The Neccesary Connection Between Mathematics, Logic & The Existence Of A Perfect Transcendent Being

[MindOverMatter]

1. I think that the reality of logic and mathematics is in fact an abstraction of an intrinsic order that we have found in the reality of being. This is my first premise.

2. Out of absolute nothing comes nothing, thus truth cannot be founded on nothing because there is no truth in absolute nothing.

3. The eternal truth and existence of logic and mathematics can only make sense in terms of an absolute perfect being that is transcendent of change and limitation. Anything which begins to exist cannot be the reason why 2 + 2 = 4 because it has limitations in its being and thus lacks an absolute order. If it where true that the truth of 2 + 2 began to exist, It would mean that truth is relative to change. Which means that it can be true at one time, but not true at another. But we know that it is always true that one cannot have a square circle and that 2 + 2 always = 4, and this true irrespective of time and change. As soon as one understands the proposition, one can see that these are self-evident and necessary truths. Thus they are not true because of anything that begins to exists or potentially exists.

Conclusion. Therefore, the reality of logic and mathematics is a necessary abstraction of an intrinsic order that is necessarily reflective of a being that is absolute, timeless and transcendent of all physical limitations.

 

[Spock]

Conclusion. Therefore, the reality of logic and mathematics is a necessary abstraction of an intrinsic order that is necessarily reflective of a being that is absolute, timeless and transcendent of all physical limitations.

The conclusion is wrong. The fact that we can come up with such propositons is indicative of the coherence of reality, that reality has attributes and relationships, which we can realize. Nothing further is needed to be assumed. Better luck next time.

 

[MindOverMatter]

The conclusion is wrong. The fact that we can come up with such propositons is indicative of the coherence of reality.

What is this coherence that you are speaking of?
Can you please take my post point for point and then show me why the conclusion doesn’t follow from the premise, so i can at least see why i shouldn’t assume that you take the world around you for granted.

Assertions will only succeed in annoying me.

 

[Spock]

Can you please take my post point for point and then show me why the conclusion doesn’t follow from the premise, so i can at least see why i shouldn’t assume that you take the world around you for granted.

If you so choose.

1. I think that the reality of logic and mathematics is in fact an abstraction of an intrinsic order that we have found in the reality of being. This is my first premise.

Wrong. Mathematics and logic are nothing but two axiomatically defined “mind games”. Some of the conclusions of mathematics can be applied to reality, others are pure “fun games”, without any reference to reality.

2. Out of absolute nothing comes nothing, thus truth cannot be founded on nothing because there is no truth in absolute nothing.

Partly trivial, partly incorrect. There is no “truth”. There is correspondence between reality and our picture of it. If the perception of reality correctly reflects reality. we speak of a “true” proposition (physical sciences). If a proposition is the correct corollary of the axioms, we speak of a correct (true) proposition.

Since your conclusion relies on these premises, and the premises are wrong, the conclusion is also wrong. Q.E.D.

 

[MindOverMatter]

If you so choose.

Wrong. Mathematics and logic are nothing but two axiomatically defined “mind games”. Some of the conclusions of mathematics can be applied to reality, others are pure “fun games”, without any reference to reality.

Some mathematics and logic can be described as pure abstractions which have no direct relation to objective being, but there is some logic that is necessarily true of the order that we find in being. There is that which is necessarily true of being. We become aware of logic because there is an explicit order in being, and we abstract logical truth from the that we find in order. In any case, all truth exists in relation to being. If there were objectively absolutely nothing, then it would be true that there were absolutely nothing; but if the truth that there is absolutely nothing objectively exists, then there isn’t absolutely nothing since the truth that nothing exists exists absolutely and objectively. This is a contradiction since there is no objectivity or being in nothing. There is no truth in that which is not real. Its meaningless. That which is real is true of an existing reality. When we speak of truth, we speak either explicitly of a real reality or that which is an abstraction of real reality. Its logically contradictory to say that an absolutely unreal exists. Thus there is an absolute eternal truth, which is being, that which is real.

Partly trivial, partly incorrect. There is no “truth”. There is correspondence between reality and our picture of it. If the perception of reality correctly reflects reality. we speak of a “true” proposition (physical sciences). If a proposition is the correct corollary of the axioms, we speak of a correct (true) proposition.

Are you saying that a circle can be a square, or that a square can be both a circle and a square? If not, then you must admit that there is such a thing as eternal truth. Are you saying that 2 + 2 doesn’t equal 4? If not, then you must admit that there is such a thing as eternal truth.

 

[hatsoff]

1. I think that the reality of logic and mathematics is in fact an abstraction of an intrinsic order that we have found in the reality of being. This is my first premise.

2. Out of absolute nothing comes nothing, thus truth cannot be founded on nothing because there is no truth in absolute nothing.

3. The eternal truth and existence of logic and mathematics can only make sense in terms of an absolute perfect being that is transcendent of change and limitation. Anything which begins to exist cannot be the reason why 2 + 2 = 4 because it has limitations in its being and thus lacks an absolute order. If it where true that the truth of 2 + 2 began to exist, It would mean that truth is relative to change. Which means that it can be true at one time, but not true at another. But we know that it is always true that one cannot have a square circle and that 2 + 2 always = 4, and this true irrespective of time and change. As soon as one understands the proposition, one can see that these are self-evident and necessary truths. Thus they are not true because of anything that begins to exists or potentially exists.

Conclusion. Therefore, the reality of logic and mathematics is a necessary abstraction of an intrinsic order that is necessarily reflective of a being that is absolute, timeless and transcendent of all physical limitations.

Math and logic are little more than complex semantic games developed by humans. For example, 2+2=4 was not true a million years ago because there was nobody around to make the statement that 2+2=4. And a statement which has not been made cannot be true or false! In fact, 2+2=4 was not true until the glyphs for 2 and 4 had been developed, along with the + sign, all of which came together perhaps less than a thousand years ago.

 

[MindOverMatter]

Math and logic are little more than complex semantic games developed by humans. For example, 2+2=4 was not true a million years ago because there was nobody around to make the statement that 2+2=4. In fact, 2+2=4 was not true until the glyphs for 2 and 4 had been developed, along with the + sign, all of which came together perhaps less than a thousand years ago.

You are right and wrong. The abstraction that we call 2 + 2 = 4, didn’t exist before we thought of it. But the truth of it certainly existed from all eternity. 2 + 2 = 4, by itself is just symbols. But the meaning which the symbols describe is actually an abstraction from the order that we perceive in being itself. We perceive mathematical and logical truth through our interaction with reality, and we do this by making abstractions of the order that we find in reality. Mathematical and logical truth doesn’t simply exist of its own accord, but is rather an abstraction of order applied to distinctive symbols. The order that we find in being existed long before we ever thought of logic and maths, but logic and maths are derivative of order, and are thus eternally true irrespective of our thinking it. Since being is that which “is” as apposed to that which is “not”. Thus being in itself is fundamentally logical. We discover mathematics and logic, we do not create it. Otherwise all mathematical truth would be purely relative. There would be no point in doing mathematics is regards to truth. There would be no reason to agree with anyone that 2 + 2 = 4, or that a circle is not a square. Either such things are always true, or they are always relative. It seems that honesty would understand fairly quickly that such things are eternally true.

 

[hatsoff]

You are right and wrong. The abstraction that we call 2 + 2 = 4, didn’t exist before we thought of it. But the truth of it certainly existed from all eternity.

Truth is a kind of value on certain sentences. If a sentence doesn’t exist, then neither does its truth value.

2 + 2 = 4, by itself is just symbols. But the meaning which the symbols describe is an abstraction from the order which we perceive in being itself. We perceive mathematical and logical truth through our interaction with reality and by making abstractions of the order that we find in reality. Mathematical and logical truth doesn’t simply exist of its own accord, but is rather an abstraction of order applied to distinctive symbols. The order that we find in being existed long before we ever thought of logic and maths, but logic and maths are derivative of order, and are thus eternally true irrespective of our thinking it. We discover mathematics and logic, we do create it. Otherwise all mathematical truth would be purely relative. There would be no point in doing mathematics is regards to truth. There would be no reason to agree with anyone that 2 + 2 = 4, or that a circle is not a square. Either a such things are always true or they are relative. It seems that honesty would understand fairly quickly that such things are eternally true.

The reasons to agree that 2+2=4 have nothing to do with physical reality. 2+2=4 is true according to the semantic rules established by arithmetic language. The meaning of 2+2=4 in this way depends on language, and language was developed by humans a finite time ago.

 

[MindOverMatter]

Truth is a kind of value on certain sentences. If a sentence doesn’t exist, then neither does its truth value.

What is this value? Its the meaning behind the symbols correct? Would you agree that such meanings require “order” inorder to be consistent in their meanings?

The reasons to agree that 2+2=4 have nothing to do with physical reality.

I agree. Yet “truth” has everything to do with “absolute being” since there is no truth in nothing.

2+2=4 is true according to the semantic rules established by arithmetic language.

No, 2 + 2 = 4, because according to consistent “order”, it cannot be otherwise, just like a square cannot be a circle. If you gather 4 objects, they are nothing other then 4 ones, or 4 objects. Its a necessary eternal truth regardless of our knowledge of it. If it were not eternally truth we would never have discovered it. This has very little to do with language. We create language in order to describe the order that we see in being and the abstractions that we can make from it. We don’t simply make all of it up, even though some of it is pure abstraction.:doh2:

All of this was just explained in my previous post.

 

[hatsoff]

What is this value? Its the meaning behind the symbols correct? Would you agree that such meanings require “order” inorder to be consistent in their meanings?

The meaning depends on the language. In math, we’re dealing with the Peano axioms.

And yes, I agree that language requires order.

I agree. Yet “truth” has everything to do with “absolute being” since there is no truth in nothing.

I don’t believe in anything called “absolute being.”

No, 2 + 2 = 4, because according to consistent “order”, it cannot be otherwise, just like a square cannot be a circle.

Sure, but the order in question is language, and that hasn’t been around forever.

If you gather 4 objects, they are nothing other then 4 ones, or 4 objects.

The objects aren’t anything other than themselves, but we can call them anything we like. We could call them goombahs or snitzels, or any other name we invent. English syntax permits us to ascribe to them certain labels, such as quantity. But these are all matters of language.

Its a necessary eternal truth regardless of our knowledge of it. If it were not eternally truth we would never have discovered it. This has very little to do with language. We create language in order to describe the order that we see in being and the abstractions that we can make from it. We don’t simply make all of it up, even though some of it is pure abstraction.:doh2:

All of this was just explained in my previous post.

See above.

 

[MindOverMatter]

And yes, I agree that language requires order.

Yep.

I don’t believe in anything called “absolute being.”

It follows necessarily from the premise. Its not a matter of belief.

Sure, but the order in question is language, and that hasn’t been around forever.

Are you saying that it hasn’t always been necessarily true that 2 + 2 = 4. Or are you just saying that the descriptive language we employ to create constructive statements hasn’t always existed?

The objects aren’t anything other than themselves, but we can call them anything we like. We could call them goombahs or snitzels, or any other name we invent. English syntax permits us to ascribe to them certain labels, such as quantity. But these are all matters of language.

Language is relative. This much i can agree with. But truth is truth. If there are 4 stars, then there are 4 stars; it is irrelevant that somebody created the symbol 4 to describe it. And it doesn’t change just because nobody knows about it. Thats like saying that the universe didn’t exist before we knew about it. Scientists could not honestly employ mathematics to describe objective truth if it didn’t have any grounding in objective reality or if it wasn’t always true of the reality for which it was employed. I would have thought that to be obvious.

 

[hatsoff]

It follows necessarily from the premise. Its not a matter of belief.

Indeed, it’s a matter of coherence. I can find no substantive meaning in the term “absolute being.”

Are you saying that it hasn’t always been necessarily true that 2 + 2 = 4. Or are you just saying that the descriptive language we employ to create constructive statements hasn’t always existed?

2+2=4 has not always been a true sentence, because it has not always been a sentence! Truth is a kind of value on certain sentences, and the mathematical sentence 2+2=4 hasn’t been around forever.

Language is relative. This much i can agree with. But truth is truth.

Truth is a valuation system on language. Without language, we can’t have any truth. Without language, we can’t construct sentences to be true or false.

If there are 4 stars, then there are 4 stars; it is irrelevant that somebody created the symbol 4 to describe it. And it doesn’t change just because nobody knows about it. Thats like saying that the universe didn’t exist before we knew about it.

The physical reality doesn’t depend on the presence or absence of language to describe it, I agree. But truth isn’t about physical reality. Rather, truth is about language. It’s a kind of relationship between sentences and some system of valuation.

No language, no truth.

Scientists could not honestly employ mathematics to describe objective truth if it didn’t have any grounding in objective reality or if it wasn’t always true of the reality for which it was employed. I would have thought that to be obvious.

Strictly speaking, mathematics doesn’t describe “objective truth” or anything else. Mathematics is more like semantic games.

To quote Hilbert, it must always be possible to substitute “table”, “chair” and “beer mug” for “point”, “line” and “plane” in a system of geometric axioms. This is because mathematics is about semantic manipulation according to inferential rules established by fiat.

 

[praise_Jesus_1]

Seems there is a difference in both of your definitions of truth.

hatsoff seems to argue that something can’t be labeled true or false until the statement has been made. That 2+2 = 4 could only be about 1000 years old. Well maybe in that writing it could, but the Babylonians also did math and they would have their own representation for 2+2=4 which would be much older than 1000 years.

If we reduce everything to a matter of language we have the problem with discoveries made in other languages. Pythagoras gave us that the square root of 2 was irrational. This was around 500BC in Greece. So is this statement then neither true nor false for those who don’t understand Greek until it the statement was appropriately translated?

Can there be truth or falsehood before a concept or notion is defined? I would argue that truth or falsehood can be attributed to a concept even before it is in the conscience of man.

 

[MindOverMatter]

2+2=4 has not always been a true sentence, because it has not always been a sentence!

Just because it hasn’t been a sentence is not proof that the truth of the sentence hasn’t always been true. If something is true, then it is true regardless of ones knowledge. Your perspective is like saying that one can have knowledge of a true proposition, but if somebody does not know about it, then its truth is not universally true, because its being true is instead relative to your knowledge of it. That doesn’t make sense to me.

Sounds like a complete re-interpretation of truth which has in the process been rendered meaningless.

Truth is a kind of value on certain sentences, and the mathematical sentence 2+2=4 hasn’t been around forever.

What kind of value are you talking about? And what arguement proves that it hasn’t been around forever? I seem to have missed it.

Truth is a valuation system on language. Without language, we can’t have any truth. Without language, we can’t construct sentences to be true or false.

With out language we cannot describe objective truth to other people or make abstractions from being that can be described to other people. Language is very important. But the fact of 3 + 3 = 6 is an abstract and necessary truth that cannot change, and we are able to perceive this truth because we have seen the order of 6 things. I see no reason why one should believe that the truth of some proposition is necessarily reliant on the existence of language. A proposition that is necessarily true is true regardless of ones ability to create sentences or ones ability to gain knowledge of a true proposition.

I agree that, that there are some truths that are relative and are heavily reliant on invented language. In order for us to know those truths we must make propositions which require the invention of certain ideas, such as integers.You are certainly correct to say that some logical truths and mathematical truths, are tautological in some respects, as in dependent on one inventing words or numbers like** -1**. It is not necessarily consistent to speak of -1 accept within the context of integers, which is an invented language. However it is still reliant on order to have any consistency at all. The reality of integers was always a possible derivative of order, and in this sense it is an eternal mathematical truth at least in regards to its possible creation; and yet not all the concepts involved in the world of integers are purely creations but are instead derivative of other abstractions which have a more closer relationship to ontological truth which is the realm of being. With out order, abstract truth would not exist at all. And there is no reason to believe that order is the creation of language, and neither is there any reason to believe that all mathematical truths have no basis in experience. In reality, we are speaking about consistent patterns which are ultimately abstractions from the order that we find in being. Or one can say that we are speaking about invented systems of language which are the eternal possibilities of an intrinsic order of being, in so far as they use that order. In any case they reflect a being that is absolute and ordered.

The physical reality doesn’t depend on the presence or absence of language to describe it, I agree.

So you are agreeing that there are truths which do not rely on our ability to create language in order for it to be true?

But truth isn’t about physical reality.

What does that mean? I know what truth is and what it isn’t and what you are talking about is not the true definition of truth. Some truth is rooted in the observation of that which is real, such as i saw a cat cross the road. The fact that i use the word “cat” does not change the truth of what i saw, accept that i gave an object of my experience a symbolic definition. Definition is important and language is important but i see no reason to make it synonymous with that which causes truth. It certainly plays a part in some truths as is true we tautologies. But Absolute order is the cause of any truth, for with out that we could not construct any coherent propositions. Everything would be a meaningless jumble of symbols and sounds. A square is necessarily different from a circle, not because we describe them as circles and squares, but because the concepts that we are describing are necessarily opposed according to their natures. There natures are eternally opposed, and this is eternally true regardless of my knowledge of circles and squares. If something is real in some way, whether its an abstraction of being or a concrete being in its self, then its reality is true in some sense depending on the context. It seems to me that you believe that the use of descriptive language is the absolute cause of truth. I don’t know what that means, especially with out an underlying reality of order.

Rather, truth is about language. It’s a kind of relationship between sentences and some system of valuation.

No language, no truth.

I have shown you why this is a flawed perspective. I refuse to do it again.

Strictly speaking, mathematics doesn’t describe “objective truth” or anything else. Mathematics is more like semantic games.

To quote Hilbert, it must always be possible to substitute “table”, “chair” and “beer mug” for “point”, “line” and “plane” in a system of geometric axioms. This is because mathematics is about semantic manipulation according to inferential rules established by fiat.

So you are saying that the mathematics of science is nothing more then tautological hearsay? Simply saying that something is this or that doesn’t help me to understand the truth of your statement. I guess that all truth is not dependent on language after all.

 

[hatsoff]

Just because it hasn’t been a sentence is not proof that the truth of the sentence hasn’t always been true.

You can’t have the “truth of the sentence” without having the sentence!

If something is true, then it is true regardless of ones knowledge. Your perspective is like saying that one can have knowledge of a true proposition, but if somebody does not know about it, then its truth is not universally true, because its being true is instead relative to your knowledge of it. That doesn’t make sense to me.

Perhaps not, but that’s likely because it’s usually not useful to analyze truth in this way. But if you are going to analyze it, then you may want to become accustomed to the relativism involved.

Let’s have a brief example…

2+2=4, right? Well, suppose we’re working with ordinary addition in the group of integers modulo 3. In that case, 2+2=1. So, 2+2=4 with respect to integers modulo 3 is actually incoherent, and not true at all. Meanwhile, 2+2=1 is true in the group of integers modulo 3, but false in the group of integers.

One way to try to escape this relativity of truth is to say that, rather than propositions, truth is a value on ideas and/or concepts. After all, 2+2=1 may be a single sentence, but it expresses radically different ideas depending on the underlying system of language. But then we’re faced with a myriad of novel problems, not the least of which is the potential uniqueness of each idea to a single human mind. More importantly, though, if we’re going to say that truth is a value on concepts, then we have a similar issue of concepts having come about only with the advent of complex life. In other words, truth still wouldn’t be eternal or transcendent.

What kind of value are you talking about? And what arguement proves that it hasn’t been around forever? I seem to have missed it.

Human beings, who are responsible for constructing such sentences, evolved a finite time ago.

But the fact of 3 + 3 = 6 is an abstract and necessary truth that cannot change, and we are able to perceive this truth because we have seen the order of 6 things.

We have already seen that 2+2=4 is not a true statement with respect to the group of integers modulo 3. We changed the truth by redefining the terms. We can do similar things for the sentence 3+3=6. Considering that, in what sense is 3+3=6 a “necessary truth that cannot change”?

I agree that, that there are some truths that are relative and are heavily reliant on invented language. In order for us to know those truths we must make propositions which require the invention of certain ideas, such as integers.You are certainly correct to say that some logical truths and mathematical truths, are tautological in some respects, as in dependent on one inventing words or numbers like** -1**. It is not necessarily consistent to speak of -1 accept within the context of integers, which is an invented language. However it is still reliant on order to have any consistency at all. The reality of integers was always a possible derivative of order, and in this sense it is an eternal mathematical truth at least in regards to its possible creation; and yet not all the concepts involved in the world of integers are purely creations but are instead derivative of other abstractions which have a more closer relationship to ontological truth which is the realm of being. With out order, abstract truth would not exist at all. And there is no reason to believe that order is the creation of language, and neither is there any reason to believe that all mathematical truths have no basis in experience. In reality, we are speaking about consistent patterns which are ultimately abstractions from the order that we find in being. Or one can say that we are speaking about invented systems of language which are the eternal possibilities of an intrinsic order of being, in so far as they use that order. In any case they reflect a being that is absolute and ordered.

Well, if we somehow traveled back through time, we could still use math to talk about the world. But we couldn’t just use math. We’d have to use some kind of natural language, as well, like English or Latin.

But notice we don’t get to infer much based on that.

So you are agreeing that there are truths which do not rely on our ability to create language in order for it to be true?

Not at all. “Truth” does not refer to a physical state of affairs. At most, it refers to a relationship between such a physical state of affairs and some proposition or idea. But even that is not always going to be so, such as in the case of abstract statements like f(x)=y.

What does that mean? I know what truth is and what it isn’t and what you are talking about is not the true definition of truth. Some truth is rooted in the observation of that which is real, such as i saw a cat cross the road. The fact that i use the word “cat” does not change the truth of what i saw, accept that i gave an object of my experience a symbolic definition. Definition is important and language is important but i see no reason to make it synonymous with that which causes truth. It certainly plays a part in some truths as is true we tautologies. But Absolute order is the cause of any truth, for with out that we could not construct any coherent propositions. Everything would be a meaningless jumble of symbols and sounds. A square is necessarily different from a circle, not because we describe them as circles and squares, but because the concepts that we are describing are necessarily opposed according to their natures. There natures are eternally opposed, and this is eternally true regardless of my knowledge of circles and squares. If something is real in some way, whether its an abstraction of being or a concrete being in its self, then its reality is true in some sense depending on the context. It seems to me that you believe that the use of descriptive language is the absolute cause of truth. I don’t know what that means, especially with out an underlying reality of order.

en.wikipedia.org/wiki/Truth

I have shown you why this is a flawed perspective. I refuse to do it again.

Then I will also refrain from repeating myself.

So you are saying that the mathematics of science is nothing more then tautological hearsay? Simply saying that something is this or that doesn’t help me to understand the truth of your statement. I guess that all truth is not dependent on language after all.

You seem to have an unusual understanding of truth, which is why axiomatic systems might throw you for a loop. But that’s how math works.

 

[warpspeedpetey]

The conclusion is wrong. The fact that we can come up with such propositons is indicative of the coherence of reality, that reality has attributes and relationships, which we can realize. Nothing further is needed to be assumed. Better luck next time.

i think he is pointing out that the coherence of reality is not possible without a necessary being for that reality to be grounded in. na being who by virtue of such necessity must be the maximal state of being.

 

[MindOverMatter]

Let’s have a brief example…

2+2=4, right? Well, suppose we’re working with ordinary addition in the group of integers modulo 3. In that case, 2+2=1. So, 2+2=4 with respect to integers modulo 3 is actually incoherent, and not true at all. Meanwhile, 2+2=1 is true in the group of integers modulo 3, but false in the group of integers.

Integers are only true given the rules of integers; its tautological; this much as been explained. 2 + 2 is an ontological proposition, because it is a direct abstraction from the intrinsic order of real being. In the real world, we know that 3 stars add another 3 stars necessarily equals 6 stars altogether, which is a necessary truth of addition and order.

 

[MindOverMatter]

i think he is pointing out that the coherence of reality is not possible without a necessary being for that reality to be grounded in. na being who by virtue of such necessity must be the maximal state of being.

Thanks for the help. Lets do a tag team.

 

[warpspeedpetey]

Thanks for the help. Lets do a tag team.

where oh where is JD?, he is better on these subjects than me. hopefully he shows up. till then, tag your it!

 

[hatsoff]

Integers are only true given the rules of integers; its tautological; this much as been explained. 2 + 2 is an ontological proposition, because it is a direct abstraction from the intrinsic order of real being. In the real world, we know that 3 stars add another 3 stars necessarily equals 6 stars altogether, which is a necessary truth of addition and order.

3+3=6 does not tell us anything directly about stars. Once we start talking about physical objects, we have left the bounds of math.