Can you ever be certain that you are reasoning correctly?

[brokenhead]

Does A=A say something about time then.......?

Logical truths are immutable, as David correctly points out. This is why they do not map to reality - exactly what you were saying - since in reality, everything always changes. Some degree of abstraction is always present. A=A is only true in the abstract "realm," as Fujaro put it, of logic.

[Diebert van Rhijn]

Logical truths are immutable, as David correctly points out. This is why they do not map to reality - exactly what you were saying - since in reality, everything always changes. Some degree of abstraction is always present.

The firs lines are contradicting. You cannot assert that everything is always changing without mapping some kind of immutable type of truth at the same time. You can never establish the change without a constant. Some degree of abstraction is indeed always present, that's the immutable constant: a 'core' abstraction that can be called the 'constructor'. In a way you cannot get more real than that, humanly speaking.

[Kevin Solway]

My understanding is that an electron doesn't behave as a wave and a particle at the same time. In which case they are not identical, for if they were identical they would occur at the same time.

Does A=A say something about time then.......?

It says something about every thing. It says that a thing is what it is, and not other than what it is. For example, it says that one moment in time is not another moment in time.

When an electron at moment t1 is mapped to A, it should be mapped at moment t2 to A, shouldn't it?

t1 would be mapped to A1, and t2 would be mapped to A2. Whether A1 has any close causal relationship with A2 is only speculation — which is to say that it is in the realm of empirical science.

Or the identity law is meaningless for every (possibly still hidden) dimension can introduce something like A(x) isnotidenticalwith A(y).

A(x) is always identical with A(x), so the law of identity is still meaningful.

[David Quinn]

Does A=A say something about time then.......?

Logical truths are immutable, as David correctly points out. This is why they do not map to reality - exactly what you were saying - since in reality, everything always changes. Some degree of abstraction is always present. A=A is only true in the abstract "realm," as Fujaro put it, of logic.

"Everything always changes" is itself an immutable truth about reality, arrived at logically. So Diebert is right in pointing out that you are contradicting yourself.

Fujaro is also contradicting himself in a similar manner.

-

[brokenhead]

"Everything always changes" is itself an immutable truth about reality, arrived at logically. So Diebert is right in pointing out that you are contradicting yourself.

Fujaro is also contradicting himself in a similar manner.

Then I should be more specific, as you are now also contradicting yourself. Let me point out how, and then I'll rephrase to help us both out.

If "Everything always changes" is itself an immutably true statement about reality, then it itself, no matter how it was arrived at, cannot be part of reality, since it is immutable. Therefore, not all true statements, even if arrived at logically, are necessarily part of reality. A=A is a true statement arrived at logically. So I am asking: is the statement A=A a part of reality?

[Diebert van Rhijn]

If "Everything always changes" is itself an immutably true statement about reality, then it itself, no matter how it was arrived at, cannot be part of reality, since it is immutable. Therefore, not all true statements, even if arrived at logically, are necessarily part of reality.

You equal reality here with the changing every-thing.

Reality, in a more Taoist sense can be only truthfully described as having two aspects: the constant and the changing. Or the finite and the infinite. In the deepest sense they're always both and neither, therefore undefinable. But it's hard to tell the difference between unspoken truth and unspoken lies, so wisdom tends to speak out nevertheless, to point out bloody obviousness.

[brokenhead]

If "Everything always changes" is itself an immutably true statement about reality, then it itself, no matter how it was arrived at, cannot be part of reality, since it is immutable. Therefore, not all true statements, even if arrived at logically, are necessarily part of reality.

You equal reality here with the changing every-thing.

Reality, in a more Taoist sense can be only truthfully described as having two aspects: the constant and the changing. Or the finite and the infinite. In the deepest sense they're always both and neither, therefore undefinable. But it's hard to tell the difference between unspoken truth and unspoken lies, so wisdom tends to speak out nevertheless, to point out bloody obviousness.

This is akin to Bohr's Principle of Complementarity, in which the wave-particle duality is regarded as recognizing the complentary nature of reality.

Logic, therefore, is a subset of reality. The set of all possible logically true statements must therefore be a subset of all possible true statements. That is to say, a statement can be true a priori.

[Fujaro]

Does A=A say something about time then.......?

Logical truths are immutable, as David correctly points out. This is why they do not map to reality - exactly what you were saying - since in reality, everything always changes. Some degree of abstraction is always present. A=A is only true in the abstract "realm," as Fujaro put it, of logic.

"Everything always changes" is itself an immutable truth about reality, arrived at logically. So Diebert is right in pointing out that you are contradicting yourself.

Fujaro is also contradicting himself in a similar manner.

-

David, I am not positing that everything always changes. So I am curious to know what you mean by 'in a similar way'.

It is enough to know that some things change in reality to realize that immutable truth can't describe all aspects of reality and therefore cannot be complete in the sense I described. I am not positing that A=A does not ever hold in reality for certain mappings of A to reality (it might hold for instance for the total energy content of our universe). I am positing that the mapping of A to the phyiscal realm is a separate step that does not involve logic alone.

In fact Kevin shows this with his attempts to interpret A=A in terms of the electron. He arrives at a multiverse sort of interpretation of QM where every instance in time of the electron corresponds to another electron, but thereby fails to account for the instant creation and annihilation of these infinite numbers of strangely suggestive aligned electrons thus defined. The instant creation and annihilation keep contradicting the A=A mantra, though.

Jamesh concludes that not just electrons but all particles for that matter must be illusory. Again this is an attempt to map reality as we perceive it to A=A (the choice of which is random btw, why not take A=B) that he employs as a skyhook. This time with a devastating result for reality as such. His stance in my opinion is possible (as odd as this may seem to you) but not probable. It in essence is a solipsistic stance. The problem with solipsism is that it fails to acknowledge (let alone effectively describe) the patterns in this illusory world most people would identify as the laws of nature. In its pure form solipsism even means the denial of other conscious minds, but when this restriction is lessened the weakened solipsism that does acknoledge the existence of other concious minds can't account for the striking correspondences between the illusory realities these conscious minds observe. Also it can't discriminate all possible solipsism-like truths about reality. For instance, this illusory reality might have been superposed on our consciousness by some yellow striped leprachaun in the zillionth dimension unknown to us. Or by what we would call (if there only was a means by which to project this to our illusory reality that did right to the thing) a red baboon in the zillionth plus one dimension. Nearly everything goes really. Hardly in correspondence with the immutable truth chosen as the skyhook for it all.

Kevin about 'pure logic' wrote:
It is logic that doesn't depend on empirical uncertainties. It is elf-evident truth (which is to say that it is self-evident to those few humans who are capable of logical thinking).

Well, I am not sure how you would like to differentiate between empirical certainties and empirical uncertainties, for that would involve a priori knowledge of truth imho, but apart from that it would mean that Euclidean Geometry (EM) is not pure logic because it is founded on axiomas that can't be proven from logic alone.. Furthermore the part in brackets exposes an elite antroposophic view on the world and does not seem to follow from pure logic itself.

Kevin about 'pure logic' wrote:
The truth that I exist right now will indeed last forever. I don't know whether I will exist a moment from now.

By this you are restating the truth you formulated earlier ("The truth that I exist is a logical truth"). That is interesting as it shows the addition of a condition ("right now") that makes a not so absolute truth into a more absolute truth. This is the process of choosing restrictive conditions I rather extensively described earlier. You can do this, but be aware that underneath are still all kinds of other 'hidden' conditions. Suppose for example that M-brane theory is right and that there are 10 or 11 dimensions to this reality. Can you be sure that your existence in say the sixth dimension is accurately described by your amended statement? No, of course not. You would need to know more about that sixth dimension before you can answer this question. You need that context of reality first before you can remap your logical truth to this part of reality.

[Fujaro]

Reality, in a more Taoist sense can be only truthfully described as having two aspects: the constant and the changing. Or the finite and the infinite. In the deepest sense they're always both and neither, therefore undefinable.

It looks we have a reformulated logical truth here.

A=A becomes: A is element of {A, the conjugate of A}

Well who's next to define new unshakable, immutable and above all absolute truths?

[Fujaro]

Logic, therefore, is a subset of reality. The set of all possible logically true statements must therefore be a subset of all possible true statements. That is to say, a statement can be true a priori.

Do you mean an a priori true statement as in: a fact residing in reality that cannot be deduced with pure godlike logic?

[Fujaro]

Logic, therefore, is a subset of reality. The set of all possible logically true statements must therefore be a subset of all possible true statements. That is to say, a statement can be true a priori.

Do you mean an a priori true statement as in: a fact residing in reality that cannot be deduced with pure godlike skyhook logic?

[Diebert van Rhijn]

Reality, in a more Taoist sense can be only truthfully described as having two aspects: the constant and the changing. Or the finite and the infinite. In the deepest sense they're always both and neither, therefore undefinable.

It looks we have a reformulated logical truth here.

A=A becomes: A is element of {A, the conjugate of A}

Any assertion 'A' implies the conjugate 'what is not A'. This is formulated with the law of non-contradiction which is basically a further consequence, or more detailed definition of identity.

Reality in a more Taoist sense, a non-dual reality cannot be defined. That is logically true.

[Fujaro]

Reality, in a more Taoist sense can be only truthfully described as having two aspects: the constant and the changing. Or the finite and the infinite. In the deepest sense they're always both and neither, therefore undefinable.

It looks we have a reformulated logical truth here.

A=A becomes: A is element of {A, the conjugate of A}

Any assertion 'A' implies the conjugate 'what is not A'. This is formulated with the law of non-contradiction which is basically a further consequence, or more detailed definition of identity.

Reality in a more Taoist sense, a non-dual reality cannot be defined. That is logically true.

I don't understand what you mean by 'implies' here. It certainly isn't so that it logically follows from 'I ate the apple' that I didn't ate the apple.

[Fujaro]

Maybe it is the other way around. Don't map a certain logic (say pure logic) to reality, but instead, choose the logic that fits reality best. Paraconsistent quantum logics takes this approach.

[Diebert van Rhijn]

Any assertion 'A' implies the conjugate 'what is not A'.

I don't understand what you mean by 'implies' here. It certainly isn't so that it logically follows from 'I ate the apple' that I didn't ate the apple.

'I' implies not someone else was eating the apple (though I might be sharing it without realizing)
'ate' implies I'm not at the same time stuffing it where the sun don't shine.
'apple' implies I was not eating something else (though I might eat a worm stuck inside it)

But in a sense 'I ate the apple' implies at least a logical context of not eating it which cannot find place at the same time and place without the whole statement losing its meaning.

[brokenhead]

Logic, therefore, is a subset of reality. The set of all possible logically true statements must therefore be a subset of all possible true statements. That is to say, a statement can be true a priori.

Do you mean an a priori true statement as in: a fact residing in reality that cannot be deduced with pure godlike logic?

Ah, no I do not mean this. "Godlike" being the operative term.

[David Quinn]

"Everything always changes" is itself an immutable truth about reality, arrived at logically. So Diebert is right in pointing out that you are contradicting yourself.

Fujaro is also contradicting himself in a similar manner.

Then I should be more specific, as you are now also contradicting yourself.

There is no contradiction. Your understanding of this material is very weak.

Let me point out how, and then I'll rephrase to help us both out.

If "Everything always changes" is itself an immutably true statement about reality, then it itself, no matter how it was arrived at, cannot be part of reality, since it is immutable. Therefore, not all true statements, even if arrived at logically, are necessarily part of reality. A=A is a true statement arrived at logically. So I am asking: is the statement A=A a part of reality?

If reality is defined as utterly everything, then A=A is certainly a part of reality. Furthermore, since A=A necessarily applies to all things in existence, it is applicable to all aspects of reality.

The fact that "all things change" isn't one that is proven empirically, since it is impossible for us to observe all things and watch them change. It is arrived at logically by comprehending what it means to be a thing.

-

[David Quinn]

"Everything always changes" is itself an immutable truth about reality, arrived at logically. So Diebert is right in pointing out that you are contradicting yourself.

Fujaro is also contradicting himself in a similar manner.

David, I am not positing that everything always changes. So I am curious to know what you mean by 'in a similar way'.

The similarity is that you are both using (what you think are) logical truths about reality in order to prove that it is impossible to arrive at logical truths about reality. In Brokenhead's case it is "everything changes" ; in your case, it is Godel's theorem, among other things.

It is enough to know that some things change in reality to realize that immutable truth can't describe all aspects of reality and therefore cannot be complete in the sense I described. I am not positing that A=A does not ever hold in reality for certain mappings of A to reality (it might hold for instance for the total energy content of our universe). I am positing that the mapping of A to the phyiscal realm is a separate step that does not involve logic alone.

This only shows that you don't really understand what A=A means. I'm not having a go at you here. You're obviously intelligent, but the subject of A=A is subtle and difficult to understand.

It all comes down to this: No matter where you care to point to in reality - whether it be to a particular phenomenon such as a quantum event, or to a principle such as change - you are, in this very act of pointing, affirming the principle of A=A.

This is because the thing being pointed to necessarily has an identity and cannot be anything other than what it is. If it didn't have an identity, we wouldn't be able to point to it. A quantum event is a quantum event and not something other. Change is change and not something other.

In fact Kevin shows this with his attempts to interpret A=A in terms of the electron. He arrives at a multiverse sort of interpretation of QM where every instance in time of the electron corresponds to another electron, but thereby fails to account for the instant creation and annihilation of these infinite numbers of strangely suggestive aligned electrons thus defined. The instant creation and annihilation keep contradicting the A=A mantra, though.

In order to have the power to contradict A=A, a thing or an event needs to have an identity of some kind. Otherwise, there exists no platform from which to launch the refutation. The existence of such a platform, however, immediately proves that A=A is still operating as ever.

When you truly understand A=A, you will see that it is utterly impossible to contradict it. Nothing can ever contradict it.

No matter how weird or counter-intuitive quantum events seem to be, they still adhere to the principle of A=A at all times. They might have the power to overturn our fixed notions of what we think should be there, but they can't overturn the principle of A=A itself.

Jamesh concludes that not just electrons but all particles for that matter must be illusory. Again this is an attempt to map reality as we perceive it to A=A (the choice of which is random btw, why not take A=B) that he employs as a skyhook.

I think he was arguing that particles are merely one expression of "fundamental matter" under certain circumstances and, therefore, the belief that it permanently exists as particles is an illusion. In other words, fundamental matter has a malliable form.

I don't really have that form do not exist the idea that fundamental matter comes in thr form of partciels is illusory. This time with a devastating result for reality as such. His stance in my opinion is possible (as odd as this may seem to you) but not probable. It in essence is a solipsistic stance. The problem with solipsism is that it fails to acknowledge (let alone effectively describe) the patterns in this illusory world most people would identify as the laws of nature. In its pure form solipsism even means the denial of other conscious minds, but when this restriction is lessened the weakened solipsism that does acknoledge the existence of other concious minds can't account for the striking correspondences between the illusory realities these conscious minds observe. Also it can't discriminate all possible solipsism-like truths about reality. For instance, this illusory reality might have been superposed on our consciousness by some yellow striped leprachaun in the zillionth dimension unknown to us. Or by what we would call (if there only was a means by which to project this to our illusory reality that did right to the thing) a red baboon in the zillionth plus one dimension. Nearly everything goes really. Hardly in correspondence with the immutable truth chosen as the skyhook for it all.

Believing in solipism is just that - a belief. It has nothing to do with uncovering what is logically true. In this instance, what is logically true is that it is impossible for a person to determine for sure whether or not other minds exist. It is essentially unresolvable.

You need to take care, in your crusade against logical truth, not to bring religious beliefs and philosophical fancies into the mix. That is, you need to take care not to mistake logical truth for what it is not.

-

[brokenhead]

You're not seeing the point I'm making. It certainly isn't meaningless, nor is it one-dimensional.

At least we agree on something. A "point" has zero dimensions.

[clyde]

I am not positing that A=A does not ever hold in reality for certain mappings of A to reality (it might hold for instance for the total energy content of our universe). I am positing that the mapping of A to the phyiscal realm is a separate step that does not involve logic alone.

This only shows that you don't really understand what A=A means. I'm not having a go at you here. You're obviously intelligent, but the subject of A=A is subtle and difficult to understand.

It all comes down to this: No matter where you care to point to in reality - whether it be to a particular phenomenon such as a quantum event, or to a principle such as change - you are, in this very act of pointing, affirming the principle of A=A.

This is because the thing being pointed to necessarily has an identity and cannot be anything other than what it is. If it didn't have an identity, we wouldn't be able to point to it. A quantum event is a quantum event and not something other. Change is change and not something other.

David;

How does it change your understanding if the phrase in bold above is presented:

This is because the thing being pointed to necessarily has a definition and cannot be (by definition) other than what it is (which is how we define it). If it didn’t have a definition, we wouldn’t be able to point to it and we define it by pointing.

In order to have the power to contradict A=A, a thing or an event needs to have an identity of some kind. Otherwise, there exists no platform from which to launch the refutation. The existence of such a platform, however, immediately proves that A=A is still operating as ever.

When you truly understand A=A, you will see that it is utterly impossible to contradict it. Nothing can ever contradict it.

David; And if there is no identity and no platform?

clyde


p.s: Just passing through . . . of course.

[brokenhead]

When you truly understand A=A, you will see that it is utterly impossible to contradict it. Nothing can ever contradict it.

I, for one, am not trying to contradict A=A.

I am in fact relying on it. And I'm not sure we are arguing, either. What I am saying, and what appears to be anathema to you, David, is that logical thinking is limited. It is not that I am saying it is incorrect or should be somehow rejected. All I am saying is that it is possible to make true statements that cannot be logically proven within the language in which they are stated. This is no great discovery. It is just a weak version of Goedel.

Here is where I started spinning my wheels:

Logical truths are immutable, as David correctly points out. This is why they do not map to reality - exactly what you were saying - since in reality, everything always changes. Some degree of abstraction is always present. A=A is only true in the abstract "realm," as Fujaro put it, of logic.

Let's try it again.
Logical truths are immutable. They exist in the realm of logic, which is a subset of reality. Reality is by definition the unique set that contains everything. The set of all logical truths must be a subset of this set we have named Reality. So there must be elements of Reality which are not also elements of the set of all logical truths. In fact, let us define another subset of Reality to be just that, that is, the set of everything that doesn't belong to the set of all logical truths. We now have two mutually exclusive sets, neither of which is empty. It also can be seen that utterly everything must belong to one of these two sets, but as they are mutually exclusive, never both. The set of all logical truths is rich and possibly infinite. The other, its complement in the set Reality, can be seen to be infinite without requiring proof.

Now in what manner can a logically true statement (from the first set) be mapped to anything in the other set?

[David Quinn]

What I am saying, and what appears to be anathema to you, David, is that logical thinking is limited. It is not that I am saying it is incorrect or should be somehow rejected. All I am saying is that it is possible to make true statements that cannot be logically proven within the language in which they are stated.

What's an example?

Logical truths are immutable. They exist in the realm of logic, which is a subset of reality. Reality is by definition the unique set that contains everything. The set of all logical truths must be a subset of this set we have named Reality. So there must be elements of Reality which are not also elements of the set of all logical truths. In fact, let us define another subset of Reality to be just that, that is, the set of everything that doesn't belong to the set of all logical truths. We now have two mutually exclusive sets, neither of which is empty. It also can be seen that utterly everything must belong to one of these two sets, but as they are mutually exclusive, never both. The set of all logical truths is rich and possibly infinite. The other, its complement in the set Reality, can be seen to be infinite without requiring proof.

Now in what manner can a logically true statement (from the first set) be mapped to anything in the other set?

If a logical truth necessarily applies to all things in existence, then it will apply to every member of both subsets.

It doesn't matter where such a truth, as a conceptual construct, happens to reside. Even if only one person in the entire Universe thinks of a logical truth which necessarily applies to all things, then that one truth from the location inside that person's head will instantly embrace everything there is.

The other, its complement in the set Reality, can be seen to be infinite without requiring proof.

How can something be seen to be infinite without using logical proof?

-

[David Quinn]

It all comes down to this: No matter where you care to point to in reality - whether it be to a particular phenomenon such as a quantum event, or to a principle such as change - you are, in this very act of pointing, affirming the principle of A=A.

This is because the thing being pointed to necessarily has an identity and cannot be anything other than what it is. If it didn't have an identity, we wouldn't be able to point to it. A quantum event is a quantum event and not something other. Change is change and not something other.

How does it change your understanding if the phrase in bold above is presented:

This is because the thing being pointed to necessarily has a definition and cannot be (by definition) other than what it is (which is how we define it). If it didn’t have a definition, we wouldn’t be able to point to it and we define it by pointing.

I find your rewording confusing because it seems to leave out non-abstract entities, such as physical objects, for no particular reason. But to be honest, I'm not sure that I understand your question to begin with.

In order to have the power to contradict A=A, a thing or an event needs to have an identity of some kind. Otherwise, there exists no platform from which to launch the refutation. The existence of such a platform, however, immediately proves that A=A is still operating as ever.

When you truly understand A=A, you will see that it is utterly impossible to contradict it. Nothing can ever contradict it.

David; And if there is no identity and no platform?

Then there is no basis to launch a refutation. A=A remains unchallenged.

-

[clyde]

It all comes down to this: No matter where you care to point to in reality - whether it be to a particular phenomenon such as a quantum event, or to a principle such as change - you are, in this very act of pointing, affirming the principle of A=A.

This is because the thing being pointed to necessarily has an identity and cannot be anything other than what it is. If it didn't have an identity, we wouldn't be able to point to it. A quantum event is a quantum event and not something other. Change is change and not something other.

How does it change your understanding if the phrase in bold above is presented:

This is because the thing being pointed to necessarily has a definition and cannot be (by definition) other than what it is (which is how we define it). If it didn’t have a definition, we wouldn’t be able to point to it and we define it by pointing.

I find your rewording confusing because it seems to leave out non-abstract entities, such as physical objects, for no particular reason. But to be honest, I'm not sure that I understand your question to begin with.

In order to have the power to contradict A=A, a thing or an event needs to have an identity of some kind. Otherwise, there exists no platform from which to launch the refutation. The existence of such a platform, however, immediately proves that A=A is still operating as ever.

When you truly understand A=A, you will see that it is utterly impossible to contradict it. Nothing can ever contradict it.

David; And if there is no identity and no platform?

Then there is no basis to launch a refutation. A=A remains unchallenged.

-

David;

My phrasing did not exclude “non-abstract entities, such as physical objects”. Since we define a thing by pointing at it and you are able to point to “non-abstract entities, such as physical objects”, the thing is defined, and since “non-abstract entities, such as physical objects” are defined, they are included. I hope that helps clear the confusion.

But my point is: in your phrasing of the bolded text, identity seems to mean an objective essence (an inherent or self-existing self) and my phrasing does not posit an objective essence.

So (we agree) “there is no basis to launch a refutation” answers the question “what if there is no platform?” But it does not answer the question “what if there is no identity?”

clyde

[Kevin Solway]

The instant creation and annihilation keep contradicting the A=A mantra

Why?

A=A doesn't say anything about how fast things are created and destroyed.

Kevin about 'pure logic' wrote:
It is logic that doesn't depend on empirical uncertainties. It is elf-evident truth (which is to say that it is self-evident to those few humans who are capable of logical thinking).

Well, I am not sure how you would like to differentiate between empirical certainties and empirical uncertainties

There are no empirical certainties. Literally all empirical observations are uncertain.

The only thing that is certain is that we observe what we observe.

Kevin about 'pure logic' wrote:
The truth that I exist right now will indeed last forever. I don't know whether I will exist a moment from now.

By this you are restating the truth you formulated earlier ("The truth that I exist is a logical truth"). That is interesting as it shows the addition of a condition ("right now") that makes a not so absolute truth into a more absolute truth.

"Right now" is implicit in the original statement. It wouldn't make any sense to say "I exist next week", or "I exist last week". Existence is always right now.

You can do this, but be aware that underneath are still all kinds of other 'hidden' conditions.

They might be hidden to you, but they're not hidden to me.

Suppose for example that M-brane theory is right and that there are 10 or 11 dimensions to this reality. Can you be sure that your existence in say the sixth dimension is accurately described by your amended statement?

A thing is always what it is, and is never what it is not. It doesn't matter how many dimensions there are.

For example, let's says that something appears to be a square from one perspective, but appears to be a circle from another perspective. A square is a square, and is not a circle. Likewise a circle is a circle, and is not a square. A=A (logic) is never violated. There is another thing we "observe", and that is something which sometimes appears to be a square, and at other times appears to be a circle, and this too is always itself, and never other than itself.

No, of course not. You would need to know more about that sixth dimension before you can answer this question. You need that context of reality first before you can remap your logical truth to this part of reality.

Since logic necessarily applies universally we can apply it with confidence without having any further knowledge about different dimensions or perspectives, etc.