That’s like trying to turn an even number into an odd number without changing the number itself.
It’s not clear what you mean by “irrational”. I know what the word means in mathematics and I know what it means outside of mathematics but I don’t know what you and the philosophers you cite mean by that word.
In mathematics, the word means “a number that cannot be expressed as a ratio of two integers”. If a number is irrational, then you’d have to change it in order to make it rational.
Outside of mathematics, the word means “a decision that does not lead to the best outcome compared to all other decisions that are available at the time”. If a decision you made is irrational, but for some reason you want it to be rational, you’d have to go back in time and either change how the world works or change your preferences at the time.
But that’s not what you’re talking about, right? You’re talking about something that “cannot be grasped by reason” and I have no idea what that means.
Ludolf’s number, also known as the number pi, the circle number, is a transcendental and therefore irrational number that gives the constant ratio of the circumference of a circle to its diameter: 3.1459265358979346… (a non-periodic, infinite decimal number). Mathematicians and meanwhile also computers cannot make a rational number out of this number, because they cannot determine the non-periodicity resp. the infinity in periodicity resp. finiteness. Is it because they are simply incapable of it? Obviously yes. Or? Why can’t they? And: Why is there such a number?
Mathematicians cannot give the answer to this question. Who can? If at all, then the philosophers (metaphysicians, ontologists).
But there is always someone who is questioning this answer. Why? Because there is irrationality in it. Why?
Why is there irrationality and not only rationality? And why is there so very much more irrationality than rationality?
Is it because of stupidity? Why is there so much stupidity?
Why can’t this question be answered with 100% rationality, but only again with more or less irrationality, even if the relative proportion becomes smaller and smaller.
I was not talking about time travels, but time travels can also be used as an example, because: Time travels are imaginable, but we can’t (yet) imagine that they are also feasible, because we don’t know whether they are feasible or not, i.e. we also don’t know that they are not feasible. We don’t know anything about it, because we are (yet) too stupid, because we can’t (yet) rationally comprehend it.
But notice that I did not ask: Does time travel exist or not? I asked: Why does it exist or not?
The arrow of time? Is there an arrow of time? And if so: Why does it exist? Why should we not be able to travel into the past? Or: Why should we?
Yes.
Why does Ludolf’s number exist? And especially: Why does it exist as such a number?
Why is Planck’s quantum of action what it is? Why is the Planck time what it is? Why are all Planck units what they are?
Or the philosophical question par excellence:
Why is being at all and not rather nothing? (Leibniz). We can only think and speak (philosophize) about it. And why is that?
Why is there so much stupidity in the universe?
Are we in the world? And if yes: Why are we in the world? And if no: Why not?
Is there individuation? And if yes: Why? And if no: Why not?
Does subjectivity exist? And if yes: Why? And if no: Why not?
Is there objectivity? And if yes: Why? And if no: Why not?
Why are there gravitation, electromagnetism and the two interactions in the nucleus of the atoms? Why are these alleged constants constant? Why do they have these amounts? Why not others?
Why does the universe exist? Or does it not exist at all?
Why does nature exist? Or does it not exist at all?
Why does God exist? Or does He not exist at all? (The same question for atheists: Why does nature exist? Or does “It” - the alleged selector, their false god - not exist at all?)
Why is there love?
Science does not deal with questions of thought. Heiddeger said: “Science does not think.”
The most of our rational statements also contain irrationality. It can only be a matter of making the share of the irrational as small as possible. Because we are not able to abolish the irrational. Why is there irrationality? Who really knows?
A thinker or philosopher must be a questioner or skeptic.
Irrationality or arationality goes beyond the rational, cannot be subjected to logic.
Also the so-called “pre-rational”, whose results are only processed by the ratio, is counted to the irrational.
I am of the opinion that we can orient ourselves very well at the definition of the irrational numbers. If it were not so, the irrational numbers would not be called as they are called. They are irrational!
Also the irrational numbers cannot be subjected to the logic, provided that one understands rationality by logic. If the irrational numbers could be subjected to the logic, they would be periodic resp. finite. But they are non-periodic resp. infinite. They are irrational!
This mathematical definition is the best starting point, in order to understand the irrational also altogether better.
And we should proceed phenomenologically. So throw away all prejudices about irrationality. Just as mathematicians do it.
So irrationality is nothing bad or good and even more nothing political in the sense of a political mission (as many of today’s politicians want to tell us, although they don’t know at all what they are talking about when they “judge” irrationality). So, no pre-judgments, condemnations or judgments, just phenomenological descriptions that serve to develop a philosophy of the irrational.
Integrating the irrational in such a way that after integration one can continue as if the irrational had not been integrated at all. That could be the strategy. Because this was also the strategy of the mathematicians, when they admitted the irrational numbers as mathematical sets, i.e. integrated them into mathematics.
But if also mathematicians already began to let the irrational dictate to them what they have to do and to omit, then mathematics would be finished. Mathematicians understand mathematics as a rational task.
I think there is a confusion between the maths’ “irrational” and whatever you mean by “irrational”.
In maths, as Magnus has pointed out, an irrational number is merely a number that cannot be expressed in a certain way. There is nothing illogical about the number itself. It is merely an issue of how it can be expressed - it must be able to be expressed by a ratio of integers - “non-ratio” - it cannot be rationed out into decimals. Why they do that - I don’t know. Why they care - I don’t know. There are numbers that cannot be expressed in decimal form (such as pi). Still there is nothing irrational about pi except that it cannot be expressed in decimals. The resolution is to truncate it - use an estimate accurate enough for the end need.
But I don’t think you are talking about ideas that cannot be expressed in a particular language. You seem to be talking about ideas that are incomprehensible or contrary to logical structure - perhaps oxymorons like a square-circle. That is a different issue than maths concerns. Math has no numbers that are illogical. Math is just logic applied to quantities - all math is just logic applied to quantities. ALL math is logical.
So as I said before, we need an example of what it is that you mean when you speak of the “irrational”. I don’t think an irrational number is what you really mean - because those have nothing to do with philosophical issues (certainly nothing to do with political issues).
There is no confusion, because I have spoken about the suggestion that one should start from the mathematical definition (read my text about it), in order to come afterwards to a philosophy of the irrational.
I never used the definition of the mathematical “irrational”, i.e. the one for the “irrational numbers”, together with the linguistic (lexical) definition or the usage in the common language.
The irrational is a cognition, thought, speech or action without the participation of the rational. More precisely, it is something characterized by no or insufficient use of reason and by a transcendent (not transzendental!) use.
I agree. The irrational is the unreasonable (illogical), is not or not completely comprehensible by the ratio, is not accessible to the logical thinking, is that which the rational simply or yet almost completely lacks.
I have not read everything here. But I think it’s up to you whether you want to talk about belief or something else. The title of this thread is: “Can philosophy integrate the irrational as mathematics can”. So this thread is not only about irrationality, which means that you can just as well talk about integrating the irrational into the rational, and that is exactly what has happened here so far, at least judging by what I have read. According to the title of this thread, I would say that it is primarily about the integration of the irrational into the rational through philosophy, and this integration can be compared to the one that mathematics has done with the irrational numbers.
“The irrational is a cognition, thought, speech or action without the participation of the rational. More precisely, it is something characterized by no or insufficient use of reason and by a transcendent (not transzendental!) use.”
The participation ( or integration may refer to both the irrational and rational, and here is the important focus: as related both sets, except it’s not made clear weather it considers a logical nexus, or a semantic one, and weather they intersect, creating a subset, or an evolving objective synthesis. This is why the comments do not appear to have neither a common theme nor degrees of separation or union.
As it stands, the partial element he refers to, the ‘forest’ may suggest a mystical participation.( Levy Bruhl)
Why don’t you just stick to the title of this thread?
Besides, the relationship of the rational and irrational numbers as subsets of the set of real numbers has long been pointed out. I guess you didn’t read that.
Moreover, the title of the thread pretends that the point is not to integrate the rational into the irrational, but to integrate the irrational into the rational. Just read it.
