I don't know if there's a single sentence in your post that's not confused or just plain wrong.

Let's take it sentence by sentence.

It's like the scientific method never happened! — tom

This is confused because just how we interpret mathematical equations as theories and just what we do or do not count as an explanation has no implications for whether it is or isn't like "the scientific method never happened."

It's just a matter of what people consider an explanation or not. And a large percentage of relevant academics consider mathematical equations read instrumentally to be explanations. — Terrapin Station

Explanation is an account of why something happens. I've just quoted Duhem, probably the main proponent of instrumentalism in the 20thC, who rejects that physical theories are explanatory. Do you have any cites to back up your contrary claim?

Now, it's when the model which is necessitated by the successful math, does not make sense, as is the case with MW, that we have to turn back to the principles whereby the mathematics is applied, to see where the mistakes are. — Metaphysician Undercover

So what about MW does not make sense, or is mistaken, on your view?

This is confused because just how we interpret mathematical equations as theories and just what we do or do not count as an explanation has no implications for whether it is or isn't like "the scientific method never happened." — Terrapin Station

Because you are confused and wrong, let me spell it out:

Scientific theories are expressed in mathematics because that is the means by which deductions are most easily made - i.e. it is the expression of the theory that is most amenable to testing.

Of course, despite Galileo's proclamation, the theory of Evolution has not yet been expressed mathematically. The theory of Evolution is expressed in ordinary language, and is nonetheless as successful as any other fundamental theory - it provides a good (the only) explanation of what it purports to explain.

You are ignoring the scientific method. For you, it is as if it never happened.

Maybe you could explain the discovery of quantum entanglement in your instrumentalist terms?

Do you have any cites to back up your contrary claim? — Andrew M

Not offhand--I'd have to search for some. What I had in mind is both people I personally know or have known and statements I've encountered over the years where there's no way I'd remember particular titles of papers. But all a citation would tell you anyway is that different people have different opinions and use words differently. Do you really doubt that?

We were talking about discoveries in (pure) mathematics, not physics.

So on your view, how we interpret mathematical equations as theories has implications for whether it's as if the scientific method never happened because _____ ?

Explanation is an account of why something happens. I've just quoted Duhem, probably the main proponent of instrumentalism in the 20thC, who rejects that physical theories are explanatory. Do you have any cites to back up your contrary claim? — Andrew M

It's quite extraordinary. Everyone, both supporters and detractors of Instrumentalism know what it means, except supporters on this forum.

Strangely enough, it is possible even to treat Evolution instrumentally, despite there being nothing to shut-up-and-calculate.

So on your view, how we interpret mathematical equations as theories has implications for whether it's as if the scientific method never happened because _____ ? — Terrapin Station

I know coherence is not your strong point, but could you translate that into something less incoherent?

We were talking about discoveries in (pure) mathematics, not physics. — aletheist

Maybe you could explain how the discovery of entanglement is a discovery in "(pure) mathematics" and not "physics" and why it therefore exist in the Reality?

could you translate that into something less incoherent? — tom

Not really interested. You should be able to understand what I wrote in the context of the current conversation.

Why would you expect me to explain something that I never claimed? I have not said anything at all about quantum entanglement.

Right, and my point was that this happens because mathematics is observational - manipulating and then reexamining a diagram can reveal new information. The difference, of course, is that we are observing our own (ideal) constructions, rather than something "out there" in the (actual) universe. — aletheist

So mathematics is "observational", whatever that means. We are "observing our own (ideal constructions)"

OK, so how did we manage to "observe our own ideal constructions" of phenomena that took 50 years to observe after their discovery?

Not really interested. — Terrapin Station

Sure, I figured that out long ago.

OK, so how did we manage to "observe our own ideal constructions" of phenomena that took 50 years to observe after their discovery? — tom

I have no idea what this means, or how it relates to anything that I have said here.

So what about MW does not make sense, or is mistaken, on your view? — Andrew M

It's a contradictory notion that all possible worlds are actual. In my understanding of possibilities, any possibility must be actualized before it can become an actuality. If all possible worlds are assumed to have actual existence, without a cause (source of actualization), then this is contradictory to my understanding of "possible".

I have no idea what this means, or how it relates to anything that I have said here. — aletheist

I realise that.

It's a contradictory notion that all possible worlds are actual. In my understanding of possibilities, any possibility must be actualized before it can become an actuality. If all possible worlds are assumed to have actual existence, without a cause (source of actualization), then this is contradictory to my understanding of "possible". — Metaphysician Undercover

MW is a causal theory - the wave function evolves deterministically with the parallel branching and merging built in. I've been making just your argument that possibilities - an epistemic term - cannot be invoked to explain interference effects. Only real superposition states can cause real interference effects.

Only real superposition states can cause real interference effects. — Andrew M

The interference effects are phenomenal. The phenomenon is described as possibilities. So the possibilities are epistemic. The possibilities are the epistemic representation of the phenomenon. We cannot invert this and say that the phenomenon is the actual existence of these possibilities, because the epistemic possibilities are simply a representation of the phenomenon. There is no principle which allows us to say that the phenomenon is the actual existence of the possibilities.

For example, we have an activity, a phenomenon, which is the flip of a coin. We can represent that as possibilities, one possibility of heads and one possibility of tails. We cannot invert this now, to say that the phenomenon which is the flipping of the coin, is the actual existence of both these two possibilities, such that in the flipping of the coin there exists the actuality of heads and also the actuality of tails. The fact that one cannot devise the means to determine the outcome, heads or tails, does not justify the claim that the phenomenon itself consists of the actuality of both the possibilities.

The interference effects are phenomenal. The phenomenon is described as possibilities. — Metaphysician Undercover

Quantum interference effects are real and are predicted by Schrodinger's equation. You won't find any mention of possibilities or probabilities in the Schrodinger equation.

Quantum interference effects are real and are predicted by Schrodinger's equation. You won't find any mention of possibilities or probabilities in the Schrodinger equation. — Andrew M

I don't think you describe this correctly. I believe that the Schrodinger equation is an interpretation of interference effects, which expresses the possible positioning of particles. Therefore the equation does represent possibilities. It is produced as an interpretation of the real phenomenon, interference effects, which renders that phenomenon as epistemic possibilities, the possible positions of particles. If a possible position is observed, it can be claimed to be actual. Otherwise there is no principle which allows us to affirm that possible positions are actual.

Therefore the equation does represent possibilities — Metaphysician Undercover

The Schrodinger Equation describes the deterministic evolution of the wave function of a quantum system. In the double-slit experiment, the system evolves from the initial state when the particle is emitted, to states at both slits and finally to states at the back screen.

This process is fully deterministic. There are no probabilities in the system, only amplitudes for each quantum state which are represented as complex numbers.

That is the ontology of the system. Probabilities only arise when making predictions about measurements within the system and this is governed by the Born rule.

The Schrodinger equation employs a Hamiltonian operator which is a description of particles within a system. According to Wikipedia: "Its spectrum is the set of possible outcomes when one measures the total energy of a system."

According to Wikipedia: "Its spectrum is the set of possible outcomes when one measures the total energy of a system." — Metaphysician Undercover

Note the word "measures".

Probabilistic language relates to the measurement of the system, not its ontology, which is what the Schrodinger equation describes. Here's Wikipedia:

The Schrödinger equation describes the (deterministic) evolution of the wave function of a particle. However, even if the wave function is known exactly, the result of a specific measurement on the wave function is uncertain.

The Hamiltonian operator is an integral part of the Schrodinger equation. There is no Schrodinger equation without it. It represents all the energy within the system. Probability is inherent within the Hamiltonian and therefore inherent within the Schrodinger.

Probabilistic language relates to the measurement of the system, not its ontology, which is what the Schrodinger equation describes. — Andrew M

In order to apply the Schrodinger, there must be some initial measurements of energy which is attributed to the system. Probability is inherent within the way that this energy is represented in the equation, it is the energy of the particles. The entire system is described in "probabilistic language". That is inherent in the Hamitonian operator which is an essential part of the description. It may be true, as you say, that the Schrodinger describes the evolution of the wave function, but it describes it in terms of particles, which is a probabilistic description.

Not true. We can easily observe that three sets of four trees equals twelve trees, for example.

We can easily observe that three sets of four trees equals twelve trees, for example. — John

How would you observe that? Wouldn't you have to actually count them, as one group of twelve, to reach that conclusion?

It represents all the energy within the system. Probability is inherent within the Hamiltonian — Metaphysician Undercover

Could you explain why probability is "inherent within the Hamiltonian?

In order to apply the Schrodinger, there must be some initial measurements of energy which is attributed to the system. — Metaphysician Undercover

Could you explain how the initial measurement is made in say a two-slit experiment, and what difference the result makes?

Probability is inherent within the way that this energy is represented in the equation, it is the energy of the particles. — Metaphysician Undercover

If probability is "the energy of the particles", why are different words used to state the same thing?

No it is easy enough to visualize three groups of four or four groups of three, and to see that it equals twelve. Of course it's not possible with larger numbers of objects. But really the idea of simple multiplication is just an extension of the idea of simple addition. For the simplest case where you have two objects it can be intuitively understood that one plus one equals two or that two times one equals two.

No it is easy enough to visualize three groups of four or four groups of three, and to see that it equals twelve. Of course it's not possible with larger numbers of objects. But really the idea of simple multiplication is just an extension of the idea of simple addition. For the simplest case where you have two objects it can be intuitively understood that one plus one equals two or that two times one equals two. — John

Personally, I find it easiest to visualise the negative inverse of the sum of all positive integers, when I think of 12.