Can philosophy integrate the irrational as mathematics can?

Objectivity refers to the idea that everything is what it is - NOT necessarily what anyone thinks it is. Both Magnus and I have been trying to explain that to Great Again by saying that a process (at any one time) is either rational or not. Nothing can be both rational and also irrational. His response has been that perhaps we mislabeled it, misunderstood it, or just don’t know. He offered a Venn diagram showing a region that is both rational and also irrational.

The objective point of view is that how we label it is irrelevant to what it actually is. But he hasn’t accepted that answer. So when he said that a Venn diagram is static while reality is always changing he revealed that he believes that the diagram that he stated to be the real case concerning rational vs irrational is itself static and so not the changing objective reality of the subject. He is saying that the diagram is both true and not true at the same time and dependent on our accuracy and knowledge.

All of that implies that he is not accepting objective reality - else how we label things would be irrelevant. When someone doesn’t accept objective reality they are claiming man-made reality.

It has nothing to do with prejudice at all. You are claiming that some things are what they are and also what they are not at the same time because we might not know what they are. The point is that what we know is irrelevant to what they are - that is objective reality and what your diagram was supposed to be representing - although obviously in error.

And now your response sounds exactly like this -

I understand. The problem comes when people don’t acknowledge that we can never truly comprehend things as they are(re: the idea that everything is what it is). We have to exercise some faith when mixing realities(internal vs external). Things are always rational and irrational in the brain - you don’t get to choose a brain state and if the brain produces the mind then the focus might be the only thing that feels rational. The Venn diagram is a very simplified version of this. I don’t think it is mandatory that Great Again accepts any answer. I think the diagram can not be in a state of true and false - this is something else. Lastly - how we label things are relevant just as external and internal realities are always changing. Nothing changes fast enough for an accepted objective reality not to be useful for a long period of time. Perhaps this explains why good metaphysics is always able to keep up.

Yes we try to describe actual reality as well as we can (by defining our words - which GA doesn’t seem to want to do). And then we apply the rule of logic - remain always consistent in our language - while observing actual reality more in order to discover if our description of reality is accurate. If we don’t do that we can never know anything at all. We can’t even estimate reality with any confidence.

AG is starting to sound like the Schrodinger’s cat quantum physicist who says that the cat is both alive and dead at the same time because we do not know and once we discover if it is alive - reality becomes whatever we discover. That is subjectivism (“reality is whatever we believe”), not objectivism (“reality is independent of what we believe”).

Let’s do what those who found problems with what the quantum magi did and add super-determinism on top(keep playing the game of matryoshka). To know anything at all, it helps to apply justified-true-belief(hence the need for faith). I just don’t want to see you boys get lost in another rabbit hole if not by choice.

I added to my last post: Perhaps this explains why good metaphysics is always able to keep up. A good metaphysics is still able to account for the irrational.

I am about to decide that AG simply has his bubble of belief and challenging that makes him uncomfortable so I should leave it alone.

- a true James fan.

Nobody said that estimates and probabilities were irrational.

“Irrational” simply means “not rational”. Whatever the word “rational” means, the word “irrational” means the opposite of it. So it’s not possible for something – whatever that something is – to be both rational and irrational because that would mean that thing is both rational and not rational. That’s a logical contradiction: P and not-P. So whoever says “Things can be both rational and irrational” is either 1) contradicting themselves, or 2) they are defining words in a different way. And if they are defining words in a different way, the problem can be easily resolved by them defining their words so that other people can know what they are talking about.

It doesn’t help that the word “rational” has different menaings when applied to different types of things e.g. numbers are rational in one way, decisions are rational in another way, people are rational in yet another way and so on. (Though, it goes without saying that, in each case, a thing is either rational or not. It cannot be both.) So it would be really helpful to know what kind of rationality we’re talking about here. And it would also be useful to know what’s the connection between the rationality of numbers (“mathematicians integrating irrational numbers”) and the rationality of people (“societies integrating irrational people”).

That’s a somewhat dangerous thing to say. It really looks like (and I really only hope it only looks like) you’re saying that it’s a bad thing to always make good decisions and that it’s a good thing to mix the two e.g. by making good decisions 80% of the time and bad decisions 20% of the time. It’s one thing to say people are imperfect, it’s another to say people should be imperfect.

Clearly, you have understood nothing at all.

It has exclusively to do with prejudice.

Your statement only confirms my previous assumption. Now the little boy is offended.

It is the bubble of pseudo-rationality that you are in. You really believe that all you have to do is keep the irrational far enough away from the rational and then you have your “solution”. Yes, the solution you are seeing right now: The irrational dominates you. That is your “solution”.

Again: You are not the first to constantly sanctify the rational and thus demonize the irrational and therefore not realize how irrational that is.

And again: You have understood absolutely nothing. You show that more and more clearly.

You falsely believe, by saying to “adhere to rationality”, that understanding is not a problem for you. In reality, this is exactly your biggest problem, as you show here more and more clearly. You are stuck in a trap, in the bubble of pseudo-rationality.

You run away from reality, always back into your bubble.

At the same time, you once said a really important sentence in a thread, but you yourself satirically dismissed it in this thread, as if you wanted to draw a caricature of yourself. I have taken this sentence to one of the occasions to open this thread. I did not know at that time how inflexible you are in thinking.

I wonder why you are even posting in this thread, because you obviously don’t like the topic of this thread.

I have stated what this thread is about. You want to make it your thread. Then go ahead and make a thread of your own. Good luck with that.

Mathematics is not free of irrationality. But it seems to be the last discipline which is still able to integrate, to include, to control parts of the irrational. Physics has already given up.

Nevertheless, mathematics has problems. And these problems started at the same time as the problems of physics - with the difference I mentioned above.

With mathematics one can do almost everything - thus also nonsense.

With the problems I do not only mean the fundamental crisis, concerning the solution of which formalism, conventionalism and intuitionism opposed each other. Not only this problem has not been solved properly. But it has given another, an important insight: that there are undecidable questions within mathematics (cf. proof of Gödel). On the other hand, definitive proofs of non-contradiction have been given for wide areas of mathematics (cf. Hilbert, Genzen).

Logical considerations play an important role, among other things, in the construction of an antinomy-free set theory and in the general theory of proof. Pioneering work in the field of mathematical logic, which is closely related to the philosophy of mathematics, was done in the 19th century by Frege, in the 20th century by Russel and Whitehead.

I have drawn the undecidability I just spoke about into a diagram in the topic “rational/irrational” and called this diagram a “dynamic, i.e. historical diagram”. That must be allowed. I don’t have to follow guidelines when I want to illustrate something. This is what I meant when I said that “Venn is not a god for me”.The antinomies of set theory speak a clear language (best known example: “set of all sets” - it must, but must not contain itself), even if one has simply taken them out of set theory. Antinomies appear again and again, and it is the task of history (in this case: the history of science or epistemology) to solve them, to which also the history of philosophy can contribute. No theory can remain static; theories change with the time: that is history (time => change <=>history). There are also still undiscovered antinomies in set theory as in mathematics as a whole.

The bivalence principle (cf. “principium exclusi tertii” resp. “tertium non datur”) as the principle of bivalence of classical logic, according to which a statement must always be true or false, has been criticized for various reasons and logics have been designed in which it is not valid and in which there are more than two truth values.

There are logic systems which use three and more, even infinite truth values. One speaks of a multivalued logic. Antinomies appear again and again, and it is the task of history (in this case: the history of science or epistemology) to solve them, to which also the history of philosophy can contribute. No theory can remain static, they change with the time: that is history (time => change <=> history). There are also still undiscovered antinomies in set theory as in mathematics as a whole.

According to Gödel’s result, one must presuppose an infinite number of truth values, e.g. in a semantics of truth values, which exactly marks out the principles as valid, which are derivable in an intuitionistic calculus. A descriptive interpretation succeeds in the framework of the possible-worlds semantics. The intuitionistic logic is a system of formal logic, which is supposed to satisfy the criticism (!) of the mathematical intuitionists against the modes of reasoning of classical mathematics.

One knows that there are statements which are undecidable. I have pointed to this - and to the fact that the undecidability is changed by the time, i.e. by the change and thus by the history, e.g. its extent is reduced or increased.

I did not say that anybody did. I was saying in the sense that estimates and probabilities are not automatically irrational, in other words, they can be rational too.

I would be tempted to frame the question in terms of philosophical branches, as in, axiology, epistemology, and metaphysics.

What kinds of things are valuable, what is knowledge, and what are first principles - how these things add up when compared/connected/or possibly even combined.

Zookers - you have gone completely nutters hostile. And if you actually believe what you just wrote - completely delusional. If you think that I was being at all hostile - that had to be your own projected hostile imaginings - and a bit arrogant.

I have been genuinely and patiently trying to get to a resolution for the question you posed (assuming your best intentions) - having to ask and guess at what you really mean by the words you use such as to forgive differences and clear up the confusions. I think Magnus is seeing the same thing. But you appear to ignore such efforts and want to keep your word usage a mystery and seemingly illogical/irrational (why not clear it up?). I think there can be only a few reasons for that -

• You didn’t want a rational and civil discussion
• You just wanted to argue for the sake of arguing
• You want the question to be unanswerable
• You have your own pet theory, or just maybe -
• You really are nutters

But maybe you have some other reason. And it is clear that you have no intention of finding resolution and have now fallen into ad homs so - you certainly aren’t going to get anywhere with Magnus.

Play your game - lecture away. It’s not my problem anymore. MIJOT dictates that I bid you adieu.

Gödel’s theorems show in practice (in mathematical method) what Heidegger’s Nietzsche shows philosophically; that reason is a method deriving from a drive, rather than anything to do with comprehensive objective reality.

Its reality is objective in the sense that its employment will have its effect. Its descriptions of reality outside of itself are only descriptions of itself.

Rational methods value the world in terms of themselves, as everything that exists does in order to exist.

This itself is the final truth we can know; it is not a model of the universe, but it destroys all false models.

Without logic - there can be no maths.
Without logic - there can be no rationality.
And without maths and rationality - there can be no Gödel’s theorems.

Do you reject the law of excluded middle?

I understand that the creation of multivalued logic does not have to be a consequence of, nor an accompaniment to, the rejection of the law of excluded middle but the impression that I get from doing what little research I did on this subject is that this is precisely why multivalued logic was created in the first place.

It seems it goes back to Aristotle’s paradox of the sea battle.

And even before Lukashevich (not to be confused with Lukashenko), there was Charles Sanders Purse (known for his obsession with number three.)

I kind of preferred this before you edited it.

I can see why.

I can also see that this issue of irrationality is all confused because as far as I can tell - there are 3 distinct and only mildly related meanings for the word “irrational” and they are not being distinguished -

• In maths it means that a magnitude cannot be exactly expressed using the language of numbers alone
• In logic it means an inconsistency in the language being used
• In behavior it means that a goal is not met

Those are 3 distinctly different uses for the same word (and there might be more).

If something is to be “integrated” (whatever that might mean) it helps to know exactly what it is that you are trying to integrate - the magnitudes into numbers - the inconsistency of language (such as in this thread) - or the accomplishment of intended purposes.

Until that is set straight - this whole discussion is - behaviorally-irrational because of the consistency-irrational that is being conflated with the numerical-irrational.

Or at least that is the way this rationalist sees it.

Through a little research it seems that the ancient Greek establishment mathematicians were insisting that all magnitudes could be expressed in numbers - a language=reality issue (similar to today’s wokism, “brave new world”, political insistence that language dictates reality). But then someone used logic to prove that it is impossible for certain magnitudes to be expressed with merely numbers - specifically the square root of 2, (\sqrt 2). No set of numbers can exactly express that magnitude (wokism in ancient Greece is cut down with logic). So the establishment declared those numbers as “irrational” - “incommensurate with our holy doctrine”.

So they began a new language for maths using “magnitudes” in place of merely “numbers”. And because it was the logic of geometry that had exposed the issue - apparently they strongly shifted to trying to express all reality in the language of geometry - a new wokism to be explored (I could already smell the Godwannabes).

Eventually it was realized that the issue of the explained much earlier idea of logic that was really the immutable determiner of what could be proven to be true or not. Logic wasn’t a language but rather a rule - “thou shalt be consistent in whatever language you use” or “keep your words straight”. So Logos became the default king of language - for a while. And even the religions of the day had to try to comply - eventually destroying Hellenism and polytheism (they could not stand to the might of logic). But a single God idea actually could stand in the face of logic and “irrational” became whatever could not be expressed with consistency - “irrational = inconsistent”.

Somewhere along the line and eventually merely consistency was unsatisfactory. Ideas could be expressed with consistency in the language yet still be proven to be untrue to reality. I’m thinking that was due to the issue of premises being false assumptions. So during the 15th century or so assumptions came under attack because when ideas were untrue - they failed to produce intended goals even though the god - logic gave them a pass.

And from there it is my speculation that that if a logic of actions did not produce the intended goal - it was declared “irrational” and not to be enacted.

So it seems that gradually the idea of being irrational grew from -

• not being commensurate with a language -
• to not being commensurate with consistency -
• to not being commensurate with real goals.

Perhaps today it might narrow down to mean - “not commensurate with political dictates” = “irrational”. Then eventually that might narrow down further to mean - “irrational = unacceptable language use” which then might further reduce back to “irrational = incommensurate with a particular language” - like maybe Woked Mandarin.

Another way to look at this is as follows:

Let’s illustrate using the concepts of emergence and reductionism. Whatever emerges must be able to be reduced to the sum of its parts.

If the irrational comes from the mind and the mind is produced by the brain and the brain is produced from matter and we can explain the matter in a logical manner using science…

…then it is not unreasonable to infer that philosophy can integrate the irrational through explanation - creating knowledge of the irrational. What I am more concerned about is the value of the irrational…

…as in, does irrational thinking have much value?

Our explanation of all that exists is also still incomplete. Metaphysics on the other hand offers us a doorway into the unknown - allows us to have insight into answering questions that science is still struggling with…

…through possibility.

Not if we can’t decide what “irrational” means.

• too many new words for me to have to investigate.

I’m still trying to see if there is a logical contradiction proof that pi is irrational. The standard proof (using an infinite series) is deductive but I feel like there should be a better way.

Simply put, my answer is yes “the irrational” as GA states in the OP can be integrated into a rational system such as philosophy(well, what I hope it to be) - I have proven this already with a computer model and it goes both ways - I can make the irrational rational and the rational irrational - but why would we want to teach anybody to be irrational - it makes no sense - teach people to stub their toes: like, huh? I said before we should acknowledge the irrational - accept or admit the existence or truth of(Google). I don’t think it should be integrated into philosophy - we can think about it, there is no issue with that. Dealing with the irrational is different to the integration of it.

Man, I want to keep going but I will pull up here for a moment.

Hmm, I also remember writing a lexer once and the language I was using did not make the lexer do what I wanted(actually, needed) it to do and I had to do something irrational(not logical) in the code to get the lexer working…

…so I guess there is that.

Mind you the language was written by a French guy, so there is also that.