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Sometimes I wonder if science has limits. On one hand; logically no; there will always be something that we don’t understand and when we create new things it leads to other new things. On the other hand; logically yes. The universe cannot have an infinite amount of types of elementary particles as we would be still be discovering them. We haven’t discovered a new particle since the Higgs Boson in 2012. A better example would be the forces. We have 4; possibly 5. That might be it.

Is there any way to get an inkling whether there is infinity in science or finite? Any fundamental truths that lean more towards one answer?

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  • You could ask on PhysicsSE whether the Standard Model puts an upper bound on the number of hypothetical fundamental particles.
    – g s
    Dec 26, 2023 at 23:12
  • I think it would require a kind of scientific “meta-knowledge” by which we could prove how much knowledge we expect there to be. I think the problem is that nobody really has access to that meta-knowledge. This might be of some relevance: Pedersen, Nikolaj Jl Linding, and Christoph Kelp. "Second-Order Knowledge." The Routledge Companion to Epistemology. Routledge, 2010. 586-596. Your question kind of reminds me of some Nelson Goodman stuff about how scientific laws can never really be known through meta knowledge (I think) plato.stanford.edu/entries/goodman/#OldNewRidIndTheSol Dec 26, 2023 at 23:22
  • But I’ll just post this here to suggest some angles on the question, until someone gives a good answer. Logic is able to use proofs about itself which gives us general information about logic in its totality, like the incompleteness theorem. But arguably, it seems like such a thing is lacking, for science in general. Dec 26, 2023 at 23:24
  • By everything we know, the universe is finite. Speculation to the contrary is just that. Yet we have an intuition of the infinite, as familiar as the counting numbers and the fact, readily apparent to every school child, that you can "always add one more." It's a mystery. Perhaps our intuition of the infinite is a clue that infinity is real. But wouldn't that be something! Higher set theory would be physically instantiated. Physics experiments could investigate the Continuum hypothesis. When physicists apply for grants to do that, I'll believe they're serious about infinity. Till then? Finite!
    – user4894
    Dec 27, 2023 at 2:43
  • I would argue, that one way to see if infinity may exist in the Universe is if we can build predictive models which assume infinity exists... and those models are equally/more effective than models which only assume finitude. Jan 4 at 22:54

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IMO the answer to your question concerning the amount of “things” (composite and elementary particles) and scientific insights leans towards infinity:

  1. Isaak Newton’s view how what is known relates to what is unknown in science:

    I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

  2. You write in your question “there will always be something that we don’t understand”.

    Concerning the amount of energy/mass in the known universum we understand only about 5%. The rest is dark matter and dark energy in the form of unknown matter and unknown radiation.

  3. More radical: More than that, which we do not understand, is what we do not even know that it exists. Each time when increasing the energy of the current high-energy accelerators, new particles are detected.

  4. Moreover I even expect that the mental capabilities of the human species are limited - because we see the limits of the mental capabilities of other species. Hence in the universe there will exist mechanisms, structures, and laws which the human mind principally cannot understand.

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Here is one way to get an inkling, perhaps. I seem to remember reading that the number of particles in the Universe was around 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. That's ten with 80 zeros, or 1080. I don't know which particles they meant, but that's not the point. Ten with 80 zero's is a big number, but it is an utterly utterly utterly (repeat utterly as many times as you like) minuscule number compared to ten with 1080 zeros. Let's call that number M1. That is ten with as many zeros as there are particles in the Universe. It is roughly the number of particles in 1080 universes. That is a big number again, but it is an utterly (repeat as many times as you like) minuscule number compared to ten with M1 zeros, which we might call M2, which in turn is utterly minuscule compared to ten with M2 zeros. I honestly have no comprehension at all of the scale of M2. However, I could I could iterate mindlessly all day, defining more and more numbers, each preposterously larger that the previous utterly unimaginable number and I could carry on doing that for the rest of my life, perhaps reaching M105 and that number is virtually nothing compared to MM, which is a number so big that I have lost all sense about how I could possibly give an intuition as to its size. Then let's go further and define N1 as ten with MM zeros, which is unimaginably bigger than MM. Then I could define N2 as ten with N1 zeros, and so on and so on. I could spend my life defining classes of numbers each unimaginably bigger than the previous unimaginable class of numbers, and the number I would eventually reach would still be zero when divided by infinity. So do I think the Universe might contain infinitely many things? Not even close.

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  • Okay but will humanity ever hit that limit?
    – Max
    Dec 27, 2023 at 20:41
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Sometimes I wonder if science has limits.

Science is some type of knowledge (essentially, that which is obtained using the scientific method). Ergo, obviously, obviously, yes, knowledge has limits.

On one hand; logically no; there will always be something that we don’t understand and when we create new things it leads to other new things.

For example, an AI model (which is essentially a set of neural weights). We can't understand how, AI models just work.

On the other hand; logically yes. The universe cannot have an infinite amount of types of elementary particles [...]

Why so?

[...] as we would be still be discovering them.

You say 12 years is the limit to say there are no more fundamental particles? Why not 13? Why not 13 googolplex years?

Is there any way to get an inkling whether there is infinity in science or finite?

There could be infinite atoms (and atomic interactions) in the universe, your brain is simply not capable of knowing each one of them. Science (formal) or human (informal) knowledge are obviously finite.

Any fundamental truths that lean more towards one answer?

Knowledge is a model of the world. All models are limited. There is no model like any original thing. Even a perfect copy of the Mona Lisa is not the Mona Lisa.

You will probably argue entering into metaphysics: consider that scientific knowledge is about physical, not metaphysical facts: you might argue that the number 2 in my head is the same as the number 2 in your head (ergo, a model can be identical to the original): perhaps they are, perhaps they are not: there is no scientific way to prove it. Metaphysical facts are not part of scientific knowledge, which is your question.

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