This room is primarily used to discuss Mathematical Logics, if you have any question on Logic feel free to ask, someone should be here shortly(more knowledgable than me) who will try to answer your questions! Nevertheless, I may attempt a discussion on the same :)
@user21820 Also, Boolos: "Thus a Godel sentence 'says of itself' that it is unprovable..."
user131753
3:47 AM
@user21820: Do you know of any formal system that has a real meaning but has no model?
user131753
@DavidReed: Have you gone through all the links that were suggested as a reference to your question "Was Mathematics invented or discovered?" in the Philosophy of Mathematics chat room?
@user170039: I should add that for set theorists who believe that the set theoretic universe somehow exists (even though meaningless in the real world) they believe that ZFC has a second-order 'model', which of course is too big to be a model in the usual sense as defined in ZFC itself.
This viewpoint can be seen in various posts, but I'm a bit lazy to find them since I'm sure you can. Just search for "second-order ZFC".
=)
@DavidReed: Anyway do you like abstract games and puzzles?
@user21820 Wanted to say I'm not convinced that there is a logical argument for existence of Supreme being and that there is one refuting we are our bodies. However I see you finished the conversation I started yesterday, maybe some other time we discuss it!
@user21820 How many times has the sun gone around you?
@LastIronStar Well it's okay to be not convinced. I'm not vested in convincing anyone. But you should think carefully about my reasoning that I linked you to at the beginning that leads to the conclusion of a lawmaker.
Basically, everything as a whole is a sufficient reason for everything, and we wish to look at a minimal part L of everything that is still sufficient reason for everything. L must be a lawmaker because L cannot itself be yet another physical law. And from the stability preserving property of the physical laws it makes sense to infer that they were not instituted arbitrarily, and hence L must have had some intent behind them.
(To me at least.)
@LastIronStar Matters of perspective do not matter because I am referring to matters of absolute truth, and not statements whose meaning changes from context to context. =)
@user21820 moreover, a logical argument means that the conclusion is inevitable for anyone willing to follow through the argument as long as they agree on your assumptions.
@LastIronStar Of course, and my argument I just summarized is actually logical even if you don't accept my premises (which I didn't really state). =)
Oh by the way, science is also based on a slight assumption of some form of free will, because for falsification of a hypothesis to be possible we have to assume we can in fact run experiments on arbitrary inputs so that we can obtain statistical data.
This is a much weaker form of free will (some may not consider it free) than the one I believe in though.
@user21820 I probably should nail down the difference between cogent and logical in my head. One keeps popping up when the other is what is needed. Now i'm confunded as to whether I believe there is not a cogent argument or a logical argument. I think it is not possible to use perception and inference to establish Supreme being. So I believe that Logical Argument is itself not possible then!
Ofc, I've not refuted your logic, which granted you will probably have to wait a bit longer for if you are interested to know.
@LastIronStar Well if you a priori assume that logic cannot achieve something, then you of course have restricted yourself to be unable to do so (or at least unable to consistently do so).
Anyway I said before that any argument involving the real world is not going to be capturable 100% syntactically.
@user21820 It's not apriori, I have had to construct counters to logical arguments for SB before this, so this one i'll have to construct one too. Just not constructed yet.
@LastIronStar Actually I didn't get your this remark the last time either. If you are saying that the physical world is not everything, then it is already an unscientific (and empirically unfalsifiable) statement, so why is it so strange that I also invoke philosophical arguments that go beyond the physical world to infer that there is a lawmaker that is beyond the physical world?
@user21820 I claim that using logic (perception and inference) it is possible to make my claim. So it is not unscientific but rather a tautology(am i using it right?)
@LastIronStar David would probably disagree with you, I think.
If however you hold that you are purely a result of biochemistry and social interactions and your physical environment, like David seems to, then you are essentially saying there is no such thing as free will. But then you have to think again about your assumptions regarding scientific experiments.
@user21820 No I'm saying we are something that is embodied. Not the body itself. and that the embodiment cannot create or destroy that something's existence.
@LastIronStar: If on the other hand you hold that you are not purely physical, then you cannot a priori dismiss my philosophical argument as invalid just because it invokes reasoning about things beyond the physical world. The concept "everything" is not something that you can perceive or infer from perceptions.
@LastIronStar Well that's a matter of perspective then. Any cogent argument can be represented by a logical argument, by translating it into some suitable language. There is still the semantic gap to go from the translation to the intended semantics, but it can be considered logical.
After all, if you take any simple number theory fact like Fermat's little theorem, it is just a symbolic string. We use it in practical real world applications like RSA by interpreting its intended semantics.
@LastIronStar: Similarly, I could write my argument in some formal system by appropriate use of symbols to represent the entities and concepts I am referring to, and you can very well disagree with the semantics I wish to imbue them with. But the argument itself can be logical; just that we may disagree on whether it means anything in the real world.
So when I said "logical" I meant that the argument has a relatively clear logical structure, so all that is left is for you to analyze its assumptions.
@LastIronStar The base assumption is that everything has a reason, which is captured by a conceptual category, which may contain more than one entity.
Thus the conceptual category "everything" has a reason, but the reason itself is part of everything. So we conclude that "everything" as a whole is a reason for "everything".
But that's not what I'm after. I wish to get to a minimal reason for "everything".
And by suitable assumptions, I can conceive of and define L to be such a minimal reason.
And then you look at the physical laws, which must too have a reason.
That reason cannot be part of the laws, because a law needs something to institute and enforce it. This again is some further assumptions. You can represent it via axioms if you wish.
Thus L is beyond the physical laws, in the sense of not being contained by the physical laws alone.
I just call L lawmaker because it's a fitting word, but you can stick to L.
Then you go on and reason about the reason for the way the laws are.
Of so many possible choices of consistent laws, this particular collection was instituted, and there must be a reason. This reason resides in L.
L has intent, and that intent must be consistent with the nature of the laws, which appear to us to be stability preserving.
Hence I infer that L's intent includes stability preserving.
Can an unconscious entity institute highly stability preserving laws? Well, of course anything consistent is possible... But unlikely (in my information theoretic sense).
@user21820 Why is reason necessary? You are saying that there needs to be a reason(which if i'm not wrong is to be understood as the perceptive and inferential faculties we possess)
@user21820 Ok, so is it right of me to think that a logical argument requires us to understand what the assumption is in order to establish whether it is logical or not?
Why not. You definitely assume this axiom in everyday life. When you encounter something, you expect that there is some reason behind it even if you cannot figure it out. That reason may be random fluctuations in some things, or it may be conscious intent by someone else, or something else.
The axiom merely says that it applies to everything, not just things in your daily life.
@LastIronStar I'm not sure what "efficient" here means. But generally most reasons are causal, and some others are of necessity rather than causal. I'm using the meaning of "reason" exactly as one of the dictionary definitions of it in English:
> c. A fact or cause that explains why something exists or has occurred
@DavidReed Yes. But here I was a bit more precise and say that a reason can be a conceptual category. So many different categories could be reason for the same thing. It is more like a relation.
And I am interested generally in the minimal reason for things.
If you see your phone broken, you immediately infer that there is a minimal reason for it. You do not tell yourself that the universe or some big bunch of random facts is the reason for it. You instead guess that someone or something did it to your phone via a direct physical interaction.
No. It's just that in logic we represent necessity via modal operators.
@DavidReed: By the way, in my opinion anyone who rejects this axiom that everything has a reason essentially does not want to address the question of why the world is the way it is. To see why, consider that our best guess is that the big bang started this universe. Where did the big bang itself come from? If you say it just arose, you're evading the issue. If you say there were previous cycles, then why are there cycles in the first place? What governs those cycles? And so on.
@user21820 Ok, well admittedly i am very tired, and have been in and out of the conversation. I should be able to give it a more alert look tomorrow. I'm off to bed for now though. Will see you guys soon.
@mercio I only briefly looked at the theoretical type theory underlying Coq, and suffice to say it's totally ad-hoc. There were a number of early version that were found inconsistent, so the current system is really a potpourri of random notions that nobody has found an inconsistency in yet. =P
@user21820 You are correct regarding me not wanting to address why the world is the way it is. Questions for me like "what caused the big bang" are very likely beyond the realm of human intellect, and at the very least beyond mine.
@user21820 I reject the axiom though, although its an implicit assumption in my day to day life as you mentioned, because it is too general and abstract for my personal taste
@DavidReed Alright. No problem. In fact, if you don't already know by now, I do not really care what people believe in, as long as they do not (except in exceptional circumstances) harm others intentionally.
=)
@mercio We were discussing non-logic stuff a while back.
@DavidReed No you haven't harmed me! I'm saying that beliefs are of secondary importance to me than morality, so it's perfectly fine for you to disagree with me strongly on beliefs that do not impinge severely on moral decisions.
@LeakyNun No I didn't. If the username does not show up when you type the @, it means that they will not get pinged (because they were not there recently enough).
