Ok. So we still have no explanation of how you came to misapprehend "=". — Banno
Is Metaphysician Undercover a product of the New Maths? :wink: — Banno
Infinity pools can indeed be awesome — ssu
I am not sure if this is so much a problem with mathematics though as it is with how it gets applied to the sciences and philosophy. It seems to me that infinite divisibility might be worth investigating even if it doesn't accurately reflect "how things are." — Count Timothy von Icarus
You have mentioned, for example, that the limit concept is flawed, although it works well most of the time. But I don't recall your argument beyond that point. A more complete knowledge of space and time and points and continuity? Oh yes, something about the Fourier transform and the Uncertainty principle. What are your suggestions to fix that up? Intuitive mathematics? Remind me where doing something specific makes it better. — jgill
Except incompleteness (in the sense of the incompleteness theorem). — TonesInDeepFreeze
Here's actually some advice to all non-mathematicians (from a non-mathematician):
If you really can ask an interesting foundational question that isn't illogical or doesn't lacks basic understanding, you actually won't get an answer... because it really is an interesting foundational question!
Yet if the answer is, please start from reading "Elementary Set Theory" or something similar then yes, you do have faulty reasoning. — ssu
And sometimes people post questions about mathematical subjects that have bearing on philosophy, such as about infinities, incompleteness and computability. — TonesInDeepFreeze
What is the proper interpretation of the cosmological constant Λ? I understand that it corresponds to a vacuum energy density, pervading all reality. Such energy is called dark energy, I gather. Since I'm sketchy on field theory, I don't know how this goes, but somehow this energy density produces a repulsive force beween any two objects in spacetime (within each other's lightcones?). Matter remains cohesive because Λ is very small compared to other forces, so that its effects really only show at an intergalactical scale (megaparsec). — DanCoimbra
ow, somehow this leads to the expansion of the Universe even in the case where the Universe is finite and bounded, which is a possibility considered by cosmologists. In this case, the Universe is increasing in total size, but not increasing *into* anywhere, so it becomes bigger because it has more internal spatial structure. This is what I meant. Why do you think this is incorrect? — DanCoimbra
I just think if mathematical axioms are to be selected, they have to be such that they do not lead to what is contradictory to Existence/Truth (or just semantics in general). — Philosopher19
If a mathematician or a philosopher decides on an axiom or theory that requires belief in the following (or at least logically implies it or leads to it): Nothing can be the set of all things (which logically implies Existence is not the set of all existents), or one infinity is a different bigger than another (or is a different quantity than another), I believe that axiom or theory should be disregarded or at least viewed as contradictory to Existence/Truth (or at least contradictory to the semantic of infinity). — Philosopher19
What the Universe's expansion means, whether it is infinite or not, is that its local energy density is decreasing. In other words, there is more spatial structure between each of its internal field excitations (particles, energy). — DanCoimbra
So true. The OPs lay out belief systems in one form or another, and sometimes they don't budge. Which I find acceptable in Metaphysician Undercover's pronouncements, for he dwells with the ancients as they ponder space, time, and points and curves - although he balks at 1+4=5 and has little patience with Weierstrass and his limit ideas: admittedly useful, but fundamentally flawed. But I see where he is coming from there. Others, like this thread, are more or less unmovable in their opinions, which clash with standard mathematics. How you deal with the frustration of offering knowledge to those unwilling to accept it is admirable. — jgill
I tried dealing with 1. and 2. earlier, in mathematical analogues, but there was no interest. I could easily deal with 3. as well, but that takes the thread away from the spectacular leap from a first cause being something imaginable to an existential realm. — jgill
Suppose someone produces an axiom. Will it not be the case that that axiom will either be contradictory in relation to certain truths or consistent in relation to certain truths? Existence determines what is true and what is false. Whether any belief or axiom highlights truths or is contradictory to truth is determined by Existence/Truth. If not, there is no truth or semantics to work with to deduce further truths. — Philosopher19
Of course: nuclear reactions have emergent aspects by themselves, but you should distinguish these from emergent chemical features.
You can of course lump everything together and say that the universe, with everything in it, is emergent as a whole. But that means that the various properties of the universe are obscured. — Ypan1944
My belief is that we can't just produce axioms. We can only recognise truths about Existence such as 1 add 1 equals 2 or the angles in a triangle add up to 180 degrees or one cannot count to infinity. — Philosopher19
Nuclear reactions have nothing to do with the features of an atom or molecule. For reactions between atoms or molecules, only the "outside" of an atom (i.e. the outermost electrons of the atom) plays a role. The emergent feature of an atom or molecule depends only on its outermost electron configuration. — Ypan1944
One is free to propose different axioms that prove differently. — TonesInDeepFreeze
I don't agree with you. The features of an atom are totally dependent on the electron configuration of the atom, which you can describe with quantummechanics (harmonic oscillator etc.). The internal structure of the nucleus is irrelevant. You only need to know the electric charge of the nucleus. — Ypan1944
Also in chemical reactions, only the electron configuration of the participating atoms or molecules is important. — Ypan1944
One might argue that the latter encompasses imagining that the count to infinity is complete, but one cannot imagine such a thing. — Philosopher19
The way set theory proves there exists a set with all and only the natural numbers is by an axiom from which we prove that there exists a set with all and only the natural numbers. — TonesInDeepFreeze
Then why do you think bijection requires counting? — Banno
In my opinion, this addition by Bedau is superfluous: you do can actually describe the properties of an emergent phenomenon with "normal" physics, where its substructure is usually irrelevant, so a form of "coarse graining" will happen (f.i. with Bohr's atomic model the substructure of the atomic nucleus is irrelevant, only the electric charge of the nucleus plays a role; and you need a new theory (namely quantum mechanics) to describe that phenomenon) — Ypan1944
Supervenience is therefore completely different from "downward causation". — Ypan1944
Problems occur if you consider the elements of a set to not be themselves sets. Set theory only talks about sets. It does not, for example, talk about individuals.
The lists only list other lists... — Banno
It wasn't meant to be a literal example, it was meant to give you a visual of something not being there, then there. The big bang is another typical example. Does that work better? — Philosophim
And I've asked you to give a concrete example. I've even noted that I believe you aren't doing it because you know if you do, your point will collapse. That's a challenge anyone who believed in their point would rise to. — Philosophim
Ok, and a first cause is that which is not caused by something else. This does not show that what I stated is wrong. Cause 'implies' change? What does that mean? The definition of cause has been clearly noted, you've recognized it, and this doesn't address the point at all. Also, no example despite my request. — Philosophim
I've already gone over reason and prior reason. I was the one to say these words first to Ludwig, " All causes are reasons, but not all reasons are causes." So are the words I used to validate my points now invalid? — Philosophim
So I think we're done. I hope our next conversation doesn't have as much animosity from you next time. Especially after we started off so nicely when I said it was good to see you. Remember that? Lets end this on a high note. — Philosophim
So what judgement call are you actually hesitant in making? That the approaching object is John? Haven’t you tacitly made that call already, by not thinking it is any particular object at all, insofar as your proposition makes no mention of what you think the approaching object may or may not be? In effect, you’ve thought it unjustifiable to name the approaching object, which your proposition in fact represents. Another way to say you’re hesitant in making a judgement call, is to say you just don’t know. Which is fine, of course. — Mww
I understand and can accept most of that, with the exception of suspending judgement. From the perspective of critical thought, to think is to judge, from which follows suspension of judgement is impossible. — Mww
It's not the judgments are compatible, its that the experience is compatible with both conclusions. If it was not compatible with both conclusions, then there would be no doubt. — Bylaw
The parts of the experience that might lead you to think John is approaching
are hard to consider evidence that John is not approaching.
But in in a situation where you are not sure John is approaching, but you think he is, the overall experience you are having contains evidence that he is not approaching. There is something about the entire experience that leads to doubt. — Bylaw
So, there must be elements of the experience that FIT with it not being John approaching.
(and for what it's worth, it seems to me FJ has been fairly patiently trying to get his point across and felt it was important that you come up with the scenario and also that the scenario had specific features. I certainly could have missed things, but it seemed like your reactions included some negative assumptions about his attitudes and intentions which did not help the discussion. ) — Bylaw
Please articulate an argument supporting this premise. — ucarr
Naive question. Am I not right that, strictly speaking energy is work done - the capacity to do work is called "potential energy", isn't it? — Ludwig V
I've given several examples. All I'm asking is for you to do the same. I'm not asking for proof that such a thing exists, just give me a possible example of something which makes logical sense that could exist. In my mind you're dodging the issue here. — Philosophim
Metaphysician...I've been kind so far and given you as much benefit of the doubt I can. This is stupid. You are better than this. Go to anyone else besides me and say that sentence and watch their confused looks. This is why I keep asking you for examples. If you cannot show how such a statement can logically exist I'm going to assume you're trolling or you are arguing in bad faith. Work on this and give me something good to think about please. — Philosophim
What? No. If there's no prior cause, then there is nothing prior which caused a first cause to exist. If there is nothing prior to cause something, there is no prior reason for the existence of it either. — Philosophim
Now we can reason about the existent thing. But we cannot say there is a prior reason, as there is nothing prior that caused it. Please demonstrate a situation in which there is no prior cause for something, yet there is a prior, and by this I mean temporal, reason for it. — Philosophim
I'll try explaining again. Lets take an example of a photon that appears without prior cause. Now, once it exists, it is bound by causality by what it is. Meaning it can't suddenly act like an atom, because it is a photon. It can't interact with other things as an elephant suddenly, because it is a photon. It is the first cause in a causality chain only because nothing caused it to exist. But its continued existence begins a causal chain with whatever happens at the next time tick of its existence. — Philosophim
If there is no prior cause, there is no prior reason. — Philosophim
Random is not inconsistent with an explanation, — Philosophim
Quite so. It's perhaps worth noting that the same applies to what happens after the heat death of the universe. — Ludwig V
As for your eyes…..the weather, the crowd, you’re being intentionally tricked, a whole menagerie of incidental evidence….. each is the content of an individual judgement, the compendium of which determines the experience you’re going to have, affirming your thought, in which case it is John, or negating it, in which case it isn’t. — Mww
You said your evidence was that you saw a guy who looks like John approaching — flannel jesus
I'm standing on the street and I see something at a distance. — Metaphysician Undercover
I don't have to write paragraphs and paragraphs about the minutiae of the philosophy of judgement... — flannel jesus
Something circular going on here. It's a feeling I have had for this entire thread. — jgill
also agree this would be a problem. But I am not using the term reason to explain another cause. That would clearly contradict my notion that a first cause is absolute, so I think even a moderately charitable reading of what I've been expressing would conclude I'm not attempting to blatantly contradict myself. — Philosophim
I have noted many times why this must be, but it might have been missed. First, I'm using 'reason' as an explanation. "Why is this a first cause?" Reason: Because it has no prior cause which caused it. Pretty simple. — Philosophim
And I'll note again, "reason" is not being used as "cause", but explanation. So to your point, "Because it exists" marks the limits of our explanations, yes. — Philosophim
Your point has largely been, "Maybe there's a prior cause to the first cause." This is what I'm addressing. I have not seen a concrete example that demonstrates a situation in which there is a first cause, then you show that logically, there is actually a prior cause to that. If we had a concrete example, we could look at that. And if you have and I've missed it, don't get mad, just repost it. — Philosophim
Look, if there's no prior cause for something, there's no prior reason for something either. — Philosophim
Give me a concrete example of what you mean by a first cause having a prior reason without that prior reason being the cause of the first cause. — Philosophim
Give me an example. — Philosophim
I just typed out the definition of reason and noted I'm using it as a synonym to 'explanation'. I'm uninterested in your opinions that I have no logic, I'm interested in if you can take the logic I've noted, and give a good example of counter object that would demonstrate that my logic is wrong. — Philosophim
Incorrect. You only have empirical evidence of things which have prior causality. As I've noted, we do not have empirical evidence of things which do not. This does not negate the logic that there necessarily must be a first cause. — Philosophim
No, I don't need to do anything. I've clearly laid out what a cause and first cause is as defined here. You need to demonstrate with some concrete examples why this definition is either impossible, contradictory, or doesn't make sense. — Philosophim
If you simply don't like it, that's not my problem. Its on you to demonstrate how one of the most basic logical statements you can construct, "There can be no cause prior to a first cause" is somehow illogical. To my mind where I have given you every benefit of the doubt I can, you have not done so. — Philosophim
Do you understand that if there is something which caused the Big Bang, then the Big Bang is not a first cause? A first cause is not an opinion or belief. It is a reality that we either know about, or do not know about. — Philosophim
The first ball being blue is strong evidence that the box now contains 99 blue balls. However, the first ball being blue is compatible with the box now containing 99 red balls, i.e. the first ball being blue does not prove that the box doesn't now contain 99 red balls. — Michael
What? YOU'RE the one who told ME it was evidence. If I'm prejudiced by granting that it's evidence, SURELY you are too, right? YOU told ME it was evidence. — flannel jesus
n fact, that's the entire reason why I asked you to come up with a scenario and an example of evidence instead of providing one myself - I was predicting exactly this sort of thing from you. I present a scenario, I say such-and-such is evidence, and you find some weird reason to decide "that's not evidence". — flannel jesus
The "evidence" points to one thing being the case, but it's not certain, and you can always conceive of ways in which you would have that eviddence, even if that conclusion is not the case. Fingerprints - a person can be on trial, and have evidence be submitted that their fingerprints are at the crime scene, and nevertheless they didn't commit the crime. It's possible for your fingerprints to be somewhere and you still did not commit a crime there? Those two things are... compatible. — flannel jesus
Evidence is not synonymous with proof. — flannel jesus
The only logical permission for the evidence to not support the approaching object as being “John”, is upon the instantiation of additional evidence in the form of different empirical qualities derived from subsequent perceptions, but not of the same evidence by which the representation was determined. It is by the analysis of these different qualities, and those of sufficient disparity from the antecedents, that the thought of the approaching object cannot in fact be “John”, which is, of course, a significantly distinct and entirely separate judgement in itself. — Mww
To me, it makes perfect sense how I framed it. — flannel jesus
You have evidence. The evidence you have increases your confidence that John is approaching, but you're not certain it's John approaching because the thing you're experiencing as evidence, you could also experience if John were not approaching. — flannel jesus
I don't think there's anything outlandish about what I'm saying here. — flannel jesus
It does not mean that Kant is correct. Scientists showed us in the 20th century that time and space are affected by physical facts. — Lionino
However, that information you have, that evidence, is COMPATIBLE with the statement "John is not approaching", isn't it? — flannel jesus
You're not certain John is approaching - the only reason you're not certain is because you know there's a way where you could experience seeing what you're seeing, while it's simultaneously true that John is not approaching. — flannel jesus
So the statement "I see what I think is John approaching" is completely compatible (but not evidence for, just compatible) with the statement "John is not approaching" - compatible because they can both be true at the same time. — flannel jesus
If they couldn't both be true at the same time, then you would be certain John was approaching.
Make sense? — flannel jesus
In the case of the Big Bang, time and space are created by it and do not exist before it. — Ludwig V
So nothing can be prior to it, whether cause or reason. — Ludwig V
But, it seems to me that a cause cannot exist outside time, whereas a reason can. So there is reason to think that there might be a reason for the Big Bang. But I don't see that there could be a cause for it. (I have no idea what the reason might be, but there seem to be some interesting speculations around.) — Ludwig V
Can you think of a situation where you have evidence for a claim, but the evidence does not leave you certain that the claim is true? Please describe that situation, the evidence, and why you're not certain the claim is true even after finding that evidence. — flannel jesus
I know where the information can be found. You have not demonstrated any specific type of other cause, only vague, "maybes". So far the main point is that a "first cause" means there can be no prior cause by definition. Since you cannot give me a concrete example that gets past this, I see no evidence of any refutation. — Philosophim
Ok, this is a much better point! What you're missing is the phrase 'prior reason'. If you noted I'm not saying that there isn't a reason for a first cause, I'm saying there is not a prior reason. — Philosophim
Just like I told him, there is overlap because if there is no prior cause, there is no prior reason. — Philosophim
The reason why there can be no prior reason for a first cause, is that there is no prior causal event. There can be a reason as an explanation for why a first cause exists, "That is it simply exists." But there cannot be a prior reason, as there is nothing prior which causes it. Does this clear up the issue? — Philosophim
This is not an empirical argument. This is a logical argument. When Einstein constructed his theory of relativity in regards to large bodies, logically, it was sound. It was only after they observed and measured an eclipse that they could empirically confirm it to be true. I make no empirical arguments here. I simply note that logically, if we continue to examine any chain of causality, whether that be finite or infinitely regressive, we will eventually run into a first cause. So no, there is no empirical observation as of yet that refutes this claim, nor any empirical observation that confirms this claim. This discussion is not an attempt at empirical proof, but a logical proof. As such, unless you can logically refute it, it stands.
And this, so far, is the only weakness I've seen in the argument. It is only a logical argument. A logical argument does not mean empirical truth. By the way, Bob Ross is the only other poster to my mind who understood and communicated this right off the bat. Well done, I consider him one of the best philosophers on these boards. :) So, if you wish to say, "I don't care about what logic says, I only care about empirical proof" then I will simply nod my head and state, "That's fine." But that in itself does not show it is a false logical argument. — Philosophim
