Can philosophy integrate the irrational as mathematics can?

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Can philosophy integrate the irrational as mathematics can?

Yes.
9
82%
No.
2
18%
 
Total votes : 11

Re: Can philosophy integrate the irrational as mathematics c

Postby obsrvr524 » Mon Jun 07, 2021 10:03 am

Magnus Anderson wrote:
Prom wrote:The actual existential experience of rationing and rationalizing always involves only what information is available to the chooser at the moment of a decision in a series of contiguous steps.


That's why I say that being rational means making the best possible decision that is available to the decision maker at the time rather than making a decision that leads to the attainment of one's highest goal.

I don't think it is ever about the highest goal. It is about the goal (a sub-goal) being pursued at the moment - the next step within view. Whether that sub-goal was a rational choice is a different issue - and I agree those choices are rarely the best available - except for one issue -

Being rational means using what information is available in making choices (a rational process). That information is never truly complete - "given what I have been told -- this is my best option." The path taken might be an irrational path - but the one taking that path is being totally rational - it is not the person but the process itself that either leads to the person's actual intentions and is rational or doesn't lead him there and is irrational.

I think to call the person irrational is to say that the person's brain literally can't rationally process information - the person is psychotic (or as James put it - "broken brain").
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    • -- but "you" have been observed --
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Re: Can philosophy integrate the irrational as mathematics c

Postby obsrvr524 » Mon Jun 07, 2021 11:32 am

-
encode-decode -

Something that I noted about the pi = irrational issue and related to the integration of irrationality into society is the following -

It was apparent to me that the only reason pi was being called irrational was because it was not commiserate with the traditional use of "natural" counting numbers - specifically modulo 10. If you have a natural number as a diameter the circumference will be irrational - because natural numbers do not get along with circles.

But what if you choose to use the magnitude pi as your basic unit of measure (rather than 1). That would be modulo 10pi. You are choosing to make what has been called "irrational" (because it didn't fit past language) as your basic number system. Then an interesting thing happens -

With the natural based unit circle a rational diameter forms an irrational circumference. But if the diameter of a pi-unit circle is \(\pi\) (meaning 1 unit in modulo-pi) the circumference will still be \(\pi (modulo-pi)\) (because it will be \(1*\pi\)). The interesting thing is that \(\pi\) (in modulo-pi = 1) is the new "rational" and the circumference of the unit circle = \(\pi (modulo-pi)\) and is still irrational.

The social implication is that even if everyone accepted a proposed particular irrational way of thinking (such as wokism - making it the new "rational thinking") some of the same events seen as irrational before will still be seen as irrational along with formerly rational events. The new norm doesn't decrease the perceived irrationality - it just makes it more due to a deeper irrationality.

So perhaps regardless of irrational thinking there are some things that everyone is going to agree are irrational regardless of their irrational thinking. Or there are some concepts that are going to be seen as irrational no matter what mental language is common - universal irrationality.

But then if there is a universal irrationality - doesn't that imply that there might be a universal rationality?

I'm thinking that a concept like a square-circle might be seen as irrational by literally anyone (regardless of what they are willing to say out loud). And perhaps the concept that "A is A" (but spoken in their irrational language - perhaps "A is not other than not-A") will still be seen as rational. The trick is merely to be able to speak the accepted irrational language. And that is what politicians and salesmen do.

Perhaps politics IS the integration of irrationality.
Member of The Coalition of Truth - member #1

              You have been observed.
    Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
    It's just same Satanism as always -
    • separate the bottom from the top,
    • the left from the right,
    • the light from the dark, and
    • blame each for the sins of the other
    • - until they beg you to take charge.
    • -- but "you" have been observed --
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Re: Can philosophy integrate the irrational as mathematics c

Postby Great Again » Mon Jun 07, 2021 8:37 pm

Great Again wrote:The two-valued logic is also not suitable for the treatment of propositions about future events, because it implies a false determinism and leaves no space for the freedom of man. If A is a proposition about future events, then the statement "A is true" can be more accurately described by the statement "There are (that is: present) causes that force the occurrence of A in the future", and the statement "A is false" can be more accurately described by the statement "There are causes that force the occurrence of non-A in the future".

A sentence like "Bill will be home tomorrow" will not usually be true or false in this sense, because there are usually no compelling causes that determine Bill's behavior. Thus, to deal with such cases, one must introduce a third truth value, which can be assigned the property "unknown" or the property "not yet" (cf. the arrows in my diagram), which a proposition A about future things takes on precisely when there are no compelling causes for A or not-A to occur.

A roughly similar argument is already found in Aristotle (the famous example of tomorrow's sea battle).
Great Again wrote:
Great Again wrote:Classical logic includes only propositional logic and predicate logic, in which the principles of forbidden contradiction (principium contradictionis) and excluded third party (principium exclusi tertii) and, related to them, the bivalence principle (see my earlier posts) are valid.

Non-classical logics are those in which at least one of the principles of classical logic is not valid. Particularly important are those systems in which the principle of the excluded third or the bivalence principle is invalid. Such logics were developed because they were motivated by developments in mathematics (cf. for example my earlier posts about antinomy).

Non-classical logics include e.g.:
- Multivalued logic (generic term for all other logics in which the bivalence principle is not valid).
- Modal logic (also: Alethian logic).
- Intuitionistic logic.
- Dialogic logic.
- Temporal logic.
- Deontic logic.
- Conditional propositional logic.
- Doxastic logic.
- Epistemic logic.
- Relevance logic.
- Non-monotonic logic.
- Fuzzy logic.

Fuzzy logicians say that most concepts are factually fuzzy in the sense that they can apply to different objects to different degrees. The fuzzy logicians are right. Whether or not a particular term applies to an object is often not a matter of a simple yes or no, but often a matter of degree. In fuzzy logic, one specifies the degree to which a term applies to a particular object by a number from the continuum between 0 and 1: If an object does not fall under a certain term at all, the term in degree 0 applies to it; if it falls completely under it, the term in degree1 applies to it; and if it falls only more or less under it, the term in degree g with 0<g<1 applies to it. For a term one has to specify a function which determines under which circumstances it applies to an object and in which degree. (This function determines a fuzzy set.) For example, one can specify that the predicate "x is a tall man" applies to men up to 1.60m in degree 0, to men from 1.90m in degree 1, and to men between 1.60m and 1.90m in certain (with height increasing) degrees between 0 and 1; a 1.75m tall man may be tall in degree 0.5, for example.

Since the 1980s, fuzzy logic has increasingly found its way into technical applications under the keyword "fuzzy control", especially where exact mathematical calculations of the processes to be controlled are complicated, lengthy or hardly possible due to the many and unmanageable influencing variables. In this case, precise measured variables are first translated into fuzzy terms such as "quite fast", "quite close to the target", etc. ("fuzzification" is the word for this), which then form the basis for simple rules that are easily accessible to human intuition: "If the car is quite fast and quite close to the target, then brake quite hard". The "outputs" of these rules are then transformed back into precise control instructions according to specific procedures. This procedure allows control on an "intuitive" basis without the availability of an exact mathematical model of the process to be controlled. Fuzzy control has found its way, for example, into the control of video cameras, washing machines, elevators and even subways.

Multi-valued logics have been around for a long time, and they all have one thing in common: statements that are either true or false according to the bivalence principle are not valid.

According to Gödel's results, one must presuppose an infinite number of truth values.

Ulrich Blau has given a number of reasons why the logic underlying everyday language is three-valued. I would say it is multi-valued.

If X is rational and irrational, and in addition something that is itself rational or irrational, but without precise assignment, i.e. not yet known, but with high probability assignable in the future, then the possibility can be kept open that this still undetermined will turn out to be something determined in the future. For this purpose, a truth value in terms of the future and a truth value in degrees are given by numbers from the continuum between 0 and 1, where 0 or e.g. 0-0.2 stands for "still undetermined" or "rational and irrational (because in each case determinable only in the future)".
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Re: Can philosophy integrate the irrational as mathematics c

Postby Meno_ » Mon Jun 07, 2021 9:21 pm

the analysis of probability on the a-priori assumption that the fuzzy logic has more sense in supposing that it's more certain probable future determination could designate less 'fuzzy' math than that analysis could tend to suggest, may be more likely then not.
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Re: Can philosophy integrate the irrational as mathematics c

Postby Sleyor Wellhuxwell » Tue Jun 08, 2021 12:41 am

Great Again wrote:
Great Again wrote:The two-valued logic is also not suitable for the treatment of propositions about future events, because it implies a false determinism and leaves no space for the freedom of man. If A is a proposition about future events, then the statement "A is true" can be more accurately described by the statement "There are (that is: present) causes that force the occurrence of A in the future", and the statement "A is false" can be more accurately described by the statement "There are causes that force the occurrence of non-A in the future".

A sentence like "Bill will be home tomorrow" will not usually be true or false in this sense, because there are usually no compelling causes that determine Bill's behavior. Thus, to deal with such cases, one must introduce a third truth value, which can be assigned the property "unknown" or the property "not yet" (cf. the arrows in my diagram), which a proposition A about future things takes on precisely when there are no compelling causes for A or not-A to occur.

A roughly similar argument is already found in Aristotle (the famous example of tomorrow's sea battle).
Great Again wrote:
Great Again wrote:Classical logic includes only propositional logic and predicate logic, in which the principles of forbidden contradiction (principium contradictionis) and excluded third party (principium exclusi tertii) and, related to them, the bivalence principle (see my earlier posts) are valid.

Non-classical logics are those in which at least one of the principles of classical logic is not valid. Particularly important are those systems in which the principle of the excluded third or the bivalence principle is invalid. Such logics were developed because they were motivated by developments in mathematics (cf. for example my earlier posts about antinomy).

Non-classical logics include e.g.:
- Multivalued logic (generic term for all other logics in which the bivalence principle is not valid).
- Modal logic (also: Alethian logic).
- Intuitionistic logic.
- Dialogic logic.
- Temporal logic.
- Deontic logic.
- Conditional propositional logic.
- Doxastic logic.
- Epistemic logic.
- Relevance logic.
- Non-monotonic logic.
- Fuzzy logic.

Fuzzy logicians say that most concepts are factually fuzzy in the sense that they can apply to different objects to different degrees. The fuzzy logicians are right. Whether or not a particular term applies to an object is often not a matter of a simple yes or no, but often a matter of degree. In fuzzy logic, one specifies the degree to which a term applies to a particular object by a number from the continuum between 0 and 1: If an object does not fall under a certain term at all, the term in degree 0 applies to it; if it falls completely under it, the term in degree1 applies to it; and if it falls only more or less under it, the term in degree g with 0<g<1 applies to it. For a term one has to specify a function which determines under which circumstances it applies to an object and in which degree. (This function determines a fuzzy set.) For example, one can specify that the predicate "x is a tall man" applies to men up to 1.60m in degree 0, to men from 1.90m in degree 1, and to men between 1.60m and 1.90m in certain (with height increasing) degrees between 0 and 1; a 1.75m tall man may be tall in degree 0.5, for example.

Since the 1980s, fuzzy logic has increasingly found its way into technical applications under the keyword "fuzzy control", especially where exact mathematical calculations of the processes to be controlled are complicated, lengthy or hardly possible due to the many and unmanageable influencing variables. In this case, precise measured variables are first translated into fuzzy terms such as "quite fast", "quite close to the target", etc. ("fuzzification" is the word for this), which then form the basis for simple rules that are easily accessible to human intuition: "If the car is quite fast and quite close to the target, then brake quite hard". The "outputs" of these rules are then transformed back into precise control instructions according to specific procedures. This procedure allows control on an "intuitive" basis without the availability of an exact mathematical model of the process to be controlled. Fuzzy control has found its way, for example, into the control of video cameras, washing machines, elevators and even subways.

Multi-valued logics have been around for a long time, and they all have one thing in common: statements that are either true or false according to the bivalence principle are not valid.

According to Gödel's results, one must presuppose an infinite number of truth values.

Ulrich Blau has given a number of reasons why the logic underlying everyday language is three-valued. I would say it is multi-valued.

If X is rational and irrational, and in addition something that is itself rational or irrational, but without precise assignment, i.e. not yet known, but with high probability assignable in the future, then the possibility can be kept open that this still undetermined will turn out to be something determined in the future. For this purpose, a truth value in terms of the future and a truth value in degrees are given by numbers from the continuum between 0 and 1, where 0 or e.g. 0-0.2 stands for "still undetermined" or "rational and irrational (because in each case determinable only in the future)".

A not entirely serious suggestion: We could declare everything irrational to be taboo.

An example from mathematics:

The idea of irrational numbers, in our notation therefore infinite decimal fractions, should remain incomprehensible to the mind, never be told in school about irrational numbers.

Euclid said - and one should have understood him better - that incommensurable distances behaved "not like numbers". In fact, in the accomplished concept of the irrational number lies the complete separation of the concept of number from the concept of magnitude, and this because such a number - pi, for example - can never be delimited or represented exactly by a distance. But it follows that in the conception of the ratio of the square side to the diagonal, for example, the number as a sensual limit, a closed quantity, suddenly touches a completely different kind of number, which remains foreign in the deepest inside and therefore uncanny, as if one were close to uncovering a dangerous secret of one's own existence. This is revealed by a strange late Greek myth, according to which the one who first brought the contemplation of the irrational out of the hidden to the public, perished by a shipwreck, "because the inexpressible and imageless should always remain hidden".

An expression like e^ix, which constantly appears in our formulas, is supposed to seem absurd to us, to be a taboo.

Only calculate with finite fractions, examine the integer ratio of two distances. Great! :lol:

Even the idea of a number zero must not even arise, because it has no sense in terms of drawing.

If one would do all that - and only all that -, such a mathematics would be already perfect, only differently perfect. :lol:
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Re: Can philosophy integrate the irrational as mathematics c

Postby obsrvr524 » Tue Jun 08, 2021 1:42 am

Sleyor Wellhuxwell wrote:If one would do all that - and only all that -, such a mathematics would be already perfect, only differently perfect. :lol:

- And inexplicable. :D
Member of The Coalition of Truth - member #1

              You have been observed.
    Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
    It's just same Satanism as always -
    • separate the bottom from the top,
    • the left from the right,
    • the light from the dark, and
    • blame each for the sins of the other
    • - until they beg you to take charge.
    • -- but "you" have been observed --
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Re: Can philosophy integrate the irrational as mathematics c

Postby obsrvr524 » Sun Jul 25, 2021 10:43 pm

-
"Male and female he created them" - the strong and the meek - the rational and the irrational.
      The East and the West.
Member of The Coalition of Truth - member #1

              You have been observed.
    Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
    It's just same Satanism as always -
    • separate the bottom from the top,
    • the left from the right,
    • the light from the dark, and
    • blame each for the sins of the other
    • - until they beg you to take charge.
    • -- but "you" have been observed --
obsrvr524
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Posts: 3132
Joined: Thu Jul 11, 2019 9:03 am

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