The scientific metaphysic relies on so many declarative/prescriptive statements which are themselves exempt from the criteria for science and are thus self-defeating on their own terms.
It is so peculiar when scientists are so dogmatic about science.
Are the formal sciences (logic/mathematics/computer science) not science? The testability/falsifiability criterion certainly excludes them from being sciences.
That statement isn't science. It's a definition. It's philosophy of science. It's the briefest summary of Karl Popper's definition of the scientific method. According to him, science can never be proven, only disproven.
If the definition of “science” excluded computer science as a science; would you say the definition is correct?
Of course there are different ways to look at science, like making a distinction between analytical (or empirical) science, and synthetic science; the science that makes stuff, rather than analysing it. Not sure if that's really a good distinction; the latter is really technology, isn't it?
This should've been clear in the context of my question:
"Are the formal sciences (logic/mathematics/computer science) not science?"
Not by this definition. The distinction between mathematical theorems and scientific theories is a useful one.
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?
I don't see it as exclusionary. You won't find many scientists in doubt about the fact that everything they do is built upon Logic and Mathematics, in addition to observation.
But don't we need a word to group fields that try to systematically describe, understand, and make predictions about the physical world? (Rather than seeking to explore and characterise idealised logical constructs?). What would you suggest?
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.
We need theory-producers to be more humble and provisional in their statements. We need theory-producers to forever remain open for their theories to be falsified or refined (whilst not being paralysed by doubt about theories that have stood the test of time). In other words, we need a slightly different culture.
But we also need a way to rebut someone who says "OK, but can you prove we're not living in a perfect simulation of reality that was created yesterday with a fabricated history?". In science, the rebuttal is "No, I can't prove that, science depends falsification rather than proof. Can you suggest a way I could falsify it? If not, then I'm going to get on with my work because it doesn't make a difference to my field either way"
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.
Sure. And I suspect a subset of pure mathematicians would want terminology to make clear that they produce theorems out of intellectual curiosity rather than because they have any regard for whether those theorems can be applied by other fields. Fortunately we can categorize things in multiple ways. I'm open to suggestions on the semantics, but something more widely understood and less clunky than my own theorem/theory-producers would be good! Perhaps "Natural Sciences" or "Empirical Sciences" might be more specific terms for fields that produce theories, if you like.
I differentiate simply because seems possible to do so. And as I said, because it's worth considering whether different processes and cultures are useful. I'm intrigued as to why you object so strongly.
I am afraid my intellect isn't quite up to the application of scientific principles to the philosophy of science itself this morning. I'll have to think harder about whether that's even a valid thing to do.
I don't think you've shown that falsifiability makes no difference in practice. The fact that it's possible to come up with some borderline or problematic examples (which themselves aren't terribly practical) doesn't mean it's not a useful criterion for a scientific theory. Falsifiability is a valuable filter for ideas that the natural sciences are not able to speak to. String theory has been criticized as unfalsifiable. I think a good string theorist would accept that it's a serious accusation that requires an answer.
To be honest I'm quite happy to say "All humans are mortal" is not a well-stated scientific theory. "Human lifespan is limited to 180 years" is better, as it may one day be falsified.
And if unfalsifiable propositons are not useful, then the Halting Problem is not useful. Isn't that silly?
I strongly object to categorizations which discriminate against valid science. 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 Carl Sagan is guilty of.
Of course, until the laws of thermodynamics are revised we can provisionally say that all programs actually running in nature will indeed stop at some point, no matter what is proven about idealized Turing machines.
And before I'm misunderstood. There are many ways the laws of thermodynamics can be tested. This prediction, unfortunately, cannot be tested. But it is a predicted consequence of the simplest known theory that explains of all sorts of observations about thermodynamics. Which is the limit of what the natural sciences aim to do here. Provisional truth based on observation vs. proven truth based on stated axioms.
I am explicitly not claiming that one truth is to be valued more than the other. I honestly don't think that. Merely noting, again, that the distinction is there to be made. I may be "discriminating between", but I'm certainly not "discriminating against".
It may or may not be a continuum. But even if only as an academic exercise can't we describe these two modes of knowledge? Curious researchers on both sides can certainly be informed and inspired by each others work, and can use the same techniques and tools.
Will the laws of nature stop running at some point?
The whole point is that the theoretical/abstract/mathematical constructs are what we use to compute consequences.
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.
Why would it be erroneous?
It's not really a car without an engine.
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.
Another problem with Popper is probably that outside of physics and chemistry, there are a lot of less exact sciences where predictions and refutations of a theory are never that clear cut. Like his issues with the theory of evolution.
Ultimately, I guess science is also simply "getting to stuff that works by trial and error".
In this reality I don’t have to do the mental gymnastics where the formal *sciences* aren’t sciences.
Take any criterion and apply it too strictly and there is some scientific discovery/progress in history which violates the rules and wouldn’t pass for “science” given any definition…
Take any given methodological approach - and you will always find counter examples in scientific history.
Almost like genius isn’t algorithmic.
There does seem to be this thing that good scientists are doing. Popper did seem to touch on some good aspects of it, like the willingness to be proven wrong.
I think maybe that's the part Popper got right, maybe Science is about an unbiased search for knoweldge with no other agenda other than a genuine curiousity. And maybe that's why demarcation is so hard, it's hard to tell a person's motives.
I donno, just throwing stuff out there. . . Still I mean at least we have a test that communists obviously fail which should make Popper happy.
> … that’s the part Popper got right, maybe science is about an unbiased search…
> …at least we have a test that communists obviously fail…
i could be misunderstanding what you’re implying and if so apologies, but Popper wasn’t some anti-communist nutbag, in fact, if he “wanted to oppose” communism, that would have been fundamentally counter to his ideal of keeping things “unbiased”
Popper was very open how much he admired Marx, he even tended to agree with Marx’ analysis of capitalism. where he disagreed was that 1) we were destined to be slaves to be servants if we 2) don’t have violent revolution.. He was quite clear that the state should absolutely be heavy handed to protect the lower classes from the wealthy’s constant tendencies to abuse the poor. Again, he agreed with much of Marx’s writing but where Marx thought it would require violent revolution, Popper believed we could use other methods such as “social engineering” to counter the rich. He was also concerned that so many people agreed about violent revolution being the only way out. He wrote about this admiration for Marx quite a bit:
> …a grandiose philosophic system, comparable or even superior to the holistic systems of Plato and Hegel. Marx was the last of the great holistic system builders.
and
> [Marx] made an honest attempt to apply rational methods to the most urgent problems of social life… His sincerity in his search for truth and his intellectual honesty distinguish him…
Popper was concerned that under unrestrained capitalism:
> ..the economically strong is free to bully one who is economically weak, and to rob him of his freedom,… Those who possess a surplus of food can force those who are starving into a ‘freely’ accepted servitude.”
Philosophy Now sums it up well, “Throughout his scrutiny of Marx, Popper treads a thin line between admiration and apprehension.” [0]
again, apologies if i misinterpreted what you were implying, just wanted to clarify that Popper wasn’t some kind of nutbag mccarthy style rabid anti-communist or whatever. he just thought we could “social engineer” our way away from psychotic nationalism and unchecked capitalism rather than requiring full blown revolution.
[0] https://philosophynow.org/issues/131/Popper_on_Marx_on_Histo...
Popper said he noticed that scientific materialism proposed by communists or Freud's theories was very different from the lecture he heard by Einstein - Einstein looked more like science.
Communism whatever anyone thinks about it is obviously not science. They claimed to be science at first and proposed scientific materialism as the future.
Today even communists seem to have recanted this idea instead preferring to criticize capitalism and present themselves as the only alternative. We all know today it's not science.
I don't want to debate politics only to say Communism was never science, it's politics - Popper noticed that quickly and it was one of the imputus for his ideas based in his own autobiography
He also dedicated his book the poverty of historicism to the countless men and women who lost their lives to fascism and Communism and their false belief in historical destiny
Open society and it's enemies also contains a long critique of Marx and the idea that history follows certain laws that must play out a certain way.
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.
Computers may be deterministic, but humans aren't.
The same software/idea produces wildly different understandings; and behaviour in differnt humans.
This is not to say that the proposition is false. It's possible that things can be unfalsifiable and true nonetheless, but those things would still exist outside the range of the scientific method (at least until/unless our understanding of reality expands enough to devise a test). That's an intentional trade-off, in order to gain greater confidence in the truth of the things we can test.
That’s simply not true.
Fr. LeMaitre developed the theory to explain observed red shifts of galaxies (deriving Hubble’s Law prior to Hubble.) He felt his theory (and science in general) had no connection or contradiction to his faith.
This actually came from the skeptics [0]. They were unwilling to believe a Catholic priest proposing a scientific theory too similar to his religious beliefs, about God creating the whole universe in an instant.
When the cosmic background radiation was discovered in 1964, the Big Bang was accepted by (mostly) everyone.
Theorems are unfalsifiable.
Secondly prospective theorems are absolutely falsifiable. Since a theorem is a statement that has been proven to be true yes they are unfalsifiable by definition - they have already passed that test. That doesn't really generalise to any sort of meaningful statement about the falsifiability of maths. Saying theorems are unfalsifiable is equivalent to saying "True statements can't be proven false". Well, yes.[1]
ie If I say Sean Hunter's theorem is that if you take a triangle with arbitrary sides a b c and angle opposite a of theta that
a^2 = b^2 + c^2 -42 b c cos theta
that statement is absolutely falsifiable (and false), which you can establish with basic geometry and trig[2]. When you demonstrate it not to be true it is not a theorem, so I was wrong to call it that. That is a demonstration of how maths is falsifiable.
[1] Even so it's often possible to make progress via proof by contradiction - showing that if this theorem were not true something else which we know to be true would be false. But in most of my maths books proving all of the theorems is the norm, so they are for sure falsifiable while you are trying to establish whether or not they are theorems.
[2] Drop an altitude from one of the angles at b and c and then use pythagoras and a bunch of cancelling. You will prove that a^2 = b^2 + c^2 -2bc cos theta of course. My statement is only true if a is the hypotenuse of a right triangle meaning cos theta is zero and my incorrect coefficient doesn't matter.
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" 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.
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 than Mathematics.
The fact that you are admitting proof-by-contradiction in your methodology tells me about your choice of foundations, but so what?
Either way, in constructive Mathematics "proof" by contradiction is not a valid proof.
...
> The presence of a counter-example to Sean Hunter's "theorem" simply demonstrates that it's not a theorem. It's a misnomer.
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. Do you see why?
You were the one who decided that the distinction between conjectures and theorems is important. I have now shown two examples of mathematics that was falsified.
Unless you're trying to say neither me nor Euler was a mathematician in which case we can agree about me but not about Euler.
>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.
What you have demonstrated is the falsification of "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.
Maybe Euler wasn't a Mathematician either. Who knows? Those sort of questions are undecidable.
You just answered the question yourself: that's a question for metaphysics and not science. Pick a lane! :)
So if the science of science is not science - is that not a contradiction?
Are you the kid who thinks he's edgy by saying in philosophy class: "It depends on the meaning of the word 'X'" every time someone tries to explain X to you?
Metaphysics is the study of "being qua being".
"[Aristotle] claims that each science studies a unified genus, but denies that there is a single genus for all beings". You're applying tautology without really understanding the construction of your own question.
https://academic.oup.com/edited-volume/28232/chapter-abstrac...
ELI5: asking about science isn't science. Like reading about painting isn't painting. Or more poetically, "Ce n'est pas une pipe"
Metaphysics.
Or as it is commonly referred to in computer science: function self-application. One example of which being the Y combinator (as in the name of this very forum).
I am applying a tautology in exactly the mathematical sense of a tautology; and I understand my construction just fine.
Had you been more charitable you would’ve addressed my argument; not your strawman of my argument.
> Or as it is commonly referred to in computer science: function self-application
No, that's recursion, not metaphysics.
Is computer science the same as programming, no. Computer science is the study of programming, not programming. You learn this in your first year of CS.
If you're smart enough to _really_ understand what a Y combinator is, this should be a piece of cake.
You can't. That's an axiom. Welcome to Philosophy of Science.
Science, at bottom, has some axioms.
1) Cause and effect
The same causes always create the same effects is an axiom. We assume that the God or the Devil don't change all the rules every other Thursday. If there is a being who arbitrarily shifts the rules, science loses a lot of its predictive power. Science will adjust to that, but it makes science much less useful.
2) Continuity
The rules "today" are the same as the rules "yesterday" are the same as the rules "tomorrow". The rules "here" are the same as the rules "there".
This is a little spicier as we do try to test that the rules haven't changed. We try to test whether or not the fundamental constants have shifted with time, for example. We try to see if things are behaving the same in our galaxy are the same as in otehr galaxies.
In fact, practically everything which defines "science" is about the ability to predict and quantify.
A) Side: "math" is NOT "science". Math, while certainly falsifiable, is neither quantitative nor predictive.
This, in fact, has provoked quite a bit of discussion: See: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
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".
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.
You still haven't figured out that "matter" is yet another man-made concept? An abstract idea. A collective noun. Itself a "fairy tale". A very useful fiction.
A substance which posesse "rest mass" in a universe where nothing is ever at rest sure is magical thinking (to me).
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.
>You can't prove a God exists
I never mentioned God, but here we are... You can't prove that matter exists either.
Matter is your God. It's the abstraction you worship.
People who live in glass houses shouldn't throw stones...