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Sure, I am willing to go there and just restate the useful discussion. Please just explain your position again, I will do the same in the following positions:
Everybody including secular materialists, Bayesian Big Yud rationalists, relativists and everybody else engages in presuppositions.
All my arguments were asking for philosophical justification of beliefs. I was specifically arguing against the naive "math is self-evident" argument that you presented, which turned the argument to "it is evident to me" as opposed to found that argument on something. I was using internal critique to find your foundation of why you believe the assertions that you make.
This ties to ability of anybody to make universal claims. I specifically wanted to use internal critique if your position. Is it mathematical realism in the vein of Gödel, Kantor, Penrose or Tegmark? Or is it nominalist in the vein of philosopher Harty Field or earlier Quine (who later became mathematical realist) or even Hilbert with his formalism or weird blend of mathematical anti-realism like Yudkowsky or Joscha Bach? We could never go there in our discussion, because I was not able to relate what universal claim is, how Hume or Descartes tried to wrestle with it.
Which leads me to the topics that we had. Asserting that 2+2 equals 4 is just lower level assertion. Again, there needs to be justification for it let's say in terms of "Justified True Belief" standard or some other standard such as nominalism, which is inherently relative. Again, these are not some stupid ideas that georgioz on The Motte said, they were discussed between top philosophers - including modern philosophers of science and Math like Kantor for centuries.
I had constant whiplash where you demanded plain English but at the same time claimed to have knowledge of Gödel and his proofs sufficient to understand it.
Anyways, I challenge you again - what is your underlying presupposition, your metaphysics, epistemology and to lesser extent ethics:
What is the nature of reality, visible (e.g. matter, energy, planets, galaxies) and invisible (math, logic, abstract concepts). How do they exist? Why do they exist?. It takes more then a baby eating alien Yuskowsky story, or just claiming - "here, I wrote number 2 on paper as an example of existence of numbers". This is the purview of ontology. As long as you say "standard numbers exist", there is a question of "how they exist" or "why they exist". And this is not just some word game. There are 150 IQ people who disagree about nature of these things. If they can have disagreements, why cannot we rehash these modern debates here?
The nature of epistemology. What is knowledge, what is "Truth" and how can we justify something as true vs not-true. Be it My name is stoatherd and I know it to 2+2=4 to all there exists is just matter and energy. These are all dogmatic claims, that need to have some justifications. Secular atheists make fun of let's say Christians that they believe in made-up unjustified entities such as God or Angels or whatnot. Now the ball is in your court, how do you justify your beliefs and how and why are they better? Why and how do you posses the knowledge of the Truth and everything else?
Also I do not like ad hominess and other rhetorical tactics, but I will meet you where you are at. I also claim that this specific game is asymmetrical but from secularist point of view. It is considered a standard argument to say that "HAHAHA, stupid Christians believe in unproven and unjustified fairy-tales". Only to then act all indignant when in turn somebody asks them about their fairy tale cosmology and empiricist dogmas that one should take on face value. If you show basic philosophical respect, then I will show the same back.
I think there are basically two assumptions that one kinda has to make in order to have a philosophical discussion:
No Cartesian Daemon fucking with our ability to do logic and philosophy.
The world exists - not necessarily "for real", but still as a whole. If we are brains in jars being fed simulated sense data, the simulation does at least model Earth and thus it is possible to deduce things about the simulation.
You need assumption #1 because if there is such fuckery, then it fatally undermines any attempt to search for philosophical truths, so what's the point?
You need assumption #2 because if the world doesn't exist, you (or from your perspective, I) probably don't exist and the discussion would again appear pointless. Also, because a deus deceptor even restricted from directly messing with our ability to do philosophy closes off huge swathes of questions to anything beyond "well, I dunno".
You do not actually need assumption #2, though, to prove that 2 + 2 = 4. Proof:
2 + 2 = 2 + (1+1) = (2 + 1) + 1 = 3 + 1 = 4.
First step is the definition of 2, second step is the associative property of addition, third step is the definition of 3, fourth step is the definition of 4. All of these are axioms (as is the transitive property of =). Maths is only ever asserted to be true with respect to some set of axioms; sure, this isn't true in Tropical but we're not talking about Tropical. Either my ability to do logic is being fucked with, or 2 + 2 = 4, no empiricism required.
Yeah, I basically gave up on arguing with philosophers (sorry, @naraburns!) after an extremely frustrating exchange in which a philosopher (actual Ph.D. in philosophy) would not stop answering every claim I made about what we can observe or think we know about reality with basically: How do you know God/Cartesian demons/the Matrix aren't fucking with you so you only think you know things? Well, fuck, I guess philosophy is pointless if we can't possibly make any statements about reality because we can't prove we're not living in a simulation.
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There's no contradiction there. I was asking for plain English because I think you are tripping yourself up using complicated phrases.
I'll do an analogy. Imagine you ask someone why the sky is blue, and they say: "Quantum decoherence causes the eigenfunction to scatter the ket vector of that wavelength". All of those are real words, and have real technical meanings. But the person saying that sentence is confused, and they're not giving a true or even meaningful explanation.
So a good approach is to ask that person: "Can you please explain what you mean in simple English?" If they have a coherent idea in mind, then they can go: "Sure! Basically, we can think of each atom as a cloud, and when a wave of light passes through that cloud, it interacts with ..." and so on.
I have sufficient knowledge of Godel and his proofs. I just think you're invoking him wrongly, and in order to argue that point, I'm trying to pin down exactly what you mean.
As I said before, I don't know what you mean by "how" a thing exists. What kind of answer does that question even invite? What do you mean?
You're presupposing that these things do exist, or that it's simple to declare that they do exist, which I think requires a bit more of a rigorous definition of "exist".
Let me split your entities into two categories: Type A (physical arrangements of matter/energy -- galaxies, planets, houses, apples, trees, etc), and Type B (everything else).
It's easy to answer why Type A things exist: because of the laws of physics acting on the prior state of the universe. A planet exists because a bunch of cosmic dust existed before it, and then gravity compacted it.
Why do Type B things exist? e.g. the universe, numbers, justice?
That's a confusing question, because the word exist was invented to describe Type A things. The meaning of "exist" concerning Type A things is clear: if you ask "does an apple exist?", you're asking whether a certain physical arrangement is present in the same universe as you. So there's a clear implicit meaning of "exist" concerning Type A things.
But when you start saying "numbers exist" or "the universe exists", it's not clear what that means. So before I can answer why these things exist, I need an explanation of what you mean by something like "numbers exist" or "the universe exists". (This is a similar issue to when you say "modal collapse": I think you're unintentionally smuggling a very complicated idea into the simple word "exists", and it needs to be broken down into simpler words.)
The possession of an accurate model of a portion of reality.
The nounified version of the adjective "true". A claim is true if it accurately represents reality.
If a claim accurately models reality, then it is true to the extent that it does so. That's what "true" means.
We can be mistaken about calling a thing true, in the same way that we can be mistaken about literally anything.
They aren't. I verify my username by repeated observation and evidence. This is the same process I use to verify 2+2=4.
I haven't claimed "all there exists is just matter and energy". I'm entirely open to the idea of there existing additional things. But either they interact with the physical world, in which case they are physical; or they don't, in which case this is a very exotic use of the word "exist" that needs defining.
Observation and testing. They are better because they work. I'm fine with that not being considered "justification"; I'll just enjoy my beliefs working.
I... don't?
I have some knowledge. Some of my knowledge is presumably wrong; I don't know which parts. I don't have complete knowledge of everything. These sentences are true of everyone.
I am not doing this, and I'd prefer if you didn't do it either.
Dude, I haven't done this. If you think I've done this, please point to where.
It seems other people haven't shown what you consider "basic philosophical respect", and you're using that as an excuse to be disrespectful to me. I don't think that's great.
It is not easy and definitely not an explanation. You just assert: "Laws of physics exist". It is a presupposition. What are these laws, why do they exist and how do they exist? Moreover how do you know that they exist? Are they uniform or do they break sometimes? Are they omnipresent and unchanging and eternal? On its own this is an outrageous statement on par of saying that "God exists".
You said that you are empiricist. You know, that no amount of evidence can prove a thing. That is the core observation of Quines Undeterminism of scientific theory. There are number of alternative theories that can explain things. This is rooted in age old sceptical tradition from Hume and Descartes. Maybe you are suffering from schizoid mental illness, or there is Carthesian Demon feeding you false information and you falsely think that you are stoatherd. Moreover you filter which evidence to examine and accept into your web of beliefs as any other schizoid person who sees everything as a proof for his own personal conspiracy theory.
Okay so I can say that God and unicorns work for me and thus they exist. Or you may object and have some outside criterion on what is "useful" and what "works" means. Then I would challenge you to either state that dogmatic yardstick, or ground it in pragmatism itself.
No, I didn't.
Good thing I didn't make that statement, then.
As I keep saying, you need to explain what this question means.
No, I didn't. You inferred that.
Sure, in the sense that literal 100% proof of anything is impossible.
Ok, then show me the unicorn.
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