So I am to discuss the question with reference to two areas of knowledge. I chose to talk about mathematics and the arts (including literature, visual arts, music, etc.).

I put a lot of thought into this, but am still confused in terms of the underlying juxtaposition of the question and the philosophical difficulty. My teacher said that this is one of the most difficult philosophical questions he has come across, but I fail to understand or see why this statement is difficult, which makes me think that I dont understand it.

  • Propositions, consisting of a subject and predicate, exemplify the basic form of knowledge. The subject is presupposed to remain uniform in some respect through time. The predicate is also a uniformity which may be applied to various subjects. Knowledge of uniformity cannot be learned from experience because all learning presupposes uniformity as necessary to make knowledge possible. Otherwise, we would have to be able to seek without knowing what is sought, and we would have to be able to find it without any means of knowing whether or not it was found. – user3017 Nov 20 '17 at 9:52
  • @PédeLeão Would you say that the title is an antithesis? – Selena Carlos Nov 20 '17 at 21:55
  • I'm not sure what you mean, but I agree with what the title says. I believe we all have an innate hunger for knowledge which somehow involves the capacity to recognize uniformities in the information which the senses provide. – user3017 Nov 21 '17 at 1:02

Long comment

Mathematics is not the only topic.

You have to consider empirical knowledge and the related Problem of Induction:

As Hume wrote, induction concerns how things behave when they go "beyond the present testimony of the senses, or the records of our memory". Hume argues that we tend to believe that things behave in a regular manner, meaning that patterns in the behaviour of objects seem to persist into the future, and throughout the unobserved present. Hume's argument is that we cannot rationally justify the claim that nature will continue to be uniform [...]

Regarding arts (mainly "visual" ones, but also music) , aesthetic perception is based on forms, and thus regularities. See e.g. Rudolf Arnheim, Art and Visual Perception: A Psychology of the Creative Eye.

Regarding mathematics, you can see: John Adam, Mathematics in Nature: Modeling Patterns in the Natural World as well as: Ian Stewart, Nature's Numbers: The Unreal Reality of Mathematics.


I believe this is one side of the more general Problem of Universals, to use the medieval designation.

If you take your "fail to understand" as the stimulus for continuing the thinking through of the issue you have set upon, you are already in the same position as the philosophers to answer this. Individuality pierces everything one comes across, an oak with resin sticking to its autumnal leaves, a person plunged into contemplation of a difficulty in philosophy, the house at the corner of the block. Each phenomenon is shaped by being part of a class of things, so that one could speak of other cases of each thing. No individuality without universality. The pervasive presence of this difficulty is hiding in each nook and corner, pacing back and forth.


It has to be difficult because it took the demolition of Logical Positivism to get to it. The hard part, historically, has been admitting that our sense of uniformity is an assumption and not some form of knowledge itself that can be acquired or tested.

Hume pointed this out very clearly, but the deduction got no purchase -- it was seen as a combination of nihilism and blind faith, and it was an argument substituting necessity for uniformity. But our sense of necessity is a presumption of uniformity itself. What if the overall rule is good, and this instance is flawed?

Kant took Hume seriously, but then addressed the problem with a distinction that lacked a difference, proposing 'noumena', a basic reality that had rules of its own, that were only partially detectable in phenomena, and much of philosophy was satisfied with that answer or some simple parallel.

Quine (and to a lesser degree Wittgenstein before him) eventually got back behind Hume's problem and realized that this is a bias that cannot be tested, not just in the sense that we cannot prove it, but that if we pursue it to its logical end, it falls apart on its own. It is necessary to our thinking to presume that simplification is what makes ideas possible. But how would we know? We only have our ideas, and we all started with this bias to begin with.

If uniformities can force themselves upon us without our coming to them ready formed to accept them (or to make them up, when we can't accept the facts without them), then we do not have the assumption of their existence we have some natural sense of their objective existence. That possibility appeals to us so much that it is an obvious basis behind all of our science, and before that, behind all of Western religion. (There is a very good argument, from Whitehead, that the West got to science first not because of our philosophy, but because monotheism, with a focus on unity, enshrines uniformity above other aspects of logic.)

But we know that science occasionally discards large parts of its basis, and we have seen the departure from Orthodoxy and the logic of Protestantism take apart and reconstitute our religion very effectively, maintaining its purpose throughout. We find these things hard to take, and almost impossible to incorporate into a functioning philosophical outlook that is not nihilistic to the point of being unproductive. Instead of some deeper form of fluid-yet-stable belief that the data calls for, we end up with modern post-modernism which oversimplifies as a matter of course because it feels like there is no reason not to.

(I am purposely not referencing this because I think it is a homework assignment, and if you want to reconstitute this argument, you need to find these references for yourself.)

  • ''it was seen as a combination of nihilism and blind faith, and it was an argument substituting necessity for uniformity'' are you suggesting that Hume, who opposed induction, proposed deduction, however his ideas were unpopular because his arguments seemed to replace necessity by uniformity. I am sort of confused, since isn't induction presuming uniformity? – Selena Carlos Dec 15 '17 at 1:45
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    @SelenaCarlos Debunking induction consisted in showing that the inherent idea of uniformity in induction cannot be justified, as opposed to deduction. I want to point out that in Kant's third critique, the idea attributed to Quine and Wittgenstein here is already there: We might assume uniformity as subjective principle, but it cannot be justified as necessary for empirical knowledge. – Philip Klöcking Dec 15 '17 at 12:38
  • @PhilipKlöcking That is not the attributed idea. The idea is, as stated "not just... that we cannot prove it, but that if we pursue it to its logical end, it falls apart on its own." The argument in 'Vagueness' and 'Natural Kinds', is that uniformity can be proven necessary for empirical knowledge and that means we have no empirical knowledge, only a subjective consensus. If the idea was already in Kant, he could not have presumed noumena solved anything. – jobermark Dec 15 '17 at 17:18
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    @jobermark: The idea always has been in Kant, it has been ignored by Neo-Kantian philosophers until Cassirer, who in turn was widely ignored by positivists. – Philip Klöcking Dec 15 '17 at 17:22

Very good question, except in the text I don't see the actual question. So I'm going to answer I hope your title.

The answer is no. There cannot be knowledge without the uniformity of the universe. Knowledge is the ultimate goal of the universe; it is why we exist, is why we observe. There is a very hot debate going on in physics right now between Hawking and the other leading scientists about knowledge. So your topic is right in line with modern-day physics. Hawking claims that knowledge is destroyed in the black hole; the other scientists in their goofy fantasy world have come up with knowledge is placed on the rim of a black hole, and then displayed across the Universe in a type of hologram.

Both are wrong the second is just ridiculous. And this is why you don't know the answer that you're asking, because of this bad information. I want you to have the accurate knowledge to answer the question. Actually, you already do; you just don't know it. Knowledge is so crucial to the universe that is actually carried by light. That sounds strange at first, but you already know this when we look at a star; the light from that star tells us what the core of that star's made of, tells us what the elements are in that star, and exactly what percentage of which. It tells us the age of the star, the distance, if it has any planets, and the list goes on and on.

To show that Hawking and the other scientists are incorrect is very simple. Right now we know what we know about black holes because of the light they admit. Scientist actually read light from black holes that are magnetically imprinted from the black hole. All the knowledge about that black hole. And it's particular to that particular black hole. This proves beyond doubt that our scientist don't do their homework. Any grade school child could have figured this out doing Google searches. But they've clouded your judgment so you didn't think you could do it; but you could have. There's a larger lesson here than just knowledge.

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