I feel like there are no concepts we cannot define, theoretically at least. Is there any argument suggesting the exact opposite? How strong is that argument?

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    An “infinite” idea might qualify? – Joseph Weissman Feb 26 '19 at 23:19
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    it can be defined. There's an English and a mathematical definition for it. – repomonster Feb 26 '19 at 23:21
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    Most concepts can not be "defined" by humans, for most of them we just settle for vague descriptions. And even in math, where we have more or less precise definitions, we define concepts in terms of other concepts. Since that has to stop somewhere there have to be concepts that remain undefined. – Conifold Feb 26 '19 at 23:43
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    have you never studied anything you couldn't grasp? I have, several times. And I'm clever. There are cleverer people than me.. and they have the same problem. I topped out at trigonometric calculus. And that's foundational for some people. What are those people grasping in the dark for? – Richard Feb 26 '19 at 23:46
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    If something is a concept then it can be defined. Are you asking about what cannot be conceived? – PeterJ Feb 27 '19 at 10:28

Yes and No.

No part

Every concept can be defined. Lets take for example concept "square-circle". Sounds stupid at first ? Yes, first impression is like it is so. But if we take things like that square-circle is html object which has CSS property of border-radius equal to 25% - this starts making sense. We get an object which looks like:

enter image description here

Yes part

If by saying "defined", you have in mind that concept must be defined unambigiously between all people - well then you will have a big problem, because HUGE amount every now and then concepts can be defined differently. And there is no true definition. As long as all conditions are met for the concept at hand - it's a valid definition. We can say only that.

  • If you have references to others taking a similar view this would be your opportunity to share them with the reader and guide the reader's further investigations. – Frank Hubeny Feb 27 '19 at 11:18
  • Re "Yes part". The definition >>is<< the concept. If several people have different definitions for what they're all referring to as the same concept, then what they have to do is, like wikipedia frequently says, "disambiguate". That is, they really have several different concepts, that they're accidentally referring to by the same name. Nevertheless, they're actually different concepts. – John Forkosh Feb 27 '19 at 11:23
  • @JohnForkosh Doesn't change anything for Yes part. Definitions itself maybe ambiguous and vague. For example about "square-circle" -> border-radius property can be "understood" differently by a Chrome and Firefox browsers. 25% - which ratio and relative to what ? HTML - XHTML applies or not ? And etc., etc. No matter how much you disambiguate - there is ALWAYS a room for a further specification. So all definitions are inherently uncertain. Even mathematical concepts/definitions because you HAVE to stop at some axiom(s) without arguing – Agnius Vasiliauskas Feb 27 '19 at 12:39

I do not think we can define the sight of the nth dimension when n is greater than 3. We can describe it vaguely, and even visualize it, but there is no way we would probably be anywhere close to actually describing what it looks like.

  • If there is a 4th spatial dimension it does not look like anything at all, the fundamental reality of things is that they do not look like anything at all, our brain constructs this 'seeming' of things. It is not like 3 dimensions look like something then we see what it looks like, it is that 3 dimensions do not look like anything, and then our brain makes it all look like this. – SmootQ Feb 27 '19 at 9:19
  • And if 4 dimensions exist AND have any significance to our biological evolution, our brains would evolve so that it 4d look like something. – SmootQ Feb 27 '19 at 9:22
  • By extending your logic - hypothetical creature which lives in 2D spatial world - can't define a > 2D dimension worlds. But we can define a 3D world. Einstein even defined 4D space-time (4-th dimension is not spatial, it's time).Thus at least theoretically 2D creature can define 3D world too. And probably we humans can define 5D,6D,... dimensions too. We can only say that at this point in time we have difficulties to do so – Agnius Vasiliauskas Feb 27 '19 at 10:06

I'd agree with you that "there are no concepts we cannot define", but my agreement is basically a matter of definition. A concept is, by definition, something accessible to human contemplation/intellect, e.g., according to https://www.merriam-webster.com/dictionary/concept it's "something conceived in the mind". So that "in the mind" part is what I'm thinking is crucial.

However, the "define" part of your question maybe itself requires further clarification/definition. If I have a concept in my mind, does that necessarily mean it's "definable" by me? An unambiguous "yes" would be if I can write down a finite sequence of symbols (from a finite alphabet), e.g., an English sentence or even an entire book, whose meaning is that concept. Of course, that presupposes that everybody understands the meanings of my symbols/words/sentences/etc the same way that I do. And for the scope of this answer, I'll just assume everybody understands English identically (or close enough).

Whether or not there exist "humanly-inconceivable things" that maybe some super-advanced outer-space alien "understands" is maybe an open question. For example, in the other direction (where we're the super-advanced ones), I don't think I'll be explaining algebra to my dog anytime soon. Nevertheless, I don't offhand see why we should consider ourselves the be-all and end-all of evolution. Just the spur-of-the-moment top-of-the-line model ... like dinosaurs once were. So, yeah, if I had to guess, I'd guess there are "humanly-inconceivable things". But they're not concepts, per se. That's, by definition, a human thing.

And I guess the one remaining loophole re (humanly-conceivable) concepts, is whether or not I can have a concept in my mind that I can't find words to explain/define. Well, that's what we have poets for.

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