — boundless

What interpretations would you suggest should be preferred to MWI for that reason? Note that MWI requires the least number of postulates of any interpretation and is also a local theory (so is naturally compatible with SR).

Aristotle IMO it is still a dualist since he makes a distinction between the sensory world and "the real world" (again, it is not directly what Aristotle thought but it is heavely implied!). — boundless

I'm curious where you find Aristotle implying this. Aristotle rejected Plato's realm of Ideal Forms and instead located form in the natural world (see hylomorphism and also immanent realism).

Again interesting! The problem I have with MWI is that there are too many worlds. I find it very problemtic. But again it does not mean that some ideas are very sound! — boundless

OK, though isn't that a problem with our expectations of how the world should be rather than a problem with the Everettian interpretation itself? Or do you think there is more to it than that?

Ok, In some sense this view reminds me Schopenhauer position that the world as an empirical object necessitates the "opening" of the first sentient "eye" in the world. It is certainly interesting. — boundless

I'm not particularly familiar with Schopenhauer's position. However I tend to identify with Aristotle's position that the intelligible world just is the sensory world (as against the various two-world dualisms held by thinkers such as Plato, Descartes and Kant). We represent things from a point-of-view, but those things nonetheless precede their representation (as the existence of the Earth prior to the emergence of humans to talk about it attests).

But how can, say, the cosmological model fit in such a description? Our "hypotheses" for the past are indeed in the "preferred basis". Do these "hypotheses" remain "true" in your view or they are a sort of "fiction"? (this point was never clear to me, I apologize if this question is obvious. But it is clear that all non-quantum theories work in the "preferred basis branches"... so if such a theory is correct how is the status of "predictions in the past"?) — boundless

Yes, they remain true. I see the bases in QM as similar to the reference frames of relativity. Just as descriptions are indexed to a relativistic reference frame, so they are also indexed to a basis (or a relative state within a basis). Any basis is valid and, if suitable language has been developed, can also be described (e.g., a particle that was detected at a particular position can also be described as having been in a superposition of momenta).

Anyway I think that your "solution" is a possiblity to avoid the rejection of "simple" MWI by Schwindt's argument. I concur, thereofore, that it is a valid "escape" from refutation! — boundless

Cool! Although, as far as I'm aware, this is the mainstream Everettian view. For example, David Wallace says, "But emergent processes like [decoherence] do not have a place in the axioms of fundamental physics, precisely because they emerge from those axioms themselves."

The idea here is that things do not need to be fundamental nor precisely-defined in order to be real. Wallace often gives an example with tigers. They are real even though the Standard model doesn't mention them.

Mmm interesting! I cannot say if it is a valid counter-argument, but maybe it is. Just for curiosity, is it based on some papers? — boundless

Yes, it's based on Carroll and Sebens' derivation which uses math from Zurek's envariance paper. Sean Carroll discusses it on his blog - here's a summary quote:

What if the amplitudes for the two branches are not equal? Here we can borrow some math from Zurek. (Indeed, our argument can be thought of as a love child of Vaidman and Zurek, with Elga as midwife.) In his envariance paper, Zurek shows how to start with a case of unequal amplitudes and reduce it to the case of many more branches with equal amplitudes. The number of these pseudo-branches you need is proportional to — wait for it — the square of the amplitude. Thus, you get out the full Born Rule, simply by demanding that we assign credences in situations of self-locating uncertainty in a way that is consistent with ESP. — Sean Carroll - Why Probability in Quantum Mechanics is Given by the Wave Function Squared

you might enjoy this paper by Max Tegmark who uses mind/consciousness as a defense to the criticism of Schwindt. — boundless

Thanks - I'm assuming it's this paper: Consciousness as a State of Matter.

However while it is an interesting defense, it posits a "fundamental role" of consciousness. Problem is that his theory about consciousness is highly speculative. Schwindt's criticism however applies to the "pure" version of MWI, i.e. one without "subsystems", like Copenaghist observer or Tegmark's mind. Positing a "mind" is adding an axiom to explain the efficacy of decoherence (which alone cannot refute Schwindt's criticism). But if you add additional structure, then the theory loses its simplicity and it is not more "simple" (mathematically) than Bohm's. — boundless

Actually I'm not suggesting an axiom for "mind" as such (that's too dualist for my taste), but I am suggesting that the human perceptual point-of-view is implicit in how we represent the world. The key distinction I'm making here is that interactions between objects (including those prior to human existence or far away from Earth) don't depend on humans or sentience. So there need be no preferred basis in the world itself, things happen (or not) in every basis but humans have evolved to perceive the world in the decoherence basis. I think this explains why humans have a basis preference without requiring additional structure or axioms in the quantum formalism itself.

In any case there is also the Born Rule problem. — boundless

In my view, the Born Rule can be explained. Briefly, in wave functions where the relative states have equal amplitudes, we would be indifferent to which state we would find ourselves measuring, so branch counting is sufficient. When they are not equal, the wave function can be transformed such that all the states do have equal amplitudes. For example, a superposition of two states with (non-normalized) amplitudes of 1 and 2 respectively can be mathematically transformed into five states each with amplitude 1. And then branch counting again gives the correct probabilities according to the Born Rule.

P.S. For those interested in interpretation of QM, I have found a nice criticism of MWI (many-worlds):
https://rekastner.files.wordpress.com/2014/07/decoherence-fail.pdf — boundless

I think the counter-argument is that the preferred basis is the decoherence basis (by which we all observe distinctly live or dead cats). That's not to deny the validity of all the other possible basis representations. But they are not preferred for us since we don't measure or observe states in those bases.

and the link to the pre-print of the paper where the criticism is found:
https://arxiv.org/abs/1210.8447 — boundless

That's an interesting paper and well worth quoting the concluding section in full. (Note: CI and EI stand for the Copenhagen Interpretation and the Everettian Interpretation respectively.)

6.4 Schrodinger’s Problem

In 'Mind and Matter', Schrodinger writes:

"The thing that bewilders us is the curious double role that the conscious mind acquires. On the one hand it is the stage, and the only stage on which this whole world-process takes place, or the vessel or container that contains it all and outside which there is nothing. On the other hand we gather the impression, maybe the deceptive impression, that within this world-bustle the conscious mind is tied up with certain very particular organs (brains), which [...] serve after all only to maintain the lives of their owners, and it is only to this that they owe their having been elaborated in the process of speciation by natural selection."

Schrodinger compares the situation with an artist who places a picture of himself as an inconsiderable minor character in one of his paintings. This seems to him the best allegory for the confusing double role of mind. On the one hand it is the artist who created everything; in the completed work, however, it is only an unimportant decoration which could have been left out without changing the total impression substantially.

The text is part of Schrodinger’s philosophical work, at that time totally unrelated to QM. But now we see that the situation in QM is similar, if we replace “mind” by “measurement”: In the CI, the measurement is central. It is the only stage on which the whole physics-bustle takes place, and the state vector is justified only as a model to predict the statistics of measurement results, with no independent existence. In the EI, the measurement process is just a little interaction process like many others, and is completely included in the picture of the state vector, as a “minor character” that could be missing without changing the picture substantially. This is the strange double role of the measurement.

It seems that one of these views alone cannot survive. If the CI is taken alone, one may respond: “But why should we mystify the measurement? I can model the measurement inside QM, as a part of the unitary evolution of the state vector, without giving it such a fundamental role.” If, on the other hand, the EI is taken alone, we have seen that the resulting picture is not a picture anymore. It is an empty nothing. Only together, as complementary views on QM, the CI and EI make sense.

The strange double role of the measurement, just as the strange double role of the mind, is a problem most fundamentally related to what we do when we do science. We create a picture of objects; a picture created by subjects. The double role is fundamentally built into science. I conjecture it cannot be resolved within science. — Nothing happens in the Universe of the Everett Interpretation - Jan-Markus Schwindt

I agree except I would claim that the EI already does incorporate the subject. The subject is not just a minor character appearing in the wave function but is also the artist that chooses the (preferred) basis for constructing the wave function. The subject is an integral part of the world that they are observing and that world-bustle is what they are seeking to represent.

I know that's the contention but you haven't explained why truth and falsity predicates are subject to a different set of rules than other predicates which can apply to quoted sentences. — MindForged

There needs to be a way to convert a mention to a use and using the subject-predicate form is an efficient way to do that.

" '2+2=4' is true"

On your view, does this work? — MindForged

Yes. To say "'2+2=4' is true" is to say "2+2=4". That is, truth predication of a mentioned expression uses the expression. So it's the inverse of quoting.

This sentence is true. — MindForged

The truth-teller sentence cycles for the same reason as the liar sentence. Here's the iterative unpacking (the => is just an arrow to indicate the transformation steps):

"This sentence is true" => "'This sentence is true' is true" => "This sentence is true" (truth predication rule). So we have a cycle.

Compare with unpacking the liar sentence:

"This sentence is false" => "'This sentence is false' is false" => "Not ('This sentence is false' is true)" => "Not (This sentence is false)" => "Not ('This sentence is false' is false)" => "'This sentence is false' is true)" => "This sentence is false". So we also have a cycle.

And compare with the English sentence:

"This sentence is an English sentence" => "'This sentence is an English sentence' is an English sentence" => true. So it's truth-apt.

This is not a use-mention issue, the inner sentence is capable of being true even if it's only being mentioned. — MindForged

This is the key issue. My claim is that a sentence is only capable of being true or false if it is used (i.e., expressed).

Consider the sentence, "'Snow' has four letters and is cold". Snow is mentioned, but that mention is not something that can be cold, only the snow itself is. So the "is cold" predication is a category mistake (specifically, a use-mention error). However we could apply an interpretive rule and say that in such circumstances, the "is cold" predication disquotes the mention and so is really saying that snow is cold. This would unpack as, "'Snow' has four letters and snow is cold". Such a rule would tolerate the above sentence and allow it to be truth-apt.

Now compare that with "'2+2=4' has three numbers in it and is true". My claim is that the mention of '2+2=4' is not something that can be true, but the expression (or use) of '2+2=4' is. If so, then the truth-predication disquotes the mentioned expression and uses it. This would unpack as, "'2+2=4' has three numbers in it and 2+2=4".

Since "This sentence is an English sentence" doesn't contain a truth-predicate, the referring expression is only mentioned, not used (i.e., only the surface aspects of the sentence are referred to). Whereas in the liar sentence, the truth-predication disquotes the mention and uses the referring expression. Thus it is cyclic.

A far as I can tell, Ryle's argument is that the sin of the Liars family of paradoxes is that they make use of impredicative definitions, they are part of the thing they are defining, and that by doing this you can never get down to a truth-apt sentence because it the subject expands indefinitely. — MindForged

Ryle is arguing against cyclic expressions (fillings of their own namely-riders), but he is not arguing against mentions of the referring expression (where quotation-marks have to be employed). As he says in the same paper:

Many of the Paradoxes have to do with such things as statements about statements and epithets of epithets. So quotation-marks have to be employed. But the mishandling which generates the apparent antinomies consists not in mishandling quotation-marks but in treating referring expressions as fillings of their own namely-riders. — Gilbert Ryle, Heterologicality

His claim is that the impredication never gets anywhere, and so when run against "This sentence is an English sentence", it would, when you ask for the "namely-rider" come out (as per your Ryle's quote): "Namely, the current sentence{namely, the current sentence etc. — MindForged

Yes, an infinite expansion results if the subject is always a truth-evaluable expression (as is indicated with the nested brackets). But that's not how we ordinarily use that sentence. Instead the referring expression is only mentioned (which I unpacked and indicated with quotation-marks in my previous post), not used as an expression. That's the use-mention distinction.

As explained in my previous post, that specific use would result in a category mistake for the liar sentence, since a mention of the referring expression would not be truth predicable.

Try this: "The sentence 'Snow is white is true' is true". The inner sentence is clearly true, we can predicate truth there. If "snow is white" is true, we can validly assert that "The sentence 'snow is white is true' is a true sentence" — MindForged

That's fine. There's nothing wrong with nested expressions. The problems only arise with cyclic expressions.

So the issue is with impredication (what I earlier called self-predication), — MindForged

The issue as I see it is not impredication, but whether the sentences in question have a truth-apt use.

"This sentence is an English sentence" would ordinarily be unpacked as, "The sentence 'This sentence is an English sentence' is an English sentence". The inner sentence is not being used as an expression but is only being mentioned. If it were used as an expression, then infinite recursion would result.

Now consider a similar unpacking for the liar sentence, "The sentence 'This sentence is false' is false". For the outer 'false' to be predicable of the inner sentence, the inner sentence must be an expression. But since it is only being mentioned, it doesn't support truth predication. So it's a category mistake. Whether a category mistake or an infinite recursion, no truth-apt use is available for the liar sentence.

whereas sentences (such as what the Liar refers to) are arguably truth-bearers — MindForged

Here is Ryle's argument which I think explains the issue well:

The same inattention to grammar is the source of such paradoxes as 'the Liar ', 'the Class of Classes ...' and 'Impredicability'. When we ordinarily say 'That statement is false ', what we say promises a namely-rider, e.g. '... namely that to-day is Tuesday'. When we say 'The current statement is false' we are pretending either that no namely-rider is to be asked for or that the namely-rider is '... namely that the present statement is false'. If no namely-rider is to be asked for, then 'The current statement' does not refer to any statement. It is like saying 'He is asthmatic' while disallowing the question 'Who?' If, alternatively, it is pretended that there is indeed the namely-rider, '... namely that the current statement is false', the promise is met by an echo of that promise. If unpacked, our pretended assertion would run 'The current statement {namely, that the current statement [namely that the current statement (namely that the current statement ...'. The brackets are never closed; no verb is ever reached; no statement of which we can even ask whether it is true or false is ever adduced. — Gilbert Ryle, Heterologicality

Thus the liar sentence is not truth-apt. It doesn't actually assert anything.

"This sentence is ungrounded" is not applying a truth-predicate to itself, it merely asserts (as the solution purports) that it's ungrounded (which means it's true). — MindForged

The ungrounded sentence has the infinite recursion problem as well and so also doesn't actually assert anything. As with the liar sentence, it's a category mistake to say that it is true (or false).

And that comparison seems disanalogous. Trees don't even have the appearance of a truth-apt object, whereas even you seem to agree that the Liars at least appear as if they are truth-apt. — MindForged

What they both have in common is that the full sentence appears truth-apt (since it has a subject and a predicate) until, of course, the content of the sentence is analyzed and the subject is found to not support the predication. It's a category mistake (as Michael earlier noted).

No no, the notion of groundedness refers to, essentially, hacking off the truth-predicate. The predicate "is grounded" (and its negation) aren't truth predicates so it's not subject to the same criticism — MindForged

Then we are using "grounded" in a different way. I mean that the subject is resolved and supports the predication, whatever it may be. In this case, the subject doesn't support the grounded predication and so the sentence isn't truth-apt. (BTW, this was essentially Gilbert Ryle's solution to the liar-style sentences rather than Kripke's.)

unless you are arguing that self-reference is itself not an allowed thing to do in language. — MindForged

Self-reference is generally fine. For example, "this sentence has ten words". The truth or falsity of this doesn't depend on the subject being truth-apt, only that its words can be counted. That is a valid predication and so the sentence is truth-apt.

If you agree the sentence is ungrounded, that entails that it is true, which contradicts being ungrounded. — MindForged

It doesn't entail that since the sentence doesn't support truth predication (because, in turn, the subject of the sentence doesn't support grounded predication). But you're treating it as if it does.

This sentence. — Luke

Not even wrong. :-)

That's just assuming the Kripke's solution and it fails for the same reason. — MindForged

I think Kripke grants that the liar sentence is a meaningful assertion but that it just lacks a truth value (and so therefore has some third value). Whereas I am claiming that the liar sentence isn't a meaningful assertion at all because it fails to meet the logical criteria for one. A bit like the sentence "the tree is false".

This notion of groundedness can be just as easily used to restate the paradox:

This sentence is ungrounded. — MindForged

That sentence fails for the same reason as the liar sentence. We can all agree that that sentence is ungrounded. But, being ungrounded, the sentence itself doesn't meet the logical criteria required for a meaningful assertion. So you can't then treat it as if it does.

That is, the sentence appears to be asserting something about itself. But it is not, despite surface appearances. Whereas our assertions about the sentence are truth-apt as long as we're not asserting that the sentence is true or false.

That is the sense in which the liar, truth-teller and revenge paradoxes are like a mirage. There appears to be water there, and it makes us think about water, but appearances are sometimes deceiving. There's no water there.

That seems false. Just take the Liar and it gives you a grounded truth value to start with (namely falsity). — MindForged

Yes, but it doesn't ever give you a grounded truth-apt subject. To determine the truth of the liar sentence first requires determining the truth of the subject ("This sentence"). That requires substitution with the original liar sentence and so on ad infinitum. There is no final truth-apt subject to ground the liar sentence.

So the liar sentence fails to assert anything about a truth-apt subject and so isn't itself truth-apt. If you disagree, then what do you think is being asserted?

I have a gut feeling the liar paradox is important. It must mean something. I just don't know what it is. — TheMadFool

The liar sentence shows that not all sentences that appear to meaningfully assert something actually do so. It's the linguistic equivalent of a mirage.

How do we make sense of this paradox? — TheMadFool

The basic issue is that the liar sentence requires an infinite recursion to ground its referents.

So it fails to state anything, not even a contradiction.

You don't think it would be a problem for the simulation computing our coming up with those idealizations? — Marchesk

It doesn't have to, the real people that are being fed the simulation will do that (assuming BIV or matrix-style simulation). They will observe their simulated surroundings and develop language and logic accordingly.

All the computer simulation has to do is simulate what is real (e.g., coffee cups with approximately-circular rims). The people in the simulation will come up with the ideas.

Here's an interesting question. Could a simulation learn about the halting problem? — Marchesk

I don't know, but the people in the simulation could which is sufficient. It's just a question of logic. No infinite storage or time is required to understand it.

Whatever you want to call it -real, ideal, virtual, a platonic object, other things-, our mathematics has a specific value of Pi. A computer simulating our mathematical capabilities would also have to simulate their associated ideational structures, irrelevant of their ontological status in the final analysis. It may be that Pi isn't 'real' in the same sense as the ideal circles (and other things) it concerns; nevertheless it must be simulated. — fdrake

The value of pi is defined as the ratio of a circle's circumference to its diameter. That is sufficient to construct actual circles that approach the ideal circle or to approximately calculate pi.

The computer simulation can have the same mathematical definition of a circle and pi as us. But in both cases they are mathematical idealizations and can only be actualized approximately.

We do have a mathematical value for PI which is irrational and cannot be computed (in full). A circle's definition is determined by the full value of PI, mathematically speaking. — Marchesk

I would put it the other way around. The meaning of pi is based on the definition of a circle (e.g., a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre)).

I think fdrake is arguing that the simulation would have to compute us coming up with irrational numbers and other things which aren't computable, such as transfinite numbers. Or the halting problem. — Marchesk

Yes. But as long as they are understood to be idealizations and not actualized, then I don't see the problem. As an analogy, we have a concept of infinity. It doesn't follow that the universe is necessarily infinite. Similarly for the simulation.

Reality does. It's Pi here, it's an approximation of Pi in simulated universes with finite memory. — fdrake

Why would you suppose reality has a value for pi? There are no perfect circles in reality, just approximations of them, like the rim of my coffee cup. There is a Planck length limit to how precise an actual circle can be. But pi can be calculated to as many decimal places as desired (within physical limits) without requiring an actual circle (e.g. 4*(1-1/3+1/5-1/7+1/9-...)).

Well, since the two photons have no measurable differentiating property at the end of the experiment, not even a different position in physical space, we cannot find out which one was above the beam splitter at the beginning of the experiment and which one was below the beam splitter. — litewave

The photons do have different positions in physical space at the end of the experiment (see figure 3 that shows the distinct photon pairs together either at the top or the bottom of the image).

The issue is only that the two photons could not have any different property while within the beam splitter. The observed destructive interference occurs because the "both photons transmit" and "both photons reflect" quantum states are identical and this entails that the photons are identical.

We might at least measure (if it is technologically feasible) whether their frequency didn't temporarily change during the experiment, to rule out that they temporarily merged into one photon (which would manifest as temporary doubling of frequency, since total energy should be conserved). If they merged into one photon and then separated again it seems that their identities were terminated at the merger and new photons came into existence at the subsequent separation. — litewave

Yes. My guess is that such an experiment would only show evidence of the two photons and also destroy the interference effect in the process. If so, it would neither confirm or rule out the possibility. But it may still be a useful way to think about it. It at least shows how preserving identity can suggest a different physical model or interpretation.

If there was no merger into one photon then the identity of the particles was preserved but since they have no measurable differentiating property at the end of the experiment we can no longer say which one is which. — litewave

Preservation of photon identity is ruled out by the observed destructive interference.

Depends on what you mean by "physical". Is "imaginary momentum" that a particle has in quantum tunneling "physical"? It cannot be measured, even in principle, but physical theory implies it is there. — litewave

Yes, I regard it as physical.

The issue I'm thinking about with the HOM experiment is this. Suppose we name the two photons that are measured at the end of the experiment P1 and P2. Can P1 be identified with the photon that was originally above (or, else, below) the beam splitter? Or does that question have no physical meaning (as a question about ontology, not merely the inability to measure it)?

That interference occurs for the "both photons reflecting" and "both photons transmitting" quantum states implies the latter. Would you agree?

So it is the theory, the structure of its definitions and rules, that differentiates the stuff into two photons and thus gives each of them a separate identity. In this theory, in its abstract space or structure (and also in the corresponding abstract structure of reality), the two photons have a different position. But physicists cannot measure this position; it's not a position in physical space. — litewave

OK, so granting that there are two photons throughout the experiment, are you saying that the property distinguishing the photons would not be physically measurable but still be physically real (a hidden variable)? Or not physically real and just part of the abstract structure (instrumentalist)? Or something else?

In theory - and also in reality if the theory is correct - there are two photons throughout the experiment, not one photon. They are numerically different, so there must be a property that ensures that they are two photons and not one. I would say that this differentiating property is the position of each photon in an abstract structure of the theory, because it is the abstract structure of the theory (including the definition of energy of a photon as a product of Planck constant and frequency) that differentiates the situation into two photons. — litewave

The problem is that quantum mechanics would seem to rule this out. The reason is that if there were a differentiating property such as position while in the beam splitter then, per figure 1, quantum states 2 and 3 would be physically distinct states and therefore would not destructively interfere (cancel out). But, as experiments show, they do.

(BTW, if the photons' positions were tracked to see how they individually traveled through the beam splitter then the interference effect would disappear and quantum states 2 and 3 would then be observed half of the time. This is analogous to the dual-slit experiment.)

So a different explanation is needed. One option is that the photons each have identity but are indistinguishable. A second option is that they don't have identity.

A third option is that the two photons merge into one photon (with higher energy) when they interact with the beam splitter and then subsequently split into two photons again. A fourth option is that the two photons are absorbed by the beam splitter (increasing its energy) which then subsequently emits two photons.

A fifth option is that the two photons actually do retain their individual identities throughout. But instead of the differentiating property being position, it is instead an index to relative branches in a very temporary world branching and merging. So both photons would be in the same spatio-temporal location in their respective branches and their interference effect would appear like the third or fourth options above. A bit like the bent-stick-in-water effect.

So at the beginning of the experiment the two photons are not identical because they have at least one different property - position in space: one is above the beam splitter, the other is below. — litewave

Yes, the two photons are initially in different positions. But the reason they are termed "indistinguishable" or "identical" is that if they somehow exchanged positions, this would make no physical difference (i.e., the quantum state would be identical).

Similarly at the end of the experiment they are measured in different positions - see Figure 3 of the earlier link. But at the time that they hit the beam splitter, their positions are also physically indistinguishable. (If they were not, then there wouldn't be interference. This is analogous to distinguishing which slit the photon passes through in the double-slit experiment.)

Also, whether each photon at the end of the experiment is the same photon as it was at the beginning of the experiment is a question of the preservation of identity through time. Identity doesn't have to be preserved in time; an object can be annihilated, or merged with another object, or separated from another object at some point in time. But at each point in time an object is identical to itself and different from other objects. — litewave

So any time that a photon interacts with something (say, the beam splitter or the detector), we could say that it is annihilated and created anew. But sometimes we want to consider the identity to have persisted (as with a photon in the double-slit experiment or things at a macroscopic level, such as humans). Even in the HOM experiment, there is some sort of continuity in that we started with two photons and ended up with two photons. But the history in terms of individual photon identity seems not to physically exist.

I never find arguments to the effect of "axiom X is inescapable and even denying it affirms it" compelling. Most of the time such arguments just assume the axiom in the metalanguage and use that assumption to claim the axiom will appear in any language whatsoever, even though it only appears in the corresponding object language because it's being assumed in the first place... — MindForged

Yes, though that objection may not apply if the object language contains its own metalanguage as natural languages do. There presumably are implicit axioms in natural language arguments.

That logic could improve so much with the advent of Classical Logic via Frege, and improve over the prior Aristotelian Logic, motivates me to try not to assume that whatever logic is dominant at present is infallible or some such. — MindForged

Agreed. I don't have any objection to formal logics, including dialetheism, and agree they can be useful. But I also think logic is integral to both ordinary language and empirical investigation and this would be the sense that logic is seen as fundamental to reality. Which is why there is generally assumed to be a principled answer to how the liar sentence should be handled, including by dialetheists.

And I am not sure what they mean by "cannot distinguish particles of the same kind". Do they mean that the particles are exactly the same? — litewave

It means that there are scenarios where you can have two (or more) particles that can't be physically distinguished, even in principle.

To see this, have a look at the Hong–Ou–Mandel effect. Figure 1 shows the four quantum states in superposition when two photons enter a beam splitter at the same time, one photon entering from above and one photon entering from below. (The minus sign for states 3 and 4 represents the phase shift for the lower photon reflecting from the lower side of the beam splitter.)

On a classical analysis, it would seem that on repeated runs of the experiment, each state should be observed a quarter of the time. However under quantum mechanics when (and only when) two states in superposition are physically identical, they interfere. What is actually observed is that the two photons always emerge together on either the upper or lower side of the beam splitter (i.e., either state 1 or 4). This means that states 2 and 3 always destructively interfere and so must therefore be physically identical, in principle. Which means there is no physical information identifying each emerging photon uniquely with one or the other of the entering photons. Thus raising an issue about our understanding of identity.

In what sense is logic supposed to be fundamental to reality? Obviously it's not supposed to be some purely empirical matter (e.g. go find a logical object), since while logic can be thought of in several ways (norms of argumentation, study of formal languages, theories of logical consequence, etc.) it's not supposed to be about anything in particular. — MindForged

Going back to Aristotle, logic was an empirical matter. For Aristotle, particular things were considered to be an inseparable composite of matter and form (hylomorphism). So logic just was the method of investigating and discovering the nature of reality (i.e., its form).

On an Aristotelian view, logical rules emerge naturally from our interactions and experiences in the world. That is, we observe, make distinctions, and find those rules that enable us to organize what we observe and to act purposefully in the world (including the LNC, ethical rules, and what have you).

It requires a different philosophical mindset that involves understanding the world holistically. That is in contrast to the familiar dualistic sense that sees matter and form as fundamentally separate and then struggles to see how they could possibly relate.

But are there only two options here - fideism, acceptance on faith, or 'scientific demonstration?'

Aside from faith (doxa or pistis) and science (scientia), I think there is another mode of knowing - sapience or sapientia. The reason being, that investigating the reality of spiritual matters, is undertaken in the context of a relationship with a Person, not, like scientific matters, measurements made of an object of perception. It is a different kind of 'knowing' - more like sapience, or gnosis, or noesis, or one of those kinds of terms that denotes a different cognitive 'style' to that of science as now conceived. But is also not strictly speaking simply a matter of belief. — Wayfarer

Fair enough (and I'll check out your link on Christian Platonism). But in the normal sense, a relationship with a person presupposes that the person exists and is demonstratively known to exist. And that presupposition, with respect to God, was just what was at issue for the Scholastics as with now.

He was also a voluntarist i.e. believed God to be forever beyond logic, and a nominalist. Some would argue that this is where the decline into materialism began. (See What's wrong with Ockham?) — Wayfarer

Yes, with the other side of the coin being the decline of Scholasticism (and Aristotelianism).

I found this quote interesting: 'Louis Dupré, for instance, has complained that “nominalist theology effectively removed God from creation…. The divine became relegated to a supernatural sphere separate from nature… thus making God largely inaccessible to reason.”'

While the writer finds that baffling, I think it accurately describes the transition from Aquinas' more holistic Aristotelian perspective to a more dualistic understanding of the world.

For me the issue is that it does not bother to explain or elucidate truth, but instead ignores it, to the extent of changing our language n order to avoid talking about it.

In other words pragmatism is not about truth but justifying belief. — Banno

On a Peircean pragmatism, truth can be explained as an abstraction that represents justified belief in the limit (i.e., when all the evidence is in). That conforms with ordinary usage.

That is in contrast to justified belief within a limited evidential context which can sometimes be false (or Gettiered).

Thanks - I am aware it is something like that. The trouble is, even after the extensive process proposed, the community might be wrong. — Banno

Yes the community might be wrong. But consider how that could be possible on the Peircean view. It implies there is further information that the community hasn't uncovered in their investigation. The true conclusion is the agreed result of the investigation in the limit (i.e., exhaustive), not necessarily when an investigation plateaus or reaches earlier consensus.

OK, if you prefer, I say it is true that Paris is the capital of France.

Again, from your answer, you can't say that. You can only approximate it in some way - and I'm not going to guess how. — Banno

There's a distinction between a definition of truth and whether some particular statement is true. Apo can say it is true. But (hypothetically) if the final consensus says that it isn't, then he just would have been wrong about that (on Peirce's definition).

The Peircean idea is that exhaustive inquiry by a community would lead to a single agreed conclusion which, by definition, would be true.

I don't know. I read that passage you linked to from the Summa, and I really don't think Aquinas does succeed in refuting Objection 1. And I think subsequent history has borne out the argument that the existence of God cannot be 'demonstrated scientifically'. — Wayfarer

The point is just that Aquinas (and the traditional Catholic church) claimed that it could be. They rejected fideism.

The point I was making was more specific - it was about the sense in which something like ‘the ontological argument’ can be regarded as persuasive. After all, none of those particular philosophers would concur that it is (granting that the first two were historically prior to it.) What I’m saying is, in order to regard it as conclusive, or to understand the terms of the argument in such a way that it seems to be, already indicates a pre-disposition to believing it; I think, perhaps, it is that very pre-disposition that is really meant by the term ‘belief’. (But I do quite agree that it’s a very delicate question.) — Wayfarer

Yes, though the defenders could claim the same about those who reject the arguments (and the Catholic church did!) However it's worth noting that not all Scholastics accepted the proofs. For example Aquinas himself rejected the Ontological argument and Ockham rejected all contemporary arguments for God's existence including Aquinas' Five Ways (he was a fideist).

I think it is fair to argue that the existence of scientific laws suggests an Author, but that whether that is so, must be a matter forever beyond scientific demonstration or (I suppose you could say) mundane certainty. That's why I said before, I think it's important to always have a sense of the unknown-ness of whatever is claimed to be ultimate or absolute; so, to say that God can be demonstrated or known scientifically seems hubristic to me. — Wayfarer

Sure, but part of that may just reflect a difference in philosophical outlook (for example, you seem to hold that such demonstrations are impossible in principle). Presumably from the Scholastics' point-of-view, their arguments seem sound to them. As they see it, those that disagree just need to critique the arguments. One's prior dispositions to belief or unbelief aren't relevant to that.

All fair points, but it's worth noting that Aquinas says the existence of God remains 'a matter of faith' — Wayfarer

In the above Aquinas says, "The existence of God ... are not articles of faith". However he also says there is nothing wrong with accepting it on faith, as long as it is scientifically demonstrable. Which is like accepting that Quantum Mechanics is true on faith rather than investigating it for oneself.

And I think it's demonstrably not the case that the 'existence of God' can be demonstrated scientifically - although I suppose a Thomist could answer that in light of the very many great unknowns that the natural sciences are grappling with, it might be yet! — Wayfarer

Keep in mind that Aristotelians have a broader conception of science than the conventional modern view. This includes the four causes (not merely a Humean efficient cause), realism about universals and substance hylomorphism. (Note: Aristotle's conception of science is actually very similar to Charles Sanders Peirce's conception that apo often describes.)

The initial problem is really one of translation. To show that the proofs do succeed or fail as scientific demonstrations in the Aristotelian sense requires familiarity with that world view (as you alluded to earlier).

This reminds me of Kuhn's thesis in his book The Structure of Scientific Revolutions which I think is just as applicable to our understanding of the Scholastic (and Aristotelian) proofs.

Kuhn wanted to explain his own experience of reading Aristotle, which first left him with the impression that Aristotle was an inexplicably poor scientist (Kuhn 1987). But careful study led to a change in his understanding that allowed him to see that Aristotle was indeed an excellent scientist. This could not simply be a matter of literally perceiving things differently. Kuhn took the incommensurability that prevented him from properly understanding Aristotle to be at least partly a linguistic, semantic matter. — Thomas Kuhn (SEP)

Certainly there were antagonists - Muslim and Jewish amongst them - but while they weren't Christian, they were also not atheist. ( I seem to recall that the Kalaam Cosmological argument was of Islamic origin.) — Wayfarer

Yes but nonetheless the Scholastics would have regarded their arguments to be applicable to atheists. Aquinas held that God's existence was demonstrable via natural experience and logic alone (without recourse to faith or special revelation). As he put it:

Whether it can be demonstrated that God exists? Reply to Objection 1: The existence of God and other like truths about God, which can be known by natural reason, are not articles of faith, but are preambles to the articles; for faith presupposes natural knowledge, even as grace presupposes nature, and perfection supposes something that can be perfected. Nevertheless, there is nothing to prevent a man, who cannot grasp a proof, accepting, as a matter of faith, something which in itself is capable of being scientifically known and demonstrated. — St. Thomas Aquinas - The Summa Theologica

True, but what would it take to make the effort? Do you think a conscientious atheist would be interested in making the effort? And what would such an effort consist of? How would they get into a kind of mental space where such Aristotelian ways of thinking would be meaningful to them? — Wayfarer

You could ask the same questions about philosophy generally. Why read Plato, Aristotle, Hume, Kant, Wittgenstein or anyone at all?

Interestingly Aquinas' answer was, "the study of philosophy is not about knowing what individuals thought, but about the way things are." And he found Aristotelian ways of thinking useful for that end.

So one motivation to understanding the arguments could be simply to find out whether they succeed or not (independently of one's prior dispositions towards theism or atheism - which I think answers Marcel's objection). Or, more broadly, whether Aristotelian ways of thinking provide insights into modern philosophical problems (e.g., mind-body, ethics, the relationship between science and philosophy and so on).

I disagree with Feser on that, at least in part because I think there were hardly any atheists in Aquinas' day, as belief in God was practically universal — Wayfarer

True, but there were theists of different types so articulating and defending the church's traditional position was seen as necessary.

The Scholastics were not fideists or truth relativists. On their view, if a proof fails, then it should be rejected by believers as well. There is nothing particularly edifying about a failed proof.

For example, Feser himself (following Aquinas) rejects the Ontological argument (see http://edwardfeser.blogspot.com.au/2010/11/anselms-ontological-argument.html).

But a further question I have for Feser is that if those proofs are as apodictic as they purport to be then how is there any room for disagreement, when there clearly is? Unless you share the basic presuppositions, then you're not going to be persuaded by such arguments, in my view. — Wayfarer

Sure and I don't think Feser denies that these arguments require considerable effort to learn and understand. That's just philosophy for you. But for anyone in the Aristotelian tradition, as Feser is, such presuppositions aren't merely subjective, they are as open to rational scrutiny as anything else. Perhaps on this, the Aristotelians anticipated Aumann's agreement theorem.

None of the scholastic 'arguments' were intended as polemical devices to convert non-believers. Nor were the psuedo-scientific hypothesis purporting to demonstrate some scientifically intelligible causal chain. They were exercises in intellectual edification that drew on various themes in the tradition of philosophy. But Anselm, Aquinas, and the rest, would never have relied on a philosophical argument to ground the truths of revelation, as they were by definition matters of faith. Given faith in the basic tenets, then the arguments are meaningful, but without that faith, they can only be empty words - and they all would have agreed with that. — Wayfarer

I think you'll find that the Scholastics intended their proofs of God's existence to be valid for believers and unbelievers alike just as Aristotle did for his own cosmological argument. Here's Ed Feser's comments on this (italics mine).

QUESTION (Jonathan): I read once on a blog post that the proofs for God were not intended as rhetorical or polemical proofs, in the sense of being intended to persuade unbelievers. They were more like edifying exercises for the faithful, but medieval theologians would not say that such philosophical arguments were sufficient to instill faith. Is this true?

DR. FESER: That is not true, and I suspect that the writers you read who said this misunderstand what “faith” means for a medieval theologian like Aquinas. The proofs were indeed meant to be completely rationally convincing even to someone who is initially coming to the question as an atheist. No faith is required at all.

The reason is that faith, as a thinker like Aquinas understands it, is a matter of believing something because it has been revealed by God. But before you can do that, you first have to establish that God really does exist in the first place and that he really has revealed something. And that requires evidence and argumentation. — Proofs for the Existence of God (#AMA with Dr. Edward Feser)

GTR has zero relevance to biological systems. It's about the problems of measurement. — Rich

There isn't a problem with measurement. Precisely-measured differences in clock tick rates have been observed that are consistent with the predictions of special and general relativity.

The Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity. — The Hafele–Keating experiment