That seems silly to me. I don’t see how the answer can be anything other than “both” for literally every field of knowledge. You can’t discover a fact of nature or consciousness separate from the invention of an articulation of said fact — or if you can, it’s moot, because your memory is just the stored articulation, no articulation means no remembrance. They’re simultaneous; one implies the other, if you’re being honest and accurate with yourself.
If I had to pick one, I’d say invented. Everything we know, math or not, was discovered in the past, but the perception of that discovery was ephemeral — it’s long gone now. What remains, what is in our head now, is our invention in the form of the articulation of that perception. The invention can be flawed — what if you’re not honest and accurate with yourself? But it is true to the extent that the invention is faithful to the discovery. A true knowledge is both discovered and invented, but a false knowledge is invented only, so the unifying feature of both true and false knowledge is that both are invented.
But I don’t think “false maths” falls into the intended context of that question.
The reason for this discussion, is that its bot clear wether math is actually a fact of nature as you phrased it (as in, wether it exists outside of human imagination). If it does and that is why we think about it, it is discovered. Otherwise its invented.
Like most philosophical questions it seems kind of silly, as it has no real application, but it is still an interesting idea.
Well it should be obvious that there is no material manifestation of the number 1 itself.
Furthermore, let’s imagine the Descartes consciousness, the one that famously proclaims cogito ergo sum, but disembodied from any material reality. In the same way that it could think cogito ergo sum without any sensory perception, it could think it again, then think “I thought that thought one time, then another one time, and that makes two times.” So there doesn’t need to be any material existence whatsoever for there to be mathematics, providing we temporarily ignore the biological fact that we are living beings who need living brains to be conscious.
So it’s obvious that mathematics isn’t of the natural material world, and it’s silly to think anything different. But this does NOT mean it isn’t discovered. Cogito ergo sum also does not require the natural material world, yet it is discovered.
Like, your entire argument here is based implicitly on the assumption that introspection doesn’t exist, that you cannot discover things within your own psyche. Your mind is not a transparent place where you can instantly know everything that’s in there. Your mind is opaque and you cannot see to the bottom of its depths, at least not at a single glance. This is why psychologists have jobs, and the demand for their work isn’t just some useless philosophical idea without application.
we shouldn’t forget that there are entire fields of maths that specifically DO NOT exist in the natural, or even artificially made, world, but are there as pure mental constructs to help with explanations of other stuff.
there’s a distinct difference of algebra going “i have two apples and get two more apples” and going “(i^2)= -1”
Well its not my idea and opinion. Its the opinion of scientists in the relevant field.
I cant be bothered to look up all the research links for you but you could do that yourself.
But if you want to believe different ,that animals and even plants can forsee the future,then that is fine as well with me
According to the 'mental time travel hypothesis' animals, unlike humans, cannot mentally travel backwards in time to recollect specific past events (episodic memory) or forwards to anticipate future needs (future planning). Until recently, there was little evidence in animals for either ability. Experiments on memory in food-caching birds, however, question this assumption by showing that western scrub-jays form integrated, flexible, trial-unique memories of what they hid, where and when. Moreover, these birds can adjust their caching behaviour in anticipation of future needs. We suggest that some animals have elements of both episodic-like memory and future planning.
At its most fundamental level nature is non deterministic and ill defined. At larger scales emergent propertys start to arise and things become defined , which also gives room for deterministic relations.
The “source” would not be outside of matter. The source would be the nature of matter itself at its most fundamental level.
Not neccesarily. We dont fully understand the natural world not even close. There is a lot of room for free will to exist within the space that we do not understand. At least that is how i see it.
In the end its a complicated subject,we simply have not enough knowledge.
It seems to be a point of discussion.
I wont argue against animals having a memory,with that i do agree.
In the end its not black or white. It most likely is a gliding scale. This would imply that some animals (certain mammals) can indeed anticipate the future to some extend. But this extend is so small compared to the extend to which humans can do this that to me it is equall to non existent.
I didn’t provide an argument for the solution of the discussion, I only provided an argument for why the discussion isn’t stupid and you just wrote two large, convicing paragraohs of why your opinion on the discussion is right.
While I do think your points are very good, I personally still believe that mathematics is invented, this may however be a question of semantics. I would argue, that while we may discover our ability for abstract thinking, this doesn’t nessecarily make us discover numbers or the concept of numbers.
Todays math is basicly just array of definitions and followings of these definitions with no reference the “real world”. These objects are made up/invented.
if you say, that everything a person invents is just the discovery of a concept or a way of thinking, that has existed in a meta-sense before, I would have to agree with you, that in such a wide understanding of the word discovery you are right and the discussion is moot.
However, if we want this discussion to make sense, we need a more constrained definition of the word “discovery” or atleast of existence.
If for example we say, that concepts noone has thought before do not exist, I would argue, that they were not discovered, but invented the first time someone thought about them. In this sense I would argue that math and numbers, were not discovered, but invented. I could however definatly see arguments for the opposite.
The is maths invented or discovered is a long and deep discussion that’s been ongoing for a long time, personally I think it’s guesswork to pick a side, but that said within the discussion there are aspects that standalone. For example I think most mathematicians would agree that maths as a means of understanding the relationships between discrete systems, like the side lengths of a triangle, is discovered.
That because it is pseudo random it designed to look like random but it is not trully random at all.
The algorithm that provides pseudo randomness supposed to make the pattern unsolvable for the users as much as possible and making a pattern more complex with equations would require more computing power so games like hearthstone where millions of games played would require too much computing power that would cost more to the company, energy wise and hardware wise.
There is nothing paranormal about it. When you play thousands of games you start to see the pattern it is just that.
I think the cat doesnt think anything. A cat doesnt have rational thoughts like humans.
A cat (and virtually every other mamal) has emotional feelings though and it will probably feel something just before pouncing the mouse. Maybe the feeling of excitement or something that comes close.
And my position of math would be that it is discovered. I do believe math lies at the very fundamental base of everything around us. math->physics->chemistry->biology. Maybe logic would fit in there as well,possibly even before math.
I dont see how it could be invented. Beeing invented seems to suggest that we could have invented a different kind of math. A kind of math where 1+1=3. I dont think this is possible.
My cat was often clearly pondering whether to come or go, does that count as “thinking things over”? Primates (beside humans) and some other “thinkers” out there (Ravens, for instance) do a good job in thinking out of their box. Whether that’s strictly rational thinking (and even if humans can really do that) is - well, debatable of course.
