Does 2+2=4? When you ask whether there’s a non-question-begging logical necessity that two rocks next to each other is correctly parsed as 1+1 rather than as a single composite, or a field of discrete particle-events, or an undivided continuum with conventional cuts imposed, the answer is that the individuation is prior to the arithmetic, and the individuation is not itself mathematically grounded. It’s perceptual and conventional.Arithmetic requires objects already counted as discrete units. But “discreteness” is something the observer imposes or detects, and whether the universe itself furnishes genuinely discrete objects, or whether we carve continuous reality at joints that are pragmatically useful for creatures like us moving at moderate speeds in 3D spacetime, is not settled.Kant tried to escape this by making arithmetic a synthetic a priori truth, not derived from experience, but also not purely analytic. The intuition of discrete units in time (counting) is a structure we bring to experience, not something we extract from it. So 2+2=4 is necessary but necessary for any possible experience for beings constituted like us, not necessarily for reality as it is independently.
didn't kant talk about this with the 1 + 1 = 1 if u talking abt drops of water or was that some other dickhead, but anyways yeah, u right, but r u goin somewhere with this?
>>25371828>But “discreteness” is something the observer imposes or detects, and whether the universe itself furnishes genuinely discrete objectsAh, it's another fucking "objects don't exist" regurgitated idea... what a genius you are. A post obsessing over a female booktoker's sexual life has probably died for this, are you happy? Don't say anything, I already know the answer. You little monster
perhaps you are overthinking itI mean if "number" is a kind of transitory reality caused by human interpretation, there is just no point at all in using such terms as "a priori truth" or "discreteness". If we cannot matter-of-factly speak about something so concrete as 2 and 2 being 4 then obviously philosophy is out of the question, isn't it?
>>25371828>the individuation is not itself mathematically groundedirrelevantyour implicit demand is for mathematics to self-consistently prove itself, which is impossible
Slop philosophy
>>25371828t. failed in trigonometry
>>25371833Probably the most relevant direction this account does is the breakdown of objectivity as a coherent idea without devolving everything into the “merely subjective”.
>>25371833It concept that exists in mathematics and is called modular arithmetic, something virtually unknown to opinionated retards like OP.
>>25371862>objects don’t existThat’s not what I said though. Just as I would like to steelman an answer to whether or not there is a logically sound explanation that “objects exist for us”, I also don’t have one for whether or not my response is what you had in mind without circular reasoning. There is no reference for what a format of reality is like where 2+2=5, so why even think of it? But none of this makes 2+2=5. But it does mean the physical substrate doesn’t obviously instantiate classical arithmetic at its most fundamental level, we impose arithmetic on it at scales where it works.We can say:1. Math is the most stable, universal, and internally consistent framework we have.2. Its applicability is extraordinarily wide3. Nothing we’ve encountered falsifies itBut none of those statements entail transcendental necessity. They’re compatible with math being a maximally general and robust framework that is constitutively tied to the kind of reality we inhabit and the kind of minds we are, which is a significant but not unlimited claim.
he means we bring structure to our observations and create social constructs of concepts
>>25371828This is just the Problem of the One and the Many; how is being unified, such that it is one (everything interacts with everything else) but also many. Aristotle explains this in the Physics.In a room with five men talking, there are not arbitrarily five men, or eight, or six hundred, or just one. We each have our own experiences and our own thoughts. Right there, you have unity and multiplicity. Likewise, in a barn with nine cows, if you kill three, you don't arbitrarily have six versus twelve living organisms. This is why living things are the paradigmatic beings. But things can be more or less unified, more or less one. A planet or star, for instance, has a life cycle and will reform under its own gravity without tremendous forces to disrupt it. By contrast, a volume of water is very easy to divide. Unity is not some univocal binary, but a Transcendental predicate. With life, we see that it is ends, "goal directedness" that unifies, just as Plato shows us how a man can be more or less unified by following Logos, the Good, as opposed to collapsing into a waring heap of conflicting appetites (the civil war in the soul). Goodness is what all things strive for, and the organism strives towards its own being. The organism is also (more or less) intelligible in itself (man being the most intelligible creature in seeking Goodness and Truth for their own sake and in being able to know being as true). As Dionysius the Areopagite says, man becomes more truly universal precisely as he becomes more truly a particular. Proclus is good here too.
Similar idea Alasdair MacIntyre puts it“Objective rationality is therefore to be found not in rule following, but in rule transcending, in knowing how and when to put rules and principles to work and when not to. Consider how practical reasoning of this kind is taught, whether it is the practical reasoning of generals, of judges in common law tradition, of surgeons or of natural scientists. Because there is no set of rules specifying necessary and sufficient conditions for large areas of such practices, the skills of practical reasoning are communicated only partly by precepts but much more by case histories and precedents.Moreover the precepts cannot be understood except in terms of their application in the case histories; and the development of the precepts cannot be understood except in terms of the History of both precepts and case histories. [i]The teaching of method is nothing other than the teaching of a certain kind of history[/i].”
>>25371828>Embrace nominalism>Become unable to distinguish between three cats versus two.>Embrace voluntarism.>"Cat" and "two" is just whatever we (or the "language community") say it is!>Embrace empiricism.>Become unable to say how anyone can know anything due to underdetermination. Then default to sheer self-assertion or procedural liberalism.
>>25371943>Math is the most stable, universal, and internally consistent framework we have.You do know Logic underpins Math, no?
If you disagree that 2 = 2 you’re either insane or can’t count or something. It’s not a question of the value of 2 being agreed upon, it’s a recognised value and if it’s not that value then it’s not that number. Like a cat is a cat, it doesn’t make cats not be cats even if everyone agreed that cats aren’t cats all that would mean is humanity has forgotten what a cat is. I suppose the idea is to replace recognition of actual value with agreed upon value thereby causing the forgetting of the thing, trees falling in the forest of the deaf. What are you trying to do here?
>>25372173Lots of people deny that cats are cats or that two is two though.>Lest this should be called loose assertion, it is perhaps desirable, though dull, to run rapidly through the chief modern fashions of thought which have this effect of stopping thought itself. Materialism and the view of everything as a personal illusion have some such effect; for if the mind is mechanical, thought cannot be very exciting, and if the cosmos is unreal, there is nothing to think about. But in these cases the effect is indirect and doubtful. In some cases it is direct and clear; notably in the case of what is generally called evolution.>Evolution is a good example of that modern intelligence which, if it destroys anything, destroys itself. Evolution is either an innocent scientific description of how certain earthly things came about; or, if it is anything more than this, it is an attack upon thought itself. If evolution destroys anything, it does not destroy religion but rationalism. If evolution simply means that a positive thing called an ape turned very slowly into a positive thing called a man, then it is stingless for the most orthodox; for a personal God might just as well do things slowly as quickly, especially if, like the Christian God, he were outside time. But if it means anything more, it means that there is no such thing as an ape to change, and no such thing as a man for him to change into. It means that there is no such thing as a thing. At best, there is only one thing, and that is a flux of everything and anything. This is an attack not upon the faith, but upon the mind; you cannot think if there are no things to think about. You cannot think if you are not separate from the subject of thought. Descartes said, "I think; therefore I am." The philosophic evolutionist reverses and negatives the epigram. He says, "I am not; therefore I cannot think." >Then there is the opposite attack on thought: that urged by Mr. H.G.Wells when he insists that every separate thing is "unique," and there are no categories at all. This also is merely destructive. Thinking means connecting things, and stops if they cannot be connected. It need hardly be said that this scepticism forbidding thought necessarily forbids speech; a man cannot open his mouth without contradicting it. Thus when Mr. Wells says (as he did somewhere), "All chairs are quite different," he utters not merely a misstatement, but a contradiction in terms. If all chairs were quite different, you could not call them "all chairs."
>>25372186>Akin to these is the false theory of progress, which maintains that we alter the test instead of trying to pass the test. We often hear it said, for instance, "What is right in one age is wrong in another." This is quite reasonable, if it means that there is a fixed aim, and that certain methods attain at certain times and not at other times. If women, say, desire to be elegant, it may be that they are improved at one time by growing fatter and at another time by growing thinner. But you cannot say that they are improved by ceasing to wish to be elegant and beginning to wish to be oblong. If the standard changes, how can there be improvement, which implies a standard? Nietzsche started a nonsensical idea that men had once sought as good what we now call evil; if it were so, we could not talk of surpassing or even falling short of them. How can you overtake Jones if you walk in the other direction? You cannot discuss whether one people has succeeded more in being miserable than another succeeded in being happy. It would be like discussing whether Milton was more puritanical than a pig is fat
>>25371828It's so cute that you choose counting and summing as an example from which to generalize as if kindergarten arithmetic was considered any kind of foundation of mathematics instead of say set or type theory. In any case mathematics isn't concerned with whether objects can be separated or not in the real world, whether "discreteness" of objects is an imposition of the mind or whatever... rather it is concerned with how objects that are continuous or discrete can relate to each other once they have been defined axiomatically.Plus your claim that "math is fundamentally based on agreement" is not the hot take you think it is considering that one of the least controversial ways to define mathematics is as "the study of axiomatic systems", and of course you have to agree on the axioms before going anywhere. The deeper issue of whether or not the axioms themselves have some independent ontological foundation, or whether the operations of pure math somehow map to real world substances and objects, is a hard fucking question though and doubt anyone on /lit/ is able to answer it to satisfaction... but mathematics isn't concerned with that
>>25372173The law of ID/non-contradiction or that things equal themselves is under fire rn with quantum particles. But the argument in the thread seems more about the fallacy involved (Hume but taken a step further) when invoking universalization about...anything I think.
>>25372219I can count 5 rocks and see it is 2 and 3 rocks in a cave by myself though. Did I do math?
Now why would you start this thread instead of bumping the TAG one with what you say here.
>>25372955 non humans seem capable of doing this. Did a penguin count 3 discrete units if one of her three offspring went missing? Does this imply that either an unconscious exists to impose the discrete quality (since penguins are unconscious) or that math is something we impose.
>>25371828>2+2=4TODAY I WILL REMIND THEM>"The fault lies with your mouldy systems, your logic of 2 + 2 = 4. The fault lies with you, Chancellors, caught in the net of syllogisms. You manufacture engineers, magistrates, doctors, who know nothing of the true mysteries of the body or the cosmic laws of existence."
>>25371828Maths is fundamentally based on axioms. From those, the entire system is extrapolated.It's got nothing to do with belief. Mathematical statements are not subjective. They are derived from first principles.
>>25373892>subjectiveI am suspicious of this word as well as objectivity. I'm starting to believe there are only stronger (closer to the center in something like Quine's holism) and weaker claims."I want pizza", instead of an opinion, is now a weak claim, because it may not be what I actually want, just what I think I want because it gratifies me rapidly, as opposed to a beet salad, which is better for my health and mood long term. "2+2=4" is now a strong claim, for reasons that should be obvious, but an absolute or unlimited one, it's doubtful.
>>25374156Part of the reason you're suspicious might be because you don't know the actual definitions of those wordsObjective merely means it's based on observable facts, evidence, and logic. By contrast, subjective means it's personal to you, derived from a belief, tastes, or emotion.It's not about strength of claim, but what rules they play by. It's very easy to change your mind about what you want for dinner, to argue with yourself about it, even to believe one thing one day and the total opposite the other. The same cannot be done with math.
>>25374202Observables would be clear to talk about in your statement or what the thread being about, whether some arithmetic has anything to do with what is observed (Euclid the notable example -> curvature near black holes it is outscoped). As what's observed is theory laden or "world disclosed" and we're already always preconditioning it with how it is already constituted. The basic problem in objectivity is the part of the definition stating >Existing independent of or external to the mind; actual or realNot because some event isn't outside the mind, but that whatever is being said applies to it in a way that isn't ambiguous, therefore "belief", or rather in my hope "warranted (the claim that is stronger)". But does the world even have perfectly tautological objects (the formal statement, P=P, either typed in a computer, written, spoken, etc.) that aren't simply in flux and which are merely idealized into tautological form when we reason about them? When can any physical token ever achieve the static, timeless self-sameness the type describes if nothing physical is static? This would mean Hume's fork between Relations of Ideas isn't clean. Logic SOUNDS perfect and empty; the world is full and never quite holds still long enough to perfectly fill logic's shape.
>>25371828crows and bees know zero, and the later loves to play with balls
>>25371828According to celebrity and polymath Terrence Howard, 1x1=2.
>>25372973? this thread is not about TAG
