Given Tarski's undefinability of truth, any system has no other choice but to receive its fundamental truths from a higher meta-system. — alcontali
But Tarski's and Godel's theorems work within a very strict - formal - mathematical framework. Do you think we can extrapolate them to the real world? — Pussycat
What is the relation between Godel’s theorem and whether we can formulate the theory of the universe in terms of a finite number of principles? One connection is obvious. According to the positivist philosophy of science, a physical theory is a mathematical model. So if there are mathematical results that can not be proved, there are physical problems that can not be predicted.
Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I'm now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery. — Stephen Hawking on Gödel and the End of Physics
Well, rather: extrapolate them to how we perceive the real world. Stephen Hawking lectured the following on the subject: — alcontali
Stephen Hawking on Gödel and the End of Physics — alcontali
The pursuit of wisdom. Wisdom, in turn, does not merely mean some set of correct statements, but rather is the ability to discern the true from the false, the good from the bad; or at least the more true from the less true, the better from the worse; the ability, in short, to discern superior answers from inferior answers to any given question. — Pfhorrest
To that end, philosophy must investigate questions about what our questions even mean, investigating questions about language; what criteria we use to judge the merits of a proposed answer, investigating questions about being and purpose, the objects of reality and morality respectively; what methods we use to apply those criteria, investigating questions about knowledge and justice; what faculties we need to enact those methods, investigating questions about the mind and the will; who is to exercise those faculties, investigating questions about academics and politics; and why any of it matters at all. — Pfhorrest
The tools of philosophy can be used against that end, but I prefer to call that "phobosophy" instead. — Pfhorrest
But saying "to any given question", this opens philosophers up, it makes them vulnerable to ridicule. — Pussycat
What does running want? An activity isn't the kind of thing that has wants. It's a means. Why run? To get somewhere fast, or for exercise maybe. Why do philosophy? I already answered that.But what of philosophy? What is its agenda? What does philosophy want? — Pussycat
How we perceive scientifically the real world. I mean, if the only means of perception we have is science, but is it? This is scientism, which may be right of course. — Pussycat
And after all, in both Tarksi and Godel, both concepts of proof and truth are extremely well defined. In the case of the real world however, even from a scientific outlook, they are completely vague: you can conjure them as you see fit. What is truth? What is proof? (well, not the TPF user) — Pussycat
"Science is increasingly answering questions that used to be the province of religion," Hawking replied. "The scientific account is complete. Theology is unnecessary." Wow! "The scientific account is complete"! — Pussycat
Or perhaps the more sensible thing to do would be to abandon any attempt to define 'truth' or even to use it in any formal system. — A Seagull
Or perhaps the more sensible thing to do would be to abandon any attempt to define 'truth' or even to use it in any formal system. — A Seagull
I personally think that Tarski's convention T is an elegant and adequate workaround for the undefinability of truth. The video below explains convention T in approximately 10 minutes and in a surprisingly simple way: — alcontali
Well I watched your video. It seems that the main aim of the T convention was to avoid the so called 'liar paradox'. — A Seagull
Without the requirement for statements to be 'true' or 'false' but that instead 'true' or 'false' are merely labels that can be appended to a statement, there is no paradox nor problem. — A Seagull
It would not even be paradoxical for a statement to be labelled as both 'true' and 'false'. — A Seagull
Mathematics has no direct empirical take on the world. Its models are always abstract Platonic worlds. It is through its influence on empirical disciplines (such as science) that it affects our real-world view. There are obviously other empirical disciplines such as history with its historical method. However, in my impression, history does not use the language nor the invariants of mathematics. — alcontali
There is no proof in empirical disciplines, simply because proof about the physical universe is impossible. The regulatory framework in use in science with which they attempt to maintain correspondence between their logic sentences and the physical universe is obviously far from perfect. Falsificationism is merely a best-effort endeavour. — alcontali
Any link to that? — alcontali
And because of this distinction between the formal/mathematical/non-empirical/logical world and the real world which is nothing like the other, we should be really suspicious of attempts made to reconcile the two. — Pussycat
Tarski's theorem is good for maths, brilliant even, but when it tries to apply itself to the real world, then it is an abomination. — Pussycat
What is the relation between Godel’s theorem and whether we can formulate the theory of the universe in terms of a finite number of principles? One connection is obvious. According to the positivist philosophy of science, a physical theory is a mathematical model. So if there are mathematical results that can not be proved, there are physical problems that can not be predicted. — Hawking
he makes the error of applying Godel's theorem to physics and the real world. There is no connection, let alone an obvious one. If one thing is obvious, this is Hawking's misinterpretation of the theorem. — Pussycat
-And as to truth, I said, is not a soul equally to be deemed halt and lame which hates voluntary falsehood and is extremely indignant at herself and others when they tell lies, but is patient of involuntary falsehood, and does not mind wallowing like a swinish beast in the mire of ignorance, and has no shame at being detected?
-To be sure.
-And, again, in respect of temperance, courage, magnificence, and every other virtue, should we not carefully distinguish between the true son and the bastard? For where there is no discernment of such qualities, states and individuals unconsciously err; and the state makes a ruler, and the individual a friend, of one who, being defective in some part of virtue, is in a figure lame or a bastard.
-That is very true, he said.
-All these things, then, will have to be carefully considered by us; and if only those whom we introduce to this vast system of education and training are sound in body and mind, justice herself will have nothing to say against us, and we shall be the saviours of the constitution and of the State; but, if our pupils are men of another stamp, the reverse will happen, and we shall pour a still greater flood of ridicule on philosophy than she has to endure at present.
-That would not be creditable.
-Certainly not, I said; and yet perhaps, in thus turning jest into earnest I am equally ridiculous.
-In what respect?
-I had forgotten, I said, that we were not serious, and spoke with too much excitement. For when I saw philosophy so undeservedly trampled under foot of men, I could not help feeling a sort of indignation at the authors of her disgrace: and my anger made me too vehement.
-Indeed! I was listening, and did not think so.
-But I, who am the speaker, felt that I was. And now let me remind you that, although in our former selection we chose old men, we must not do so in this. Solon was under a delusion when he said that a man when he grows old may learn many things–for he can no more learn much than he can run much; youth is the time for any extraordinary toil. — Plato
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.