You still haven't figured out that "matter" is yet another man-made concept? An abstract idea. A collective noun. Itself a (very useful) "fairy tale".

A substance which posesses "rest mass" in a universe where nothing is ever at rest sure sounds like magical thinking (to me). And what do you even make of point-like particles in physics? They have no volume - so they are not matter. And what about anitmatter?

You haven't yet come to the self-realization that you are committing the reification fallacy by promoting a man-made concept to a totalizing/generalizing/all-encompassing ontological status.

Matter is your God. It's the abstraction you worship.

You are right in saying that we'll never agree; for if I were to agree with you I too would be wrong.

Assume complexity then move towards simplicity.

Assume simplicity then move towards complexity.

One of them will succeed sooner than the other. Dialectic...

Notice how you are constantly appealing to abstract unobservables to make your claims. No shame in that - all science does it. Quantities, numbers, fields, processes etc. etc. etc.

That is precisely the metaphysical woo woo you are busy criticising. Formalism is all about turning that woo-woo into well-defined concepts.

What's a "process"? Show me one.

Only way I know how is to give you more metaphysical woo woo.

https://en.wikipedia.org/wiki/Process_calculus

You know all that religious woo-woo about omniscience? We are still talking about it and even using it...

https://ncatlab.org/nlab/show/principle+of+omniscience

All this religious/devine woo-woo...

  The central dogma of computational trinitarianism holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation. There is no preferred route to enlightenment: each aspect provides insights that comprise the experience of computation in our lives.

It is your philosophical predisposition to dismantle things and understand how they work.

But when you are done learning you need to put all the parts back together and form one coherent/cohesive whole for a system to function.

It is the same old tension between reductionism, holism and systems thinking in the balance.

If you have no formalisms you can't compute any consequences - there is nothing to test. You have no science.

So treating Mathematics and science as "separate disciplines", even though they function as one symbiotic whole - that's the conceptual error.

It's not really a car without an engine.

In this reality I don’t have to do the mental gymnastics where the formal *sciences* aren’t sciences.

In this reality there is at least one unfalsifiable (not even in principle) true claim: the halting problem

This renders falsifiability as a modal criterion. Useful in some scientific contexts - useless in others.

It is just as possible to differentiate as it is to integrate.

If it is determined a priori that unfalsifiable propositions are not useful, then knowing the result of the Halting Problem is not useful. Isn't that silly?

I strongly object to categorizations which discriminate against valid science (knowledge? truth? understanding? reasoning? Useful facts?). Is all.

The human process of trying to udnerstand reality is continuous, not discrete, so it's silly to reason about it in terms of discrete categories. It necessarily leads to confusion; and the sort of gatekeeping and self-justification Carl Sagan is guilty of.

Science benefits much more from being defined too broadly; than being defined too narrowly.

I'd rather be too permissive then ignore the junk; than be too restrictive and never even encounter good ideas which were erroneously discarded as junk.

Alan Turing: The claims made in the Halting Problem is genrally true, and is therefore unfalsifiable even in principle.

Carl Sagan: Propositions that are untestable, unfalsifiable are not worth much.

All computer scientists in synchronized act of distributed consensus: Bullshit.

It's like a dependency graph. Or something.

Your insistence on "making a difference" seems to echo the sentiment of many pragmatists:

  It is astonishing to see how many philosophical disputes collapse into insignificance the moment you subject them to this simple test of tracing a concrete consequence. There can be no difference anywhere that doesn’t make a difference elsewhere – no difference in abstract truth that doesn’t express itself in a difference in concrete fact and in conduct consequent upon that fact, imposed on somebody, somehow, somewhere, and somewhen. The whole function of philosophy ought to be to find out what definite difference it will make to you and me, at definite instants of our life, if this world-formula or that world-formula be the true one. --William James

Is "All humans are mortal." falsifiable or unfalsifiable? It sure is falsifiable in theory, but unfalsifiable in practice. Any living human is potentially immortal until they actually die.

Any running process is potentially non-halting, until it actually halts.

If falsifiability doesn't make a difference in practice (and it doesn't!) then I guess we can all get on with whatever scientific discipline we are busy practicing.

So, I'm going to carry on my life knowing at least one unfalsifiable scientific truth: the theorem known as The Halting Problem.

It's not even wrong, because it's right.

Anybody who insists the Halting Problem is falsifiable (even in principle) is welcome to solve it in principle.

Maybe it's the science of science? Maybe it's the philosophy of philosophy? Maybe it's the science of philosophy? Maybe it's the philosophy of science?

Maybe it's all the same under naturalism?

Studying science (itself a natural process) using our computational understanding of what a "process" is and does sure fits the Oxford definition of "science".

It's precisely the grouping I am talking about.

If you group science in such a way so that logic/mathematics/computer science falls outside the group then isn't that an erroneous grouping?

Isn't that a silly definition?

True and False are idealized logical constructs. It's the idea; and the idealization of the notion that there is a difference between Truth and Falsehood. Or if you want to get biblical - there is a difference between Right and Wrong.

If True ≡ False then... fuck it.

Which is precisely the problem with all definitions I am drawing attention to - they are exclusionary in nature.

Sometimes creating distinctions is useful. Sometimes erasing distinctions is even more useful.

How much physics could you do without Noether's theorem?

>That is what I said. I showed a mathematical statement and I showed how you could falsify it. >Since you said "mathematics is not falsifiable" I have shown your statement is not true.

You have taken it upon yourself to interpret "Mathematics is not falsifiable" as broadly as needed in order to confirm your own biases; and then proceeded to attack a strawman instead of a steelman. That's the lack of charity...

>You were the one who decided that the distinction between conjectures and theorems is important.

And you were the one who decided that it isn't; so you falsely equated them.

What you have demonstrated is the falsification of the statement "X is a theorem"; not the falsification of "mathematics is not falsifiable." - a hasty generalization fallacy.

Which doesn't demonstrate anything of import or relevance whatsoever. Obviously a non-theorem is not a theorem. This is no more interesting than demonstrating that non-Mathematics is not Mathematics.

This in no way diminishes or falsifies my own claim that theorems are unfalsifiable! And neither is Mathematics.

Because if you do falsify it - then it was never a theorem. By definition. Theorems are true, not false. A false theorem is a contradiction in terms. A misconception. An error in reasoning.

Maybe Euler wasn't a Mathematician either. Who knows? Those sort of questions are undecidable.

I have some idea about what you do and don't know about definition and definability (in general) given the words you've said so far and the way you've used them.

Prospective theorems are not theorems until a proof is presented. At which point they become retrospective theorems.

All that "falsification" and counter-examples prove is that the so-called "proof" of a "theorem" wasn't. If you have indeed provided a counter-example that's a proof of negation which raises questions: what was wrong with the original "proof" of the theorem? Since proofs are programs - there must have been a bug in the proof. Better type-check that proof/program...

The presence of a counter-example to Sean Hunter's "theorem" simply demonstrates that it's not a theorem. It's a misnomer. Theorems are exactly those Mathematical stataments for which no proof of negation exists.

You seem to be presupposing some particular kind of mathematics. I am talking about all possible Mathematics in general; of which the particular Mathematics you are currently using is just one particular instance. A historical and cultural coincidence.

There's a Mathematical paradigm in which proof-by-contradiction is a valid proof method e.g mathematics founded upon classical logic.

And there's a Mathematical paradigm in which proof-by-contradiction is not a valid proof method e.g mathematics founded upon intuitionistic logic. This is basically what we call Computer Science. It has fewer axioms than Classical Mathematics (e.g the axiom of choice is severely restricted) and so it's a much stronger proof-system. You could even say Intuitionistic Mathematics (which is basically CS) is "more foundational" (it is much closer to the foundations?) than Mathematics.

The fact that you are admitting proof-by-contradiction in your methodology tells me about your choice of foundations, but so what? There's a foundation which axiomatically pre-supposes choice; and a foundation which doesn't.

And in the foundations where choice is not axiomatic "proof" by contradiction is not a valid proof.

The reasoning goes something like this:

1. Choice implies excluded middle. 2. Excluded middle implies all proposition are either true or false. 3. Excluded middle implies that proof by contradiction is valid.

Rejecting 1 results in the rejection of 2 and 3 also.

https://en.wikipedia.org/wiki/Diaconescu%27s_theorem

What always seem like great ideas in theory, innevitably has to cope with the (mis)understanding; (mis)interpretation; and (mis)application of said idea by the mass population.

In the domains where simplicity prevails Occam's razor is more probable.

In domains where complexity prevails Hickam's dictum is more probable.

Is is true? What makes it true?

>A concept which will in no way ever make a difference, is meaningless.

So what would falsify this statement? How would you convince yourself that you are wrong?

This should've been clear in the context of my question:

"Are the formal sciences (logic/mathematics/computer science) not science?"

metaphysics /ˌmɛtəˈfɪzɪks/ noun the branch of philosophy that deals with the first principles of things, including abstract concepts such as being, knowing, identity, time, and space.

First principles? Like logical/mathematical axioms? Sprinkle abstraction. Identity? f(x) = x ?

Time? Space? Spacetime? Minkowsky space?

On a fuzzy-match that sounds ludicrously similar to the sort of stuff the formal sciences concern themselves with. Almost as if the distinction between science and philosophy is non-existence given the demarcation problem.