If we allow that "zero" implies both positive and negative (in a self reflecting way) in common applications, instead of neither (as we actually do), this would destroy the integrity of "zero" — Metaphysician Undercover

But when we get down to the nitty gritty, of analyzing the representation for accuracy, we see the flaws, the differences between the supposed representation and the thing represented. — Metaphysician Undercover

You've demonstrated that by using this definition of inverse, zero is opposite to itself. — Metaphysician Undercover

But a thing being opposite to itself is contrary to common usage of "opposite". — Metaphysician Undercover

Additive inverse is different from multiplicative inverse, because neither represents a true inversion, — Metaphysician Undercover

What's of interest is what happens to points lying on the line (or point or plane) of reflection. Under the reflection, such points do not move! Thus a point on the surface of a mirror will reflect onto itself! — Real Gone Cat

Hmm. So was some sort of consensus reached as to which view was correct? — Banno

We have thus seen various proposals for how one could resolve the FR paradox. Some of them amount to giving up some of the most basic assumptions that underlie physical reasoning (like disallowing the use of standard logic, or postulating that future actions on an agent’s brain can invalidate conclusions drawn by the agent in the past). The others basically correspond to rejecting one of the explicit assumptions, Q, C, or S. — Testing quantum theory with thought experiments - Nuriya Nurgalieva and Renato Renner (section 6)

That's a clever, intriguing paper. Thanks. So where I above supposed that there may be two differing but agreed descriptions, the paper argues that there may be disagreement between what each observer deduces that the other observer sees; but Aaronson suggests this relies on the contradiction of a measurement not measured. — Banno

I've read through an explanation of Wigner's friend twice and can't figure it out how it applies beyond just plain old "quantum weirdness." — T Clark

I really don't think you've provided any "mathematical definition of opposite". — Metaphysician Undercover

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number),[1] sign change,[2] and negation.[3] For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself. — Additive inverse - Wikipedia

Here's a brief demonstration to help you understand what I am saying. Assume the smallest possible positive number is directly opposed, or inverse, to the largest possible negative number. In other words, we get as close to zero as possible on both sides, and maintain a balance of opposition between the two sides.

Now, let's assume that the quantity represented on each side is so near to nothing (zero) that we might be inclined to round it off. If we do such a thing, then the two quantities on each side become equal to each other, and the same as each other, as zero, instead of opposed to or inverse of one another.

Clearly, two inversely opposed and balancing quantities is not the same thing as one quantity, because that would mean that the positive number closest to zero is exactly the same as the negative number closest to zero, rather than having the two opposed to each other. — Metaphysician Undercover

If I could check something - Wigner's friend agrees that Wigner sees interference effects; and WIgner agrees that his friend sees a definite result? — Banno

That is, they agree as to what each of them sees.

Arguably, there is then 'a way that things are', but one that has two differing, yet agreed, descriptions. — Banno

I much admire the clarity of that post. — Banno

Taking the theme further, realist logic has it that a given statement has a truth value regardless of the whether that value is known, and so uses two truth states - true and false. Antirealism uses three truth states, true, false and a third that is neither - we might call it "undecided".

So we can ask, given your quantum coin, should we make use of a realist or antirealist grammar? — Banno

So the statement "The coin shows heads" implies a contradiction by Bells theorem, as does the statement "the coin shows tails", and prima facie we drop biconditional logic as a description of how things are (Putnam's realistic view) or we include measurement as fundamental to physics (shut up and calculate) - see Quantum Logic and Probability Theory for a discussion of the options, which become very complex very quickly. — Banno

I'm trying to decide the best way of dealing with the ideas of "real" or "reality" are, given quantum mechanics. The options, as I see them 1) Reality only applies at the classical level. 2) Reality exists at the quantum level, but it is a different kind of reality. 3) There is a broader meaning of "reality" which encompasses both classical and quantum scales. 4) There is no such thing as reality.

I'm willing to go with 3 as long as we keep in mind that it has to remain consistent with our everyday reality. I'm not even sure that's possible. — T Clark

No physicist questions the reality of the experimental equipment that they are using when performing these experiments, or of the measured outcomes.
— Andrew M

I wonder if that's true. — T Clark

Sorry Andrew, but "opposites" don't work that way. A thing is the same as itself, it cannot be opposite to itself. "Opposite" requires two. — Metaphysician Undercover

If numbers have an opposite, what is the opposite of zero? — Metaphysician Undercover

The idea of “real” or “reality” comes up frequently on the forum, often in relation to quantum mechanics. It has struck me the concept is not usually defined explicitly or carefully. — T Clark

One of the reasons I came up with the criteria for reality I did was that in several discussions posters claimed that quantum behavior at atomic and subatomic scale called into question the reality of phenomena at human scale. I reject that idea. — T Clark

OED: invert: reverse the position, order or place of. — Metaphysician Undercover

Obviously, negatives are not treated as the direct inverse of positives, because two positives multiplied together produce a positive number, and the two negatives multiplied together also produce the same positive number. — Metaphysician Undercover

-3 * -2 = -(-(3 * 2))
        = 6

That's the "additive inverse". It does not mean that negative numbers are the inverse of positive numbers in a general sense, only in the operation of addition. Without that qualification it wouldn't make sense to say that a thing (zero) could be the inverse of itself, because there would be no inversion involved there. — Metaphysician Undercover

I’m just looking up superdeterminism and trying to get my mind around it. Does the idea imply that causes somehow change things from one thing to another? — invizzy

I was assuming realism. In that case isn’t it true that Bell’s theory implies non-locality? (And also the fact that the measurement of spin in one place cause the spin in another?) — invizzy

The implication for so-called ‘entangled’ particles seems to be that the detection of a particle here can cause the spin of a particle on the other side of the galaxy. — invizzy

This is NOT to say the detection of a particle here can cause you to KNOW the spin of a particle on the other side of the galaxy, which would have been a more easily explainable fact. — invizzy

But negatives are not the inverse of positives — Metaphysician Undercover

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself. — Additive inverse - Wikipedia

The problem is that zero occupies a position on the number line. If it was a simple inversion, the count would go from one to negative one, as the two directions would be the inverse of each other. But there are two spaces between one and negative one. So zero occupies a place in the count, it plays a real role, and this is why the negatives are not a simple inversion of the positives, because that would rule out a position for zero. — Metaphysician Undercover

The issue of imaginary numbers is different though. It is an issue of there being two distinct conventions, yet each convention is correct in its own field of application. In the one case there is no square root of a negative number, in the other case there is. — Metaphysician Undercover

This means that there is two completely distinct ways of conceiving negative numbers, and not a simple matter of negative being the inverse of positive. It is how the negative are conceived to relate to the positive, that creates the problem, i.e. it is not a straight forward inversion due to the role that zero plays. — Metaphysician Undercover

Something I have wondering about recently is whether perhaps math is simply a better language to understand quantum mechanics than English, as English (and all other ordinary languages) are encumbered with too much normal macroscopic experiences and intuitions built into the way they are used. — PhilosophyRunner

Light and matter are both single entities, and the apparent duality arises in the limitations of our language. It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme — the quantum theory — which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies — the wave picture and the corpuscular picture. — The Physical Principles of the Quantum Theory - Werner Heisenberg

For a long time, understanding of negative numbers was delayed by the impossibility of having a negative-number amount of a physical object, for example "minus-three apples", and negative solutions to problems were considered "false". — Negative number, History - Wikipedia

That this subject [imaginary numbers] has hitherto been surrounded by mysterious obscurity, is to be attributed largely to an ill adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question. — Carl Friedrich Gauss

I see what you're trying to say, but you can't say "part" because parts are concrete rather than abstract exactly in the sense that they can exist independently. (That much I learned from Andrew M's explanation of hylomorphism.) And you really shouldn't be saying "collection" because that's a soft word for "class" and you precisely can't have classes without universals or predicates to define them. Clearly you're hoping to get structure — which is crucial, particulars aren't bags of properties — out of how the various collections are arranged.

Stepping back, this begins to sound like breaking down an object into its fundamental particles and then reassembling it, down the chain through chemistry to quarks and then back up again. We assume such a thing is possible in principle, I guess, but the argument for special sciences has always been that on the way back up, you have no way to know where you are and what you're building, so the particulars of interest are gone forever, leaving just an undifferentiated sea of particles. — Srap Tasmaner

A foreigner watching his first game of cricket learns what are the functions of the bowlers, the batsmen, the fielders, the umpires and the scorers. He then says ‘But there is no one left on the field to contribute the famous element of team-spirit. I see who does the bowling, the batting and the wicket-keeping; but I do not see whose role it is to exercise esprit de corps.’ Once more, it would have to be explained that he was looking for the wrong type of thing. Team-spirit is not another cricketing-operation supplementary to all of the other special tasks. It is, roughly, the keenness with which each of the special tasks is performed, and performing a task keenly is not performing two tasks. Certainly exhibiting team-spirit is not the same thing as bowling or catching, but nor is it a third thing such that we can say that the bowler first bowls and then exhibits team-spirit or that a fielder is at a given moment either catching or displaying esprit de corps. — Concept of Mind - Gilbert Ryle

I just can't get around the idea that in most, but not all, cases we use the words we do because they're the right ones. I don't think a linguistics that is all pragmatics with no syntax or semantics is a real option. — Srap Tasmaner

I wouldn't deny that there are choices we make, sometimes implicitly, which enable us to enact our purpose; I just don't think that makes our purpose constitutive of the objects we interact with. I think they have to be there, as they are, for us to have the options we do, among which we select the one that aligns with our purpose. If you can sometimes sort papers by author and sometimes by keyword, depending on your purpose at the moment, it's because they have authors and keywords. If they didn't, these wouldn't be options for you. — Srap Tasmaner

This situation is so simple than I think what we're really seeing is not exactly language at all but something more like dominance signaling that happens to use language because, well, there it is; we tend to use words even when what we're doing is really nothing more than growling articulately. — Srap Tasmaner

Are there any proposed experiments that could show which of locality and counterfactual definiteness is incorrect, or is it entirely dependent on an untestable interpretation? — Michael

Theorem 1. (No-go theorem for “observer-independent facts”) The following statements are incompatible (i.e., lead to a contradiction)

1. “Universal validity of quantum theory”. Quantum predictions hold at any scale, even if the measured system contains objects as large as an “observer“ (including her laboratory, memory etc.).

2. “Locality”. The choice of the measurement settings of one observer has no influence on the outcomes of the other distant observer(s).

3. “Freedom of choice”. The choice of measurement settings is statistically independent from the rest of the experiment.

4. “Observer-independent facts”. One can jointly assign truth values to the propositions about observed outcomes (“facts”) of different observers (as specified in the postulate above). — A No-Go Theorem for Observer-Independent Facts - Caslav Brukner

It says in the article that their experiments showed entanglement. I thought that meant that they showed non-locality. Are you saying that entanglement under the Copenhagen interpretation can be local? — Michael

If by "real" you are referring to counterfactual definiteness then Bell's theorem says that either counterfactual definiteness or locality (no "spooky action at a distance") are false.

The Nobel Prize in Physics is being awarded this year to three scientists who have shown locality to be false.

I don't yet know of any experiments that have shown counterfactual definiteness to be false. — Michael

I know it's prevalent. I was asking if it's declining in popularity. — frank

Do you think the idea of a collapse is on the way out? — frank

Heisenberg did not try to specify exactly what the collapse of the wavefunction meant. However, he emphasized that it should not be understood as a physical process.[11] Niels Bohr also repeatedly cautioned that we must give up a "pictorial representation", and perhaps also interpreted collapse as a formal, not physical, process.[12] — Wave function collapse - History and Context - Wikipedia

Dirac (1947) wrote “a measurement always causes the system to jump into an eigenstate of the dynamical variable being measured.” Here, we must be careful: a quantum jump (also called collapse) is something that happens in our description of the system, not to the system itself. Likewise, the time dependence of the wave function does not represent the evolution of a physical system. It only gives the evolution of probabilities for the outcomes of potential experiments on that system (Fuchs and Peres, 2000). — Quantum Information and Relativity Theory - Peres, Terno

Helpful video. I now "understand" the experiment Andrew M was trying to explain to me over in the truth thread, and it — sadly or happily — connects to the discussion I'm having with @Metaphysician Undercover about past, future, alethic modalities and determinateness. Was so hoping I could stay out of quantum stuff, but I guess I'll have to give up that dream. — Srap Tasmaner

I haven't watched all of this, because I try not to think about quantum mechanics, but Alastair Wilson has interesting things to say about the relation between physics and metaphysics as someone near the frontlines. — Srap Tasmaner

We noted that our various versions of quantum mechanics with collapse were, near
enough, empirically equivalent. But this equivalence does not extend to the no-collapse
hypothesis. If it is true, each of us will eventually gain evidence that supports it. When you
find yourself still alive after facing repeated danger, and you have far outlived the people
around you, that is just what you should have expected under no-collapse quantum
mechanics, according to the corrected intensity rule. However it is an enormously improbable occurrence under quantum mechanics with collapse. Thus no-collapse quantum
mechanics has enjoyed a predictive success which quantum mechanics with collapse fails
to match. Thus you have gained evidence against collapse.

On fictive verbs, or, ordinary language use gone irredeemably haywire — Mww

The gist of which is that if I see that it is raining, I also thereby know that it is raining. If I remember that I have an appointment, then I thereby also know that I have an appointment. — Srap Tasmaner

— Insofar as the point being made by Mww is about our conceptual apparatus and its role in our mental acts, I’ve got nothing helpful to say about that. — — Srap Tasmaner

In knowledge-first terms, I know it is raining because I already know what it is to be raining.

A precise reduction to the thread’s original question. I know what is true because I already know what it is to be true. I know what is true because I already know what truth is. — Mww

Most epistemologists agree that while knowing entails believing truly, believing truly does not entail knowing. Someone does not know something he believes truly on the say-so of his guru, who invents things to tell him at random without regard to their truth or falsity. Although merely believing truly involves a sort of success—getting the answer right—it also involves, unlike knowing, a sort of cognitive malfunction. Thus knowledge is a more full-blooded success condition than true belief. Knowledge first epistemology understands cases of cognitive malfunctioning in terms of their deviation from cases of cognitive functioning, as opposed to treating the two kinds of case more symmetrically. — Knowledge First Epistemology, Timothy Williamson - The Routledge Companion to Epistemology

We don't know with deductive certainty. But that's not the relevant or appropriate standard. The relevant standard is to look out the window and see whether it's raining.
— Andrew M

But this is just going around in a vicious circle. The example says that someone might be hosing the window. So according to the example, looking out the window doesn't give us the certainty required to know whether it is raining. — Metaphysician Undercover

In knowledge-first terms, I know it is raining because I already know what it is to be raining.

A precise reduction to the thread’s original question. I know what is true because I already know what it is to be true. I know what is true because I already know what truth is. — Mww

And we do not know whether it is raining or not, if knowing requires truth in your sense, — Metaphysician Undercover

One motive for demanding a guaranteed mistake-proof brand of observation seems to be this. It would be absurd to say that there are, or might be, matters of empirical fact which could not, in principle, be found out by observation; so, since any ordinary observation actually made might be mistaken, there must be a special sort of mistake-proof observation, in order that ‘empirical’ may be defined in terms of it. And then sensing is invented to play this role, for it is certainly improper to speak of a mistaken sensation. But the reason why sensation cannot be mistaken is not because it is a mistake-proof observing, but because it is not an observing at all. It is as absurd to call a sensation ‘veridical’ as to call it ‘mistaken’. The senses are neither honest nor deceitful. Nor does the argument justify us in postulating any other kind of automatically veridical observation. All it requires is what familiar facts provide, namely that observational mistakes, like any others, are detectable and corrigible; so no empirical fact which has in fact been missed by a lapse, need be missed by an endless series of lapses. What is wanted is not any peculiar certificated process, but the ordinary careful processes; not any incorrigible observations, but ordinary corrigible observations; not inoculation against mistakes, but ordinary precautions against them, ordinary tests for them and ordinary corrections of them. Ascertaining is not a process which bases upon a fund of certainties a superstructure of guesses; it is a process of making sure. Certainties are what we succeed in ascertaining, not things which we pick up by accident or benefaction. They are the wages of work, not the gifts of revelation. When the sabbatical notion of ‘the Given’ has given place to the week-day notion of ‘the ascertained’, we shall have bade farewell to both Phenomenalism and the Sense Datum Theory. — Gilbert Ryle, Concept of Mind

No, sorry. I’m reading his book, Knowledge and Its Limits. — Srap Tasmaner

“Knowledge first” is a slogan for epistemology that takes the distinction between knowledge and ignorance as the starting point from which to explain other cognitive matters. It reverses the direction dominant in much twentieth-century epistemology, which treated belief as explanatorily prior to knowledge, attempting to analyze knowledge as belief that meets further conditions, such as truth and justification. By contrast, a knowledge first epistemologist might treat believing something as treating it as if one knew it.

The most striking difference between knowledge and belief is that knowledge entails truth while belief does not. There is false belief but no false knowledge. Some people believe that Africa is a single country, but since it is false that it is a single country, they do not know that it is a single country. They just believe falsely that they know that Africa is a single country. In this sense, all knowledge but not all belief is successful. Thus knowledge first epistemology gives explanatory priority to success. This does not mean that belief first epistemology gives priority to failure. Rather, it gives explanatory priority to conditions that are neutral between success and failure: some beliefs constitute knowledge, others are false. — Knowledge First Epistemology, Timothy Williamson - The Routledge Companion to Epistemology

There’s a whole lot I don’t know yet, but my understanding is that a number of problems in epistemology present somewhat differently if you take knowledge seriously. One of the best-known claims of the book is known as “E = K,” that is, your total evidence is your total knowledge. When it comes to rational belief formation, for instance, it is your knowledge you rely on in deciding what to believe. There’s a similar transformation with assertibility, because we can specify the maxim as “Do not assert what you do not know,” rather than something about honest belief, evidence, justification, warrant, all that business. — Srap Tasmaner

Yes, and the hypothetical consists of statements which someone makes, therefore, assumptions. — Metaphysician Undercover

Do you understand that there is a separation between the hypothetical, which states the condition "it is actually raining", or "if it is raining", and the real world? — Metaphysician Undercover

The claim is that knowledge is a first-class mental state, distinct from belief, not a particular variety of belief. — Srap Tasmaner

If S knows that p, that also entails that S believes that p, and entails that p, but for all that, believing that p is not a component of knowing that p and neither is p being true. It’s Timothy Williamson’s “knowledge first” program, and I find it pretty persuasive, though I haven’t gotten through all the technical stuff yet. On his account, knowledge has no such components, and cannot be analyzed into, say, justified true belief. — Srap Tasmaner

The subject we were discussing is the issue with the use of "true", in the formulation of "knowledge" as justified true belief.
— Metaphysician Undercover

Which I for one have not defended, and would not defend, but Andrew M has said some things along those lines. I claim only that knowledge entails truth, not that truth is a component of knowledge. Make of that what you will. — Srap Tasmaner

I for one would appreciate it if you stopped saying things like this. Andrew and Michael are clearly not trying to deceive you. If they are mistaken, then they are mistaken, but there’s no deception here. — Srap Tasmaner

the problem is that your assertions that it does, and attempts show that it does, are nothing less than deception — Metaphysician Undercover

The hypothetical shows the logical consequences which follow from the assumption that it is actually raining in the real world. — Metaphysician Undercover

And, there is a very big difference in meaning between "it is actually raining in the real world", and "I assume it is actually raining in the real world". The latter recognizes the possibility that it is not raining in the real world. — Metaphysician Undercover

Andrew M Srap Tasmaner: we had a discussion about that Rovelli paper a few years ago here. — fdrake

You've discovered the attractor of philosophical discourse.
— Isaac

It's been done before, many, many times. (And whether I discovered it or invented it is exactly the debate.) — Srap Tasmaner

Your example only applies to a hypothetical world, in which it actually is raining. What good is it, if it doesn't apply to the real world? — Metaphysician Undercover

In other words, in the real world, it is possible that Alice could have real knowledge, — Metaphysician Undercover

but it is also possible that it is not knowledge. — Metaphysician Undercover

So we cannot correctly judge Alice as having knowledge because we cannot know the answer to this. Alice may have knowledge, or she may not. — Metaphysician Undercover