[ukj]

How can we disprove the hypothesis “If we can’t disprove it - it isn’t science.”?

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.

[mcv]

> How can we disprove the hypothesis “If we can’t disprove it - it isn’t science.”?

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.

[ukj]

It is in the nature of definitions to include some things and exclude others.

If the definition of “science” excluded computer science as a science; would you say the definition is correct?

[mcv]

In this context, most of computer science is more a form of applied mathematics.

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?

[JohnFen]

There is such a thing as computer science, but the majority of what gets called that is really engineering, not science. People often get those two things confused because they have a fair bit of overlap in the Venn diagram, but they are two different things.

[ukj]

I am talking about (theoretical) computer science, not (practical) software engineering.

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

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

[mcv]

Math is itself indeed not science. It is the language of science. It follows different rules than empirical sciences. But note that word "empirical" there; Popper was really only talking about empirical science, and according to him, that was the only real science. You could argue that there are non-empirical sciences.

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".

[ukj]

Ok… I reject your reality and substitute my own.

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.

[anonymous_sorry]

> "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.

[ukj]

>Not by this definition.

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?

[bsder]

> How can we disprove the hypothesis “If we can’t disprove it - it isn’t science.”?

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...

[ukj]

Is it the "philosophy of science"? What is now called "science" was once called "natural philosophy"?

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".

[seanhunter]

When did maths become unfalsifiable? Someone should have told these guys https://www.ams.org/journals/bull/1966-72-06/S0002-9904-1966...

[ukj]

Someone should tell you that there is a difference between a conjecture and a theorem.

Theorems are unfalsifiable.

[seanhunter]

Firstly there's no need whatsoever to be rude even if I'm wrong. It doesn't help the discussion and isn't nice. You also don't know anything whatsoever about what I do and don't know about maths or the definitions of words.

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.

[ukj]

I merely attempting to reciprocate/mirror your tone. You are the one (self)identifying it as "rude".

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

[seanhunter]

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

...

> 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.

[ukj]

Your failure to understand what I am saying is abysmal.

>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.

[demondemidi]

> How can we disprove the hypothesis “If we can’t disprove it - it isn’t science.”?

You just answered the question yourself: that's a question for metaphysics and not science. Pick a lane! :)

[ukj]

One way to view metaphysics is as the science of science.

So if the science of science is not science - is that not a contradiction?

[demondemidi]

That's not what metaphysics is about.

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"

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

[ukj]

The study of being qua being; or science qua science; or mathematics qua mathematics; or X qua X for any X.

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.

[demondemidi]

I'm charitable by trying to teach you with examples.

> 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.

[ukj]

I am struggling to spot the charity in all your condescension.

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.

[Kranar]

No because metaphysics is not the science of science.

[ukj]

What makes this assertion; or the assertion “If it isn’t disprovable - it isn’t science” true?

[demondemidi]

What makes this assertion? The literal definition of the term.

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?

[vivekd]

and you hit one of the main objections to the theory of falsifiability as the criterion of science. There are also other more serious ones, like the obvious fact that actual science does't seem to actually work this way. The idea is more to explain observations in a coherent way rather than to be falsifiable for example. One example is the big bang theory being proposed by a Catholic astronomer who didn't like the then prevaling idea that the universe did not have a beginning or end because it went against his religious beliefs. Or Kepler looking for planets at locations in accord with musical harmonies because he though it was consistent with the existence of a God

[JackFr]

> One example is the big bang theory being proposed by a Catholic astronomer who didn't like the then prevaling idea that the universe did not have a beginning or end because it went against his religious beliefs.

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.

[borlanco]

> One example is the big bang theory being proposed by a Catholic astronomer who didn't like the then prevaling idea that the universe did not have a beginning or end because it went against his religious beliefs.

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.

[0] https://en.m.wikipedia.org/wiki/Big_Bang#Development

[JohnFen]

The reason that falsifiability is a core requirement of science is because if there is no way a proposition can possibly be falsified, then there is no way to objectively assess whether or not it is true.

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.

[ukj]

Personally, I am weary of the notion of “actual science” since science is not a well-defined term. The demarcation problem isn’t solved; and philosophers like Fayerabend in his book “Against method” suggest that science is more of an anarchic enterprise than any particular set of methods.

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.

[vivekd]

sure, but I mean, it's pretty hard to call flat earthers or proponents of voodo unscientific if we have to admit that we haven't solved the demarcation problem. Also more importantly for Popper, he wanted to oppose communists' ideas of "scientific materialism."

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.

[pengstrom]

I mean, the non-schizo proponents for flat earth does approach it with scepticism. It's just that the their required level of proof are unreasonable. Any experiment, no matter how genuinely designed, is exempt from flaws. Science works because the detractors doesn't have the energy to waste decades in the academic apparatus, unlike true curiosity.

[toofy]

> … he wanted to oppose communists' ideas of "scientific materialism."

> … 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...

[vivekd]

He wrote an autobiography - he was a young man who was a communist because he believed in scientific materialism. He later recanted after some of his friends were shot and killed by the police.

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.

[ukj]

The problem with all ideas is always their reification. Computers may be deterministic, but humans aren't. The same software/idea produces wildly different understandings; and behaviour in differnt humans.

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.

[stjohnswarts]

Because they have worked over time, empirically as opposed to a lot woo woo stuff proposed by religion, spirituality, metaphysics, mentally ill, etc. which can never be disproved but which really don't have any value in those areas where we apply science like technology and attempting to understand natural processes

[ukj]

You seem to be speaking from a place of greatly diminished self-awareness.

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.

https://ncatlab.org/nlab/show/computational+trilogy

[stjohnswarts]

If you want to believe in fairy tales then enjoy them. I prefer materialism. We will never agree on this. You can't prove a God exists, so I simply don't care about the topic other than how it affects civilization negatively by promoting magical thinking and religious fanaticism/intolerance. I tolerate people who are religious, I don't wish them any harm; the opposite is quite untrue for a large proportion of the religious world for atheists/"infidels".

[ukj]

The deep irony in valuing matter more than valuing values is never wasted on me.

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.