Is objective truth mathematics?

[STT]

I don’t see the mathematical equation for that.

I don’t that free will can be expressed in term of a single equation. It should be a set of nondeterministic equations.

 

[STT]

A definition of a word that uses the same word is circular. I offer the conformance definition of truth below.

I didn’t define truth in here but objective truth in term of state of truth.

The conformance definition of “truth” allows no adjectives of degree. Knowledge is either true or false. Applied to “truth,” the adjectives “absolute,” “objective,” or “subjective.” do not add to, diminish or categorize “truth” in any meaningful way.

I don’t understand what you are trying to say here.

Mathematics deals with ideal objects, not real things. However, mathematics, as you point out, is quite fruitful and practical in its explanatory power for understanding the natural and social sciences.

That is necessary to deal with ideal objects in order to derive any outcome which can be useful in a practical situation.

Knowledge is neither subjective or objective but merely true or false. True knowledge is knowledge that conforms to reality. Reality is singular and independent of any created thinking mind.

Knowledge is subjective if we define it as state of mind of an intellectual being which reflect reality.

Mathematics is a science and, akin to its cousins, has a future. However, unlike its cousins, mathematics (despite Godel’s argument) is the science upon which we expect the most complete agreement among all its practitioners.

That is correct.

 

[tee_eff_em]

Have you ever heard of Kurt Gödel?

Yes. How this is related to this discussion?

Do you know *why *you’ve heard of him?



tee

 

[STT]

Do you know *why *you’ve heard of him?



tee

I forgot. I have a bad memory.

 

[Tomdstone]

I don’t that free will can be expressed in term of a single equation. It should be a set of nondeterministic equations.

I doubt that you can give me a set of mathematical equations which will tell us when I will move the big toe on my left foot.

 

[STT]

I doubt that you can give me a set of mathematical equations which will tell us when I will move the big toe on my left foot.

Lets look at the problem in another way. Do you believe that God’s knowledge is absolute truth? If so how do you define absolute truth? Do you agree with the definition provided in OP?

 

[GEddie]

If you would kindly give me a mathematical formula which will tell me exactly when I want to raise my hand and when I want to move the big toe on my left foot, then I will believe you.

There is a mathematics of our bodies, but it has yet to be discovered.

ICXC NIKA

 

[Tomdstone]

There is a mathematics of our bodies, but it has yet to be discovered.

ICXC NIKA

I don’t believe that there are any set of mathematical equations that can say when i will move the big toe an my left foot. It is true that mathematical equations can tell us the time of the next high tide and the next low tide in Gloucester, Massachusetts. But I don’t see how free will choices can be predicted by a set of mathematical equations.

 

[tee_eff_em]

I forgot. I have a bad memory.

Well, twice you said

Lets define objective truth as a set mind independent rules that every state of truth can be derived from it.

Objective/absolute truth is defined as a set mind independent rules that every state of truth can be derived from it (evil for example).

So I presume you meant it.

Gödel proved that math cannot derive all states of truth. Informal language from Wikipaedia:

[F]or any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that:

1. 
   *]If the system is consistent, it cannot be complete.
   *]The consistency of the axioms cannot be proved within the system.

1. 
   Or from Wolfram:
   

   Informally, Gödel’s incompleteness theorem states that all consistent axiomatic formulations of number theory include undecidable propositions…

   A statement sometimes known as Gödel’s second incompleteness theorem states that if number theory is consistent, then a proof of this fact does not exist using the methods of first-order predicate calculus. Stated more colloquially, any formal system that is interesting enough to formulate its own consistency can prove its own consistency iff it is inconsistent.

   Quod Erat Demonstrundum?
   
   tee

 

[STT]

So I presume you meant it.

Gödel proved that math cannot derive all states of truth. Informal language from Wikipaedia:

Or from Wolfram:

Quod Erat Demonstrundum?

tee

Well, if that is true then what is the right framework that absolute truth is depicted on?

Moreover, I have an objection to Gödel. Lets define absolute truth as a set of mind independent rules between objects that can explain every state of reality. Isn’t this the definition of mathematics?

 

[PseuTonym]

Objective/absolute truth is defined as a set mind independent rules that every state of truth can be derived from it (evil for example). The main column in starting a mathematical framework is to define rules. The rest is derived from by analytical thinking so I don’t see any difference between absolute truth and mathematics. Do you?

Although the question was not directed to me, I will take the liberty of answering. Yes, I do see a difference between absolute truth and mathematics. I suspect that you are using the word “mathematics” to refer to some imaginary, future works that don’t contain any major defects.

An important work in the history of mathematics is Euclid’s Elements. One reason for the importance of Euclid’s Elements is that it includes a definition of proportion created by Eudoxus. If we construct magnitudes given by the four variables A, B, C, and D, then we need to say what it means to claim that A is to B as C is to D. The problem arises because of so-called “irrational numbers” such as the square root of two. It is almost certain that before the discovery of so-called “irrational numbers”, there were geometry books based on the (false) assumption that all distances and areas can be expressed as ratios of whole numbers.

Now, one problem with Euclid’s Elements is that it omits Pasch’s postulate, while relying in passing upon Pasch’s postulate. In particular, the very first attempted proof of a proposition in Euclid’s Elements is invalid. The conclusion doesn’t follow from the specified assumptions. Conveniently, we can claim that Euclid’s Elements, because it is very old, is part of the history of mathematics, and not part of present-day mathematics.

So, what is the date of the beginning of today’s accepted mathematics? When did we arrive at absolute truth? It seems to be sometime after June 16, 1902.

Russell wrote to Frege with news of his paradox on June 16, 1902. (For the relevant correspondence, see Russell (1902) and Frege (1902) in van Heijenoort (1967).) The paradox was of significance to Frege’s logical work since, in effect, it showed that the axioms Frege was using to formalize his logic were inconsistent.

Link:
plato.stanford.edu/entries/russell-paradox/

 

[STT]

Although the question was not directed to me, I will take the liberty of answering. Yes, I do see a difference between absolute truth and mathematics. I suspect that you are using the word “mathematics” to refer to some imaginary, future works that don’t contain
any major defects.

Yes. I am thinking of a framework which is defect free. I however cannot imagine any difference between mathematics and absolute truth given the definitions: Lets define absolute truth as a set of mind independent rules between objects that can explain every state of reality. Isn’t this the definition of mathematics?

An important work in the history of mathematics is Euclid’s Elements. One reason for the importance of Euclid’s Elements is that it includes a definition of proportion created by Eudoxus. If we construct magnitudes given by the four variables A, B, C, and D, then we need to say what it means to claim that A is to B as C is to D. The problem arises because of so-called “irrational numbers” such as the square root of two. It is almost certain that before the discovery of so-called “irrational numbers”, there were geometry books based on the (false) assumption that all distances and areas can be expressed as ratios of whole numbers.

Now, one problem with Euclid’s Elements is that it omits Pasch’s postulate, while relying in passing upon Pasch’s postulate. In particular, the very first attempted proof of a proposition in Euclid’s Elements is invalid. The conclusion doesn’t follow from the specified assumptions. Conveniently, we can claim that Euclid’s Elements, because it is very old, is part of the history of mathematics, and not part of present-day mathematics.

So, what is the date of the beginning of today’s accepted mathematics? When did we arrive at absolute truth? It seems to be sometime after June 16, 1902.

Link:
plato.stanford.edu/entries/russell-paradox/

Well, we don’t know if these sort of paradox is resolvable. I think that I heard of a couple of paradoxes which finally were resolved. Do you recall anything?

 

[Tomdstone]

Although the question was not directed to me, I will take the liberty of answering. Yes, I do see a difference between absolute truth and mathematics. I suspect that you are using the word “mathematics” to refer to some imaginary, future works that don’t contain any major defects.

An important work in the history of mathematics is Euclid’s Elements. One reason for the importance of Euclid’s Elements is that it includes a definition of proportion created by Eudoxus. If we construct magnitudes given by the four variables A, B, C, and D, then we need to say what it means to claim that A is to B as C is to D. The problem arises because of so-called “irrational numbers” such as the square root of two. It is almost certain that before the discovery of so-called “irrational numbers”, there were geometry books based on the (false) assumption that all distances and areas can be expressed as ratios of whole numbers.

Now, one problem with Euclid’s Elements is that it omits Pasch’s postulate, while relying in passing upon Pasch’s postulate. In particular, the very first attempted proof of a proposition in Euclid’s Elements is invalid. The conclusion doesn’t follow from the specified assumptions. Conveniently, we can claim that Euclid’s Elements, because it is very old, is part of the history of mathematics, and not part of present-day mathematics.

So, what is the date of the beginning of today’s accepted mathematics? When did we arrive at absolute truth? It seems to be sometime after June 16, 1902.

Link:
plato.stanford.edu/entries/russell-paradox/

I don’t see Russel’s paradox as being that important. All it does is show that you can’t have all inclusive sets.

 

[PseuTonym]

Yes. I am thinking of a framework which is defect free. I however cannot imagine any difference between mathematics and absolute truth given the definitions: Lets define absolute truth as a set of mind independent rules between objects that can explain every state of reality. Isn’t this the definition of mathematics?

Allegedly, there is a species of featherless bipeds, and members of this species communicate with each other via some complicated systems of so-called “language.” If that is fantasy, then “linguistics” is like the study of dragons and unicorns: it has no actual subject matter to deal with. However, if such language-using featherless bipeds exist in reality, then the subject area called “linguistics” can explain some aspects of reality.

In linguistics, it is common to distinguish between “prescriptive grammar” and “descriptive grammar.” I think it is a fair comment to say that “prescriptive grammar” was deliberately invented as a pejorative term. Interestingly, if we create the term “descriptive mathematics” to describe mathematical claims that people actually assert and believe when they aren’t consulting textbooks, then we can probably prove that descriptive mathematics consists of little more than a combination of falsehood and incoherent gibberish. Thus, the term “prescriptive mathematics” cannot have a pejorative connotation.

Now, if the generally accepted basis for prescriptive mathematics is itself defective, then mathematics is not merely defective, but non-existent. After all, you claim that mathematics and objective truth are the same thing.

 

[STT]

Allegedly, there is a species of featherless bipeds, and members of this species communicate with each other via some complicated systems of so-called “language.” If that is fantasy, then “linguistics” is like the study of dragons and unicorns: it has no actual subject matter to deal with. However, if such language-using featherless bipeds exist in reality, then the subject area called “linguistics” can explain some aspects of reality.

In linguistics, it is common to distinguish between “prescriptive grammar” and “descriptive grammar.” I think it is a fair comment to say that “prescriptive grammar” was deliberately invented as a pejorative term. Interestingly, if we create the term “descriptive mathematics” to describe mathematical claims that people actually assert and believe when they aren’t consulting textbooks, then we can probably prove that descriptive mathematics consists of little more than a combination of falsehood and incoherent gibberish. Thus, the term “prescriptive mathematics” cannot have a pejorative connotation.

Now, if the generally accepted basis for prescriptive mathematics is itself defective, then mathematics is not merely defective, but non-existent. After all, you claim that mathematics and objective truth are the same thing.

Isn’t mathematics prescriptive? How do you define prescriptive mathematics? At the end all you could have is a set of axioms to start with. What else we could do? Is absolute truth axiom free? If it is then we have to make a distinction between rules and axiom.

 

[PseuTonym]

Here is a test for a list of premises:

If they seem self-evident, and – on the basis of those premises – some previously accepted theorems are now rejected, then the premises might actually be the basis for some conclusions.

If, on the other hand, there is a body of theorems that aren’t subject to rejection, then the alleged premises aren’t actually the basis for believing that the theorems are true.

Now, imagine that Euclid’s Elements had included Pasch’s postulate, but that the author had not attempted to formulate or prove any theorems. It would have been a very thin book! Would the premises have acquired status as being beyond doubt merely because the thin book (consisting of a list of premises) was written a long time ago, many copies of it had been made, and many people claimed to believe that the premises were true? I doubt it.

However, Gauss didn’t publish his work on non-Euclidean geometry because he anticipated – with good reason – a strong negative reaction. Building theorems and proofs on top of premises does nothing to establish that the premises are true. However, an impressive hierarchy of theorems and proofs built on top of premises might give the premises a special status in popular opinion, with all alternatives considered to be intolerable.

 

[tee_eff_em]

Moreover, I have an objection to Gödel.

Okay.

Lets define absolute truth as a set of mind independent rules between objects that can explain every state of reality. Isn’t this the definition of mathematics?

That is not an *objection *-- That is a denial. I can with equal authority deny that mathematics is objective truth. There.

Yes. I am thinking of a framework which is defect free. I however cannot imagine any difference between mathematics and absolute truth given the definitions: Lets define absolute truth as a set of mind independent rules between objects that can explain every state of reality. Isn’t this the definition of mathematics?

Then you are begging the question (assuming the premise).

:ehh:
tee

 

[STT]

Here is a test for a list of premises:

If they seem self-evident, and – on the basis of those premises – some previously accepted theorems are now rejected, then the premises might actually be the basis for some conclusions.

If, on the other hand, there is a body of theorems that aren’t subject to rejection, then the alleged premises aren’t actually the basis for believing that the theorems are true.

Now, imagine that Euclid’s Elements had included Pasch’s postulate, but that the author had not attempted to formulate or prove any theorems. It would have been a very thin book! Would the premises have acquired status as being beyond doubt merely because the thin book (consisting of a list of premises) was written a long time ago, many copies of it had been made, and many people claimed to believe that the premises were true? I doubt it.

However, Gauss didn’t publish his work on non-Euclidean geometry because he anticipated – with good reason – a strong negative reaction. Building theorems and proofs on top of premises does nothing to establish that the premises are true. However, an impressive hierarchy of theorems and proofs built on top of premises might give the premises a special status in popular opinion, with all alternatives considered to be intolerable.

I am sorry but I don’t understand how your comment is related to my questions?

 

[STT]

That is not an *objection *-- That is a denial. I can with equal authority deny that mathematics is objective truth. There.

Well, that not fair since I am arguing that their definitions are equal.

Then you are begging the question (assuming the premise).

I don’t understand where. I am just arguing that the definition of absolute truth and mathematics are equal.

 

[Tomdstone]

Well, that not fair since I am arguing that their definitions are equal.

I don’t understand where. I am just arguing that the definition of absolute truth and mathematics are equal.

Which definition of mathematics are you using? There are several different definitions of mathematics, many of which are controversial and not accepted by the majority of mathematicians. Are you a mathematician? If not, then why is your definition of mathematics the one we should accept?
en.wikipedia.org/wiki/Definitions_of_mathematics