your ultimate question in philosophy?

They are not based in assumptions in practice e.g. in computing. At most there would be at least two categories, maths based in or not in assumptions. At root where we can relay back to real info, then we can make true statements, it is only when en masse where ambiguities arise.

You can observe its utility and therefore what numbers are in that. That’s what fundamental laws of physics are, and they are observable even though abstract conceptually.

If everything were an assumption, then that is also an assumption and can’t be true [had to say it lol].

We at least have a tree of variation from physical info and computer data, through knowledge of utility right up to knowledge of how things work. What’s left after that is the ambiguous and the smaller proportion of mans knowledge base.

You can certainly know what a number is, and not assume. It is through understanding and conceptualization of what it means to be a number and what that number represents.

Morphy - you clearly can’t tell when you’ve lost an argument.

WW III - “number”, not “a number.”

So we don’t know what “numbers” are?

Depends what you mean. Formal knowledge rests upon assumptions. Which is okay. Mathematics is surely formal knowledge. Rests upon assumptions. Doesn’t mean we don’t have knowledge. Knowledge is not metaphysical certitude. Okay - some errant philosophers believe that. But no one lives their lives that way.

Well Kant labeled math as a priori synthetic - and what is wrong with that? How is that an assumption - unless you’re getting into the separation of things and blurring up our categorizations?

I need more energy than I have right now to debate the Idiot Kant. Another time…

Lol, Yeah, maybe put yourself in a dark room - solitary confinement for 3 months. Then when you’re ready drink a pot of coffee and a liter of vodka, then you should be good to go.

Mathematics is knowledge via definitional logic, not assumptions.

You really don’t see the assumptions? You have to assume identity at the very least.

There are tons of papers that deal with identity theory. To say that something equals something else is to assume an identity. There’s all kinds of shit that can be said about it.

Seriously? :confused:
I thought only the meekest of philosophers didn’t know better than that.

Identity is not an assumption, but a declaration. A dog isn’t a “dog” by discovery, but by declaration.
2 = 1+1 because that is how “2” is defined in the language. It has absolutely nothing at all, nothing whatsoever, nothing period, to do with any kind of assuming of anything.

I agree with James.

I don’t think assumption is what appropriately occurs here. There’s justification for conceptualizing the identity of things - Yes errors could occur, yes you could wrongly identify a banana as an apple, but if you inspect an item thoroughly enough, I don’t see where there’s an assumption. Even through empiricism, seeing a building isn’t an assumption that its a building. Unless its a holograph - but that’s not reasonable, there is no evidence that a holograph can be projected the size of a building, or would be. So depending on the level of how you are describing that thing, which most of the time it is a vague description compared to all the actual properties of what that thing is, it can be known appropriately very easily.

Then we get to a point and use their knowledge to surpass them.

James…assumption, declaration, whatever.

James, an assumption is merely a premise that cannot be derived from another premise. This is not a Big Filosophical Deal (BFD). There is no proof for “dog”. Or for any other word. There are mathematical proofs. You are equivocating about “language”. It’s apples and oranges.

Baaaaaaaasic stuff.

“1” would be “1” no matter what we called it.

“Dog” has a taxonomic definition. Not just because it names an animal. Everyone with any education knows this. But you don’t need to know it to use the word.

“Number” has a theoretical definition, which is not necessary to know in order to do mathematics, but which does exist. Many terms are attached to more than one kind of definition. The philosopher is not restricted to one type of definition. It’s not an either/or situation.

Again - as a philosopher, if not as a mathematician, we can look for several types of “technical” definitions. Taxonomic, theoretical, stimulative, etc. We have been asked for our ultimate question in philosophy, not in taxonomy or arithmetic.

You guys really gotta calm down.

WWIII - the important part about identity is not that you may be in danger of mistaking an apple for an orange, or a 1 for a 2. It’s more about the preservation of “apple” over different instantiations, or instances. Not that 1 might equal something else, but that 1 always equals 1. There is an occasional assclown on this site who will state otherwise. Which is why this assumption is important. Just for the assclowns.

This is not to say that this preservation is anything earthshaking. It’s just a basic assumption necessary to figure a tip or do your taxes. It’s necessary to math theory but not in practice. Just like i don’t have to know anything about physics to fill my bike tire with air.

Kris

Peashooters Vs abrams tanks? If we are not as advanced as the aliens, then I would think at best catching up would come in increments. All the while with their superior knowledge, said aliens would be observing what we are up to. When I say observing, they will have [at least] quantum computers which will know the information in our brains as it is [memory], and as it occurs or arrives and leaves the conscious mind. We would have to have brains, computers and what have you, high enough to even understand their systems. Then we would have to adapt, where they have been doing that for millions [or billions] of years.

Probably the best plan would be to say ‘hello sir/madam’!

Philosophically I would suggest that humans have their limits, and although we can understand possibly everything about the physical universe, understanding the mind is far off. Then when/if we get to an understanding of our minds, we’d be conversing with beings who have been there, learned their minds, and have been repeatedly expanding on that to the nth degree on an exponent we couldn’t possibly understand. Not unless we do a similar thing for the same amount of time.
On the other hand, there may well be limits to mind and computing, where once we get there we are all the same. I hope that cosmic communism isn’t true, and that we live in a reality which truly doesn’t have limits. It kinda all gets pointless otherwise?

Faust

Indeed! there is a difference between the group of things which are the same irrespective of used terms, and the group of applied terms ~ which is secondary knowledge. A dog even, is perhaps still the thing we are using that term for, same as a 1 is a 1? the ambiguity is in our valuing of the thing, and not the thing itself. It follows that a great many things are being describe efficiently, possibly 90% or more of all man’s knowledge.

My main complaint of course is that; ‘if only ambiguity, then no philosophy’?

When I first came here to ilp, I was dumbstruck by the amount of things one couldn’t say without be confronted with ambiguity, all the mental qualia, subjectivity, brain in a vat stuff. I wondered if the greek philosophers would have wrote any works et al, with such crumbling foundations. Which is why I try to attack it wherever I see it.

I wouldn’t make a claim myself on what is more important, identity or identifying.

They seem of equal importance to me. Just as the preservation of apple over different instances of apples is important, so is identifying is as an apple still, over different instances of apples.

I don’t see what you’re saying is an assumption though, are you declaring that do we not know what the identity of numbers are? Instead we must assume what numbers are? If so, I don’t understand that and would need elaboration.