@shintuku Yes. For sure, though, the privation of those essences do not exist as essences--that would be a metaphysical contradiction, and a thing is possible only if it has no metaphysical contradiction--but rather by necessity can only exist as ideas within the mind of creatures.
These things are called logical beings to distinguish them from actual begins (things that are essences, or which have essences).
For example, nothingness isn't a thing that has real existence per se. By definition, nothingness is the privation of being, so if nothingness did exist, it would both exist and not exist, therefore the essence nothingness doesn't exist, only the idea of nothingness.
Nevertheless, it is objectively so that as a concept or notion, it exists, and thus excuses it from being merely called the invention of man.
Privation of being in itself is not contrary to existence; nothingness is the absolute privation of all being.
@Franklin And yes, you are right, but then when you got to your inequality with the factored parts, how did you conclude that $-2\leq x\leq 3$ if you prior assumed that $x\geq 0$?
Ok, but why does truth need to be involved in the actual possibility or impossibility of things? This seems to me more like truth about reality or being, i.e. an added judgement, a proposition, about possibility or impossibility @AMDG
I'm not seeing again why truth is being distinguished from true knowledge
Why is it that truth consists of two species, possibility and impossibility, instead of being about two ways of being, possibility and impossibility?
@anak ok, ok, ok,....Let me clear it by saying: A. $-3\leq x\leq 3$, B. A circle and a pair of straight lines C. -2<=x<=3, D. $-6\leq x\leq 3$ . These are the options given. Actually, while copy-pasting, the options part gets mixed up....
"that which is possible" and "that which is impossible" seem to me to be propositions, so I don't see where truth is beyond the judgment by a brain that things are so
@shintuku Well you basically demonstrate it in what you just said. Impossibility and being are wholly contradictory. I recognize this non-conformity of impossibility and being, and this recognition is a conformity of that which is in my mind, and that which is in reality.
@shintuku Propositions are just propositions. There is something in them which of their essence is true or false.
@anak Umm...Here, I will say, that $-2\leq x\leq 3$ is the solution set for this inequality: $x^2-x-6<0$ and not for the inequality $\sqrt{x+6}\geq x$. The solution set of the given inequality is actually, a subset of the solution set of this $x^2-x-6<0$ under the assumption $x\geq 0$
How do you think anyone judges? That judgement must be coming from somewhere. Something must be compared against. What is it that man is comparing against? None other than truth: the idea is compared with what is true, and the pronouncement of that idea's conformity or non-conformity is a judgement.
@AMDG no but these are phenomena which are produced by the brain. you were arguing that these must appear beyond the brain, in the intellect or spirit, otherwise reality ceases. i don't understand why
Well because as we've defined truth, if something is impossible, it cannot exist. The possibility of an object existing must first exist before the object itself can exist.
@anak ohh... I solved it like this: if $-6\leq x\leq 0$ then, $0\leq x+6\leq 6$ and thus , $0\leq \sqrt{x+6}\leq \sqrt 6\leq 6$. On the other hand, $-6\leq x\leq 0.$ Comparing the range of $\sqrt{x+6}$ and $x$ the given inequality becomes obvious , right ?
@Franklin You have convoluted it a bit, but that's the idea. Really just look at the sign on both sides. On the left, it's $\geq 0$, while on the right it's negative.
@shintuku That conformity itself as opposed to your having the awareness. You are quite literally stating the species of knowledge (which necessarily correspond with the species of truth) as knowledge of what is true, and knowledge of what is false (your wording there is ambiguous).
That recognition is distinct from the reality being recognized. Electrons flowing in the brain are not knowledge in themselves anymoreso than data is not information.
Now that is all well and good to claim, but the brain is insufficient to explain why we have understanding of an idea, and why we can go up and down a hierarchy of ideas, and why these ideas are the same for everyone who has their knowledge.
That would be a decision, but if it's merely a brain which chose it, then we must be obliged to say that the horse's actions have a specification of action and chronology which is software. Anything that operates according to it will never deviate. If that's true of humans, then we should observe within ourselves an incapacity to resist hunger, or any impulse at all, yet you can disregard it for arbitrary reason, therefore there must be a cause greater than the brain itself.
Why is it scared of wolves? You don't see any necessity for truth to be immaterial, or even that there has to be any immaterial agent whatsoever, yet neurons are, if wholly material, dictated by the laws of physical reality, and the motion of atoms, and in spite of the stochastic or random nature, order somehow proceeds from it deterministically, so that means that given sufficient memory and resources, a brain can be fully simulated.
If something is deterministic, it necessarily proceeds from necessary being and will simply execute and do nothing but its programming.
Can anyone please help me understand how are they getting the equation: $(x(k+1)-kx_0)^2+(y(k+1)-ky_0)^2=r^2$ in this question : math.stackexchange.com/questions/3193174/… ?
@shintuku Ok, then it should produce repeatable results, but in reality, I as a human am capable of contradicting any such simulation of my brain as it exists right now, therefore there must exist some cause greater than the brain, therefore greater than atoms, and therefore greater than material being according to your definition of material being.
@AMDG sure, you can contradict it if, for instance, that simulation is not aware of you, but you, to spite it, or to spite the scientists, decide you will do something otherwise. no need to follow the rest of your chain of consequences
@AMDG depends a bit on what we mean by deterministic. Suppose you have a system which is entirely governed by a sequence of inputs. Then that sequence determines the outputs, so formally it’s deterministic. But if the inputs are essentially random, then that determinism doesn’t really help you predict anytging
@shintuku What, the fact that if truth were material, i.e., constructible of material being per your definition, it would mean that the truth only exists for as long as the object exists, or we exist?
Philosophically it’s an interesting question whether the brain itself is deterministic, but as a practical matter the inputs to the brain are certainly stochastic.
@AMDG no that part is fairly understandable, that's just true knowledge. if no one knows something, then, well, that knowledge disappears from reality. i don't get why you're positing that you need immateriality otherwise reality itself disappears
yes we established objects are not contingent on our minds
@shintuku Because knowledge or truthcan't disappear from reality. If we agree that possibility and impossibility are true knowledge, then your statement reduces to the absurdity that truth is contingent on the mind of man, i.e., possibility or impossibility themselves are contingent on the mind of man and his knowledge of them, ...
...but you're saying that if no one knows something, then that knowledge disappears from reality, but that would have to mean that the possibility or impossibility must cease also, but the object having possibility itself needs to be capable of existing by definition of possibility, so it would have to cease existing, therefore truth is immaterial.
So if the knowledge of possibility and impossibility cease to exist, then you must also claim that either possibility and impossibility cease to exist, or that they continue to exist despite our not knowing them to exist, and therefore must admit that truth is an immaterial being.
The better question is why aren't you drawing this consequence? If a material being is made of atoms, etc., then it is a material being; if not, then it is an immaterial being by definition.
Ok, so then if I understand correctly, then the question that you need to answer is: what are possibility and impossibility apart from the knowledge of possibility and impossibility?
Not so. Atoms are possible. This is self-evident from the fact that they exist, and their existence is empirically proven, even if their constituents are still a matter of reasonable belief.
How then can it be said that this is simply a property of an atom's physical state?
You've mentioned two kinds of state, so I suppose you could start with telling me what you say is the kind of being that physical state and state of mind have.
then I could make an imaginary configuration of space of my room
i use such configurations of space to memorize things using a technique called memory palaces, to remember quotes, historical dates, etc.; in my mind i can make things arbitrarily far away from one another
I'm not asking if you can construct a configuration of atoms. That would be asking me to arrange atoms in a certain way. I'm asking if you can construct a configuration itself of atoms which is not to be found in the atoms themselves.
Atoms are just there, existing in space. They don't relate one to another. The configuration is a recognition of their relations in space.
Can I construct a recognition of a material being using a material being?
do you mean if I can construct the word itself, or the idea itself, with atoms? no, those aren't the type of things you can do with atoms. the word maybe, as it is the collision of air atoms in a particular way, but the idea can be constructed from atoms through a brain
@shintuku So your claim is that ideas are constructed from atoms through a brain? I see. So your claim is then equivalent to saying that ideas are arrangements of electrical impulses? Is that correct?
In other words, do you believe that a series of abstract concepts which are not literally equal to electrical impulses are in fact just electrical impulses literally?
@AMDG they are equal in the sense that they can be recognized as a configuration inside the brain, or as the organization of the brain at a particular moment, yes
I mean all things considered, surely you don't believe that an electrical impulse along a wire is literally, e.g., the essence of the set of all reals for instance?
Rather, that the idea must exist accidentally within it? That the arrangement or configuration of those impulses, of which each has no meaning in itself, is something subject to an interpretation?
@shintuku Literally reductio ad absurdam: the electrical impulses cannot themselves be the concepts or ideas themselves, nor can their arrangements in themselves constitute the ideas. They must be subjective representations... of something greater than themselves.
Because these things in themselves... only mean what they are in themselves.
@TedShifrin this book uses the notation $\alpha''$ for a curve $\alpha$ on a Riemannian manifold to mean $\nabla_{\dot\alpha}\dot\alpha$. Is this pretty standard?
Quite frankly, I don't see what's so hard to see. We've just acknowledged that the idea is not the electrical impulses. Ok. So what is an idea, then? What is it made of? is it material or immaterial? If material, then the only thing it can be is electrical impulses and their arrangement, but obviously, neither of these tells of themselves, e.g., the numbers, or life and death, or existence and being, etc.
So we are forced to conclude that an idea is immaterial, and if immaterial, then the things which ideas either are or represent must also be immaterial.
@AMDG the idea is a configuration of electrical impulses in the brain, understood physically. understood phenomenologically from a point of view within a subject, it is, e.g., what I experience happening when I do 2 +2 in my subjective experience
the subjective experience has a material manifestation in brain activity
welp matrix multiplication doesn't serve as the definition since it doesn't even work in $\mathbb{R}^3$ since the sizes are off
unless you did the transpose of one, but you'd then have a 3x3 matrix..
I see the problem, you can't get the determinant of a non square matrix.
not sure if this has any merit but defining a cross product in higher dimensions would require more vectors so $\mathbb{R}^n$ only works with $n-1$ vectors
but what $A \times B \times C$ in $\mathbb{R}^4$ means I do not know
well, that wouldn't even work for circles, would it? so it's got to be something else. i don't have intuition for the non-unit-speed formulas.
i just think of them as 'the complicated thing that you get if you don't have a unit speed parametrization'
the formula (whatever it is) should be invariant under changing r(t) to r(kt), k nonzero constant. that rules out a lot of candidates (including that one). it should also scale inversely with changing r(t) to k r(t) (which your candidate formula does do). i don't think scaling alone clearly immediately spits out the right formula, though.
Funny guy you....when would one of all those sorts of combinations every be anything but an indeterminate form?....It may be the case, but I'm just going off of all the beginner's calc....
shin: what would that mean? OK, you have a function f(x) going to -infinity, and a function g(x) going to 0. but what would f(x)^g(x) mean in that case? what is (-1)^(1/2) for example.
shin you're basically wrestling with defining the complex exponential. you can do that, but it does not have all of the nice properties of the real exponential. why are you doing this? are you just trying to assign meanings to expressions?
i'm trying to figure out if $-\infty^0$ is an indeterminate form, i.e., if two functions that go to $-\infty$ and $0$ might make something not nice happen
@D.C.theIII just working my way back in slowly. i flew to Rome for a nephew's wedding and them spent a day in Dublin with my 94 yo aunt. very nice, but i am too old for this sort of travel
normally when people talk about indeterminate forms in calculus, they mean that the value of one real-variable limit cannot be determined from other real-variable limits. the "0^0" stuff is shorthand for statements about limits. here, we're saying, you don't even have real-variable limits.
and before you discuss limits of a^b where things might be complex, you need to discuss complex numbers in general, i.e. what that means before you take any limit. the base a being real isn't much of a simplification here - once a is negative, you're in complex land and have to consider the whole nightmare realm of complex numbers.
the properties of the complex exponential are subtle and not as nice as the real exponential. that restriction to positive real bases in real analysis books is a very meaningful one. even for rational exponents.
e.g. your calculator can probably take a stab at what (-1)^(1/3) is, and then square the result. and it's probably not going to be the same as what your calculator will spit out if you ask for (-1)^2 = 1 and then take the cube root of that. so a^(2/3) for negative a is subtle.
@D.C.theIII i made the mistake of paying for, and going through the interview process for a global entry card. complete waste of time for me. my preferred airline does not participate in tsa precheck, so no savings on this end. on my return, used the global entry station, but it was slower than the normal immigration line. so, more more experiment.
I'll have to take note of Conway's text for future reference. I was more saying Ahlfors in jest because I know it is complicated, from what I've read
Normal immigration for US citizens entering the US is pretty fast, it is nightmare when you're not though. It's why I try to avoid the US on my international travels
@TedShifrin Thanks! i was following two ladies, quite by accident, of course. One had global entry, the other didn't. The other won the immigration race.
I wasn’t sure, but I am pretty sure that if the next election goes badly, billions of US citizens may try to become Canadian, and Canada wants no part of any of it.
I suppose I should read the article, but I'm not sure how that will play out in real time, there are plenty of places where people can cross if they are eager enough.
We could ship the Texans to Alberta, they would fit in there
But then again they'll be happy in the good ol US of A if DeSantis wins........( I would laugh, but we all know what happened before..)
