Can you ever be certain that you are reasoning correctly?

[brokenhead]

Don't make me laugh. It's not that good of an argument. You are playing with deductive logic, but you don't seem to have much, if any, training in it.

I don't? What sort of training are you talking about, Trevor?

[Fujaro]

Kevin:The only way we could suggest that it might persist in time is if we had solid empirical evidence, and with empirical evidence we are always in the realm of mere speculation.
Fujaro: A=A itself also cannot be proven.

It doesn't matter that A=A cannot be proven, because it is self-evident.

Self-evident means nothing more than that it is considered clear from reality straight away. As if we have direct access to absolute truth in this case.
As a philosopher you are aware that there are serious questions as to whether self-evident is logically valid at all.

The only reason to accept it is the congruence with reality as you perceive it.

Absolutely not.

Then what is your reason Kevin?

We don't "accept" logic (A=A) because the only way we could possibly "accept" it is if we already had logic in the first place.

Logic is automatically built-in to the conscious mind. It is not something that can be accepted or rejected.

I assume that you can show me how you have logically arrived at this conclusion? Because if you can't logically arrive at this, it shows that you are assuming things about reality. And that's cheating to your own standards of rigorous logic.

]So in that you are also using empirical evidence.

In normal science, empirical evidence is something that can be duplicated and tested over time. This is in sharp contrast to pure logic which can be carried out by an individual in the moment, and doesn't require further testing and verification.

I see your confusion. I will rephrase it for you to 'experiences': You are using experiences not logic to accept A=A.
NB: Do you mean 'normal' science as in contrast to pseudo science?

"Empirical evidence" only exists because logic is already in operation.

You are confusing logic and reason again. Reason is a mix of inductive and deductive skills, it's not purely deductive logic.

You can't construct existence from logical thought alone.

Nobody is trying to construct existence from logical thought that I know of.

You should Kevin, for you are one of them. You accept A=A not only as a logical truth, but on top of that as a truth of all existence.

In your snapshot view there is no interaction between objects, because everything is frozen in time.

"The present" is a snapshot, yet the present is caused by the past.

So while there is no interaction between the present and the past (since the past has already gone) the present is caused by the past.

You only have a set of frozen snapshots to go on. Can you be logically certain that snapshot 23456 'causes' snapshot 23457? Or is it also logically possible that snapshot 25000 caused 23457? And how can tou tell logically? Consider this carefully, are you doing this by deduction from A=A (then please show me how), or are you saying to yourself something like "Wait a minute! That the position of the electron in adjacent snapshots is varying relatively little as compared to snaphots that lie farther apart, must mean something significant about the nature of things. Could it be that this is a trajectory of the same electron trough time?!" And there you go, you are in the conjecturing business before you know it.

You cannot possibly conclude anything about causation between different snapshots without inductive reasoning

I can conclude that a thing was caused by that with is not itself entirely with deductive reasoning.

In the snapshot logic it's even worse than I confided to you before: you would not even suspect a phenomenon called 'event', for in every snapshot everything is frozen and all is new, has new identity. There's no event happening to any electron, because all the electrons in adjacent snapshots are different, remember?

This strict kind of philosopher is not participating in knowledge gaining but is like a donkey refusing to walk on because on logic alone it can't be deduced that the road will lead anywhere.

The practitioner of pure logic can tell us that the road will definitely lead somewhere - even if it is round in a circle - and he can tell us that through pure deduction.

Only when inductive reasoning is applied as I have shown.

There is a time-aspect in the existence of physical things, such as electrons.

You have only instantanious existence within the snapshot when you say that in every snapshot there is another electron.

We can have an observation of an electron (a "snapshot") and we can still ask "What caused the electron?" and "What will become of the electron?" Hence we have a snapshot, and we also have time.

Forget time in snapshot logic. Your sense of time may delude you. You must rely on deductive logic only and then there is only 'now' as you suggested yourself. Inferring a timeflow from the comparison of adjacent snapshots is an inductive reasoning.

For example, the first electron definitely has effects. There are consequences to its existence. It's just that we don't know that the second electron is one of them.

The word 'effect' you use is based on experience of existence through time, or in other words on the inductive comparison (pattern recognition) of snaphots in a row. You are not allowed to use it in your strict snapshot view.

No. I know that a thing has causes (and effects) through deductive reason alone. It's not something I have learned from empirical experience (which is always uncertain).

Then, please show me the purely logical deduction of it.

. . . it is conceivable in logical sense that between the first and the second statement a new I is inserted with the collective memory of the old I. You cannot be any more certain about this conclusion than about the existence of an electron through time.

A thing only "exists" when observed. Things naturally have no boundary separating them from the rest of Nature. The human mind provides that boundary. That is, the human mind draws a boundary and says "electron", where no boundary previously existed. Similarly with the "I".

Please substantiate your claim that a thing only exists when observed. I assume this is another logical deduction from A=A? I'm very interested. Also I'm curious to know in what way this helps the 'I' to escape from the snapshot logic. The observation of 'I' in the first part of the sentence is still in another snapshot than the observation of 'I' in the last part.

A=A has no bearing on existence itself, it's a purely logical concept, placed not only out of time, but also out of reality.

A=A is not a logical concept, but is logic itself. So its value is the value of logic itself.

Let me get this clear. Is A=A a logical statement or is it more than this statement alone? And if such is the case, what other logical statements or methods should we understand it to be?

1) A=A cannot be verified empirically

True, since all empirical evidence requires logic.

I agree that (1) is true, but for other reasons. Absolute verification is impossible empirically.

2) A=A cannot be proven logically

True, since A=A is itself logic.

Again, I agree that the statement is true, but for other reasons. The acceptance of the statement A=A is either relying on experience of resemblance with reality, or on the unsubstantiated assertion that we can perceive this as true with alleged infallable logical faculties implemented in our being. In both cases the step of adopting A=A as true is non-logical.

3) From A=A alone non-trivial sentences cannot be built

This depends on what you mean by "trivial".
Pure, deductive logic, independent of all empirical evidence, can deliver incredibly profound, valuable, and significant knowledge that can be very hard-won. If all this can be called "trivial" then logic alone can deliver no more than this.

A simple sentence like "the boy is outside" is an example of a non-trivial sentence. With A=A alone these sentences cannot be formed.

4) The reason for adopting A=A is it's congruence with macro-level appearences

A=A comes built-in with any appearance at all. If you can identify anything at all, then logic is already taking place.

You cannot objectively know what is taking place. That would have to mean that you could give a full and detailed account of how this 'device' is operating (from neuron firing to conclusion drawing).

5) A=A can have no complete mapping to reality for it is impossible to know if all properties are known about a thing existing in reality

This statement doesn't really mean anything, since it draws a false distinction between "reality" and logic.

I'll rephrase to:
5) A=A can have no complete mapping in reality for it is impossible to know if all properties are known about a thing existing in reality.
There now is only one substance in this statement. Please reconsider the statement.

[David Quinn]

Kevin wrote:

It doesn't matter that A=A cannot be proven, because it is self-evident.

I'm not sure that "self-evident" is the right way to describe it.

While it is self-evident once you see it, the process of opening one's eyes and seeing it is a logical act. It involves seeing that it is impossible to challenge A=A without also affirming it at the same time. The moment that one attempts to formulate a challenge, A=A immediately comes into play and is automatically affirmed. The challenge thus collapses before it has even begun.

In any case, it is interesting to observe Fujaro's stated affirmation of the principles of doubt and open-mindedness in conjunction with his closed-mindedness, even hostility, towards philosophic logic. Something is wrong there.

He seems to think that science is somehow threatened by philosophic logic, that the two are incompatible with one another.

-

[David Quinn]

1. Let A be the subset of the Totality that includes all possible logically true statements and nothing else. Totality is an infinite set, and set A may also be infinite.
2. Let B be the subset of the Totality that includes every member of the Totality not in set A. We call B the complement (in the set Totality) of set A. B may itself be infinite. We agreed that it doesn't matter. Given its definition, it seems as though it must be - it is the set of everything that is not a logical truth.
3. The intersection of A and B is the empty set; it contains no members by definition.
4. The union of set A and B is the set Totality, by definition, which is infinite.
5. The Totality is unique. A is unique. B is unique.

Are we agreed so far? If not, please tell me why not, specifically.

Logical truths are not mountains or clouds. Got it.

It is your next step in the argument which will decide whether I agree or disagree with your line of thinking.

You have not shown it to be possible that a logical truth can necessarily apply to all things in existence. Instead, you introduced the term "things," and I objected , calling this another example of double-talk.

Giving the term "things" a definition so that we can meaningfully talk about how a logical truth necessarily applies to all things in existence - this is double-talk?

I can't see it. Seems pretty straightforward to me.

I simply refered to the members of each of our defined sets as "members." I will agree to the term "things" if you are saying that 1.) Every possible logically true statement is a "thing," and 2.) Whatever is not a logically true statement is also a "thing." That is, a golf ball is a thing, sorrow is a thing, indecision is a thing, the wind is a thing, etc.

Yes, that is what I mean. All these phenomena are portions of the Totality and therefore qualify as "things".

There can be no concept, named or unnamed, or anything preconceptual or unconceived, that is not a thing.

Indeed.

Therefore, the term "Thing" can convey no information whatsover, because there is and can be nothing that is not a thing.

At the very least, it conveys the information that nothing can ever constitute the Totality.

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.

Again, you have not shown this to be possible.

We have just agreed that every phenomenon in the Universe is a "thing". So straight away our logic is embracing everything there is.

You're not seeing the simplicity of this kind of thinking and thus you're not seeing its heart - mainly because of an attachment to a God whose survival depends on things remaining unnecessarily complicated.

Again, have I mentioned God once in this line of questioning? You are using what you erroneously believe to be my concept of God to defend yourself, which is interesting, don't you think? Why don't we leave Him out of it, since if your position is sound - which it isn't - you have no need of Him.

It's your agenda on this forum and shines through in everything that you say - that of affirming the existence of a personal god. But I'm happy to leave it aside until you start reintroducing him more overtly.

-

[brokenhead]

It's your agenda on this forum and shines through in everything that you say - that of affirming the existence of a personal god.

It happens to be on the agenda of my own life, not just this forum. And "shines through" is much better than "reeks of," thank you very much.

You are with me so far, then, David. On that fine note, I will leave you hanging. Hold that thought. I cannot stay up all night tonight as I sometimes do when I am engaged at GF. I have commitments on the morrow and must catch badly-needed Z's. I shall return.

[Fujaro]

Kevin wrote:

It doesn't matter that A=A cannot be proven, because it is self-evident.

I'm not sure that "self-evident" is the right way to describe it.

While it is self-evident once you see it, the process of opening one's eyes and seeing it is a logical act. It involves seeing that it is impossible to challenge A=A without also affirming it at the same time. The moment that one attempts to formulate a challenge, A=A immediately comes into play and is automatically affirmed. The challenge thus collapses before it has even begun.

In any case, it is interesting to observe Fujaro's stated affirmation of the principles of doubt and open-mindedness in conjunction with his closed-mindedness, even hostility, towards philosophic logic. Something is wrong there.

He seems to think that science is somehow threatened by philosophic logic, that the two are incompatible with one another.

-

Well, I really don't think that logic (or philosophic logic as you call it) isn't compatible with science. My statement would be that they need each other as in symbiosis. And I have stated such several times before. But I do think that you and Kevin are using the word 'logic' as a trojan horse into the arguments presented. There is a real issue here in your perception of deductive logic versus inductive logic. Only the former leads to truths in a strict sense and at least Kevin also agrees on this. In the above reply you become very fuzzy about the actual logical rules you are using to infer that A=A is true. All you say about it is that it is a logical step, that it is not just assuming. But you don't provide rigorous logical evidence you demand from your opponents.

Although I do acknowledge that from experience A=A is pretty hard to deny, there is no logical evidence for it. Russell once proposed to test it empirically, but that ran into obvious problems with the lack of aboluteness about empirical measurement. Everything I read on the subject denies very strongly that a logical proof for it exists. Finally Kevin comes forward with an appeal to knowledge a priori ("logic is automatically built-in to the conscious mind") and thus all hinges on the truth of this statement. Well the statement has had a strong proponent in Kant, but ever since Kant it has been heavily debated among philosophers. To claim this direct link to The Absolute, you should be able to give a detailed account of how this is supposed to come about or it should be distrusted. Non is given so far. To refute it under the strict regime of deductive logic all that is really needed is to present the possibility that you can think that it is absolute truth that is residing in your mind without it actually being the case.

As I see it, you are in a dilemma. Allowing inductive reasoning removes rigour from your deductive stance and opens the door to other inductive axiomas as more promising guiding principles, prohibiting inductive logic is the end of the application of A=A to existence.

Furthermore I do think that I can point to a thing in reality without referring to rigorous A=A. I simply restrict myself to a limited set of properties to define that the thing is A. I can do that logically, and I can do that empirically. So I allow that I might discover empirically that this table in the ninth dimension that I yet can't investigate in no way is the table I thought it was. I would from it suggest another way of dealing with A=A. And I also allow that I might discover empirically that this table has ome proprties in the second spatial dimension I had overlooked up till then. I would allow my own fallible judgement. From this I'd like to suggest another way of dealing with A=A. The central problem from reality that is adressed with the A=A is the problem of identity. Not the A=A as a logical statement is the real issue at hand, but the meaning of identity in the real world. When can we be sure about the identity of a thing in a reality that may have hidden properties at the moment?

I think that philosophy in the end is more about finding ways to deal with tentativenes, probabilities and inaccurateness than it is about finding absoluteness and working the way up. That is not to say that deductive reasoning has no place in it. It is very usefull to investigate all kinds of deductive logic very extensively. This has shown its use for science very clearly in past centuries. But philosophy entails much more than an excercise in strict deductive logic.

[Kevin Solway]

.It doesn't matter that A=A cannot be proven, because it is self-evident.

Self-evident means nothing more than that it is considered clear from reality straight away. As if we have direct access to absolute truth in this case.

That's right. With logic we indeed have access to absolute truth.

As a philosopher you are aware that there are serious questions as to whether self-evident is logically valid at all.

These are non-questions. It doesn't mean anything to ask whether logic is logically valid.

The only reason to accept it is the congruence with reality as you perceive it.

Absolutely not.

Then what is your reason Kevin?

Logic, as suggested by its symbol "A=A", is the act of identification. If anything at all is identified then it must be accepted that there is logic. Since I personally identify things, which is to say that I observer that a thing is what it is and not other than what it is, it follows that I have no choice but to "accept" logic. I do not really accept it, but it is forced upon me.

Logic is automatically built-in to the conscious mind. It is not something that can be accepted or rejected.

I assume that you can show me how you have logically arrived at this conclusion?

The reason you can't choose whether to accept logic is because if you are conscious then you are already using logic and are thoroughly committed to it.

I will rephrase it for you to 'experiences' [rather than empirical evidence]: You are using experiences not logic to accept A=A.

See above. If anything at all is experienced, and identification is taking place, then there is already logic, so there is no question of "accepting" it.

"Empirical evidence" only exists because logic is already in operation.

You are confusing logic and reason again. Reason is a mix of inductive and deductive skills, it's not purely deductive logic.

Reason uses logic. Logic does not use reason. Logic is the atomic element.

You accept A=A not only as a logical truth, but on top of that as a truth of all existence.

It could be called the truth of all existence in the sense that all things which exist do so through identification, which is what logic is.

All truths are dependent on A=A, on logic, but logic is not the whole of Reality. It is only a tool.

"The present" is a snapshot, yet the present is caused by the past.

So while there is no interaction between the present and the past (since the past has already gone) the present is caused by the past.

You only have a set of frozen snapshots to go on. Can you be logically certain that snapshot 23456 'causes' snapshot 23457?

In the case that snapshop 23457 is "state of the Universe now" and snapshot 23456 is "the state of the Universe a moment ago", then I can be certain that the earlier snapshot is the cause of the later snapshot - since there is nothing else that could possibly have caused it.

Or is it also logically possible that snapshot 25000 caused 23457?

If one snapshot is a prior state of the Universe, then it is definitely a cause if the other.

And how can you tell logically?

Because the past is the cause of the present - by definition.

In every snapshot everything is frozen and all is new, has new identity. There's no event happening to any electron, because all the electrons in adjacent snapshots are different, remember?

A thing is called an "event" when it is conceived as happening in time. The current state of the Universe is an "event", and this particular event is caused by the past state of the Universe.

The practitioner of pure logic can tell us that the road will definitely lead somewhere - even if it is round in a circle - and he can tell us that through pure deduction.

Only when inductive reasoning is applied as I have shown.

No inductive reasoning is necessary, since it is inherent in the definition of a road that it leads somewhere.

Forget time in snapshot logic.

A "snapshot" only means something in relation to time, since it happens in an instant of time.

Your sense of time may delude you.

Your "sense" of time can't delude you, but only your interpretation of your sense of time.

What appears to be the passage of 5 minutes is indeed what appears to be the passage of 5 minutes, regardless of what any clocks might say. No delusion is taking place in such a case, so long as the person experiencing the passage of what appears to be 5 minutes doesn't make any unnecessary assumptions.

You must rely on deductive logic only and then there is only 'now' as you suggested yourself. Inferring a timeflow from the comparison of adjacent snapshots is an inductive reasoning.

Firstly, we don't "infer a timeflow". Rather, we experience time, which is a completely different thing.

There is an experience of the "now" and an experience of something other than now, which we call "the past", which we define as being prior to the present. The present must, logically be caused by the past, since there's nothing else that could cause the present.

Please substantiate your claim that a thing only exists when observed.

This is part of the definition of what "exists" means. A thing is said to "exist" when it is observed or imagined.

We can imagine a category which contains all unknown things (ie, all things not as yet consciously experienced). In this manner, all the things that we are not consciously aware of, exist.

I'm curious to know in what way this helps the 'I' to escape from the snapshot logic.

The "I", as a logical entity, does not occur in time, and therefore it is not a snapshot.

The observation of 'I' in the first part of the sentence is still in another snapshot than the observation of 'I' in the last part.

It is an observation of the same "I", at different times, just as the number "1" is always the same "1", no matter when you observe it.

A=A is not a logical concept, but is logic itself. So its value is the value of logic itself.

Let me get this clear. Is A=A a logical statement or is it more than this statement alone? And if such is the case, what other logical statements or methods should we understand it to be?

"A=A" is a symbol which means "Logic". Logic is the recognition that a thing is what it is, and not other than what it is. All purely deductive thinking can be summarized by the expression "A=A".

the step of adopting A=A as true is non-logical.

Logic cannot be "adopted", since whenever something is adopted, logic is already in existence. Logic either exists or it doesn't.

A simple sentence like "the boy is outside" is an example of a non-trivial sentence. With A=A alone these sentences cannot be formed.

Logic never says "the boy is outside", but rather "That which appears to be a boy, appears to be outside" (which may be shortened for convenience).

Science too, when it is logical (which happens rarely), only says "That which appears to be a boy, appears to be outside".

You cannot objectively know what is taking place.

I objectively know that I am having experiences.

That would have to mean that you could give a full and detailed account of how this 'device' is operating (from neuron firing to conclusion drawing).

It doesn't follow that just because I know some things objectively that I can obectively know all the infinite detailed interactions of the Universe.

A=A can have no complete mapping in reality for it is impossible to know if all properties are known about a thing existing in reality.

Let's take the category of all unknown things as an example. This category perfectly describes that which it is intended to describe.

Things like "left" and "right" also perfectly describe that which they are supposed to (ie, the left and right sides of an observed thing).

[Kevin Solway]

I think that philosophy in the end is more about finding ways to deal with tentativenes, probabilities and inaccurateness than it is about finding absoluteness and working the way up.

When philosophy finds things about which we should be tentative, and reveals which things are inherently inaccurate (such as empirical measurement), it makes these findings absolutely, and does so through deductive logic rather than empirical measurement. For example, we don't need to measure, say, the length of a piece of string a billion times to know that there is at least a margin of error in the measurement, and possibly no piece of string at all. This knowledge can be arrived at through logical reasoning alone. That absoluteness is what distinguishes philosophy from science, although every scientist should ideally also be a philosopher, since science without philosophy is nonesense, and philosophy without science (a system of empirical knowledge) is impossible.

[Carl G]

Kevin wrote:

"A=A" is a symbol which means "Logic". Logic is the recognition that a thing is what it is, and not other than what it is. All purely deductive thinking can be summarized by the expression "A=A".

Logic never says "the boy is outside", but rather "That which appears to be a boy, appears to be outside" (which may be shortened for convenience).

Science too, when it is logical (which happens rarely), only says "That which appears to be a boy, appears to be outside".

I appreciate these in-a-nutshell definitions and particular examples. Agree that true science employs logic. In true sense of the words, logic and science are practically synonymous.

[brokenhead]

First of all, a few points of agreement are in order.

Pure, deductive logic, independent of all empirical evidence, can deliver incredibly profound, valuable, and significant knowledge that can be very hard-won. If all this can be called "trivial" then logic alone can deliver no more than this.

This is obviously true. Pure mathematics has many, almost uncountably many, branches that are bearing fruit day in and day out, with no applications in sight.

A thing only "exists" when observed.

And yet we say that the earth existed before life appeared upon it. No life, no observers, no existence, a logical contradiction. Therefore, we must assume an observer prior to the advent of Man. Is this not a logical deduction? If not, why not?

And now to my proposed sets A, B, and T.

My point is very simple, and it seems, to me at least, to be in accord with some of Fujaro's points. All possible logically true statements are things in set A. Anything that is not a logically true statement belongs to set B. For a logically true statement to be a statement about anything that is not also a logically true statement, we need a mapping from set A to set B. My argument is simply that any such mapping must be a "thing" in set B. (I would have preferred to use the term "member" to be consistent with basic set theory terminology, but I concede that we shall call it a "thing" so we can discuss it, as David has said.)

Now was that so hard?

I am making the point to show the limitations of logic in as clear-cut a way as I know how. Any part of a logically true statement about something, such as a premise, belongs to set B. Any "things" about which we can make a logically true statement, if they are not themselves logically true statements (such as theorems or axioms) also belong exclusively to set B. Set B may be thought of as the "empirical" realm.

Just to beat this humble point further to death, let me give an example or two.

"If all Australians hate American beer, and Dan is an Australian, then Dan hates American beer." This is a logically true statement and, as such, belongs to set A. But if I said, "All Australians hate American beer," this would not be a logical truth, and would therefore be a "thing" in set B. In fact, it might not be a truth at all (though I rather suspect it is.) Now if I said, "Dan is an Australian," this would be a true statement, but it would not be a logically true statement, and therefore would also be a "thing" in set B.

Again, I am not trying to argue against logical thought processes. I am, in fact, trying to use only logical thought processes as much as possible in my argument. But one of you, Kevin or David, said in this thread and I can't seem to find it, that rational thought does not consist merely of logic, but that empiricism plays an integral role in rational mentation as well.

In many instances, your mind thinks faster than "you" can. What one may call "intuition" may be a vast inductive leap your mind takes with "you" as a bystander, left to deductively verify as you are able. Your mind, as both Kevin and David have said repeatedly, has logic built in. But other forms of "knowing" display themselves as well. The discovery, or invention, of non-Euclidian geometry is a case in point. Lobachevsky actually pared away assumptions which were prevalent up until then. One can say there was no logical or rational reason for him to do so. In fact, his contemporaries strongly advised him to abandon his research, as it would bring him scorn and hinder his advancement in academic circles. He ignored them, and they were proven correct in their predictions. Yet the creative impulse defied rational objections as well as theretofore prevailing logical thought. The great Gauss himself was making the same "discoveries" at roughly the same time, but kept them to himself for fear of public reaction. Today, non-Euclidian geometry is a rich vein of mathematical inquiry and has physical applications as well.

See, David? I didn't mention a personal God once. But if that disappoints you, I'm sure I can come up with something...

[Tomas]

.


Brokenhead writes:
See, David? I didn't mention a personal God once.



-tomas-
You just did!


.

[Fujaro]

That's right. With logic we indeed have access to absolute truth.

You should know better. It is like the first cause argument in the theistic cosmogony. There is no hard proof for a first cause in logic either. Every logic you choose has basic tenets that cannot be proven but are adopted. For Euclidean Geometry these are the five axiomas Euclides singled out. For A=A it is among others the uniformity of nature, which cannot be proven, but merely inferred. At some point one must accept the foundations of logic as true, or no logic will emerge at all. Another example is the principle of distributivity, which is valid in classical logic, but invalid in quantum logic.

One cannot provide evidence for logic, without appealing to logic and your argument for direct access is not deductive. All deductive reasoning uses deductive arguments to move from premises, which are assumed to be true or proven true in other deductive arguments, to conclusions, which must be true if the premises are true. This means there is no absolute basis to deductive reasoning. Every premise needs its own deductive argument to be deductively rigorous and a miracle is needed to escape infinite regress. A different choice of axioms results in different logical structures. In an earlier post you used a priori knowledge as a plug to the bathtub but were unable to defend it with deductive reasoning alone. This is no shame for there is not one philosopher who has been able to supply it, but it is simply hardheaded to persist in the claim of deductive proof through a priori knowledge. The claim is outdated in modern philosophy, but still persists in religion.

Not being able to recognize this resembles the deadlock situation physics was once in regarding the speed of light. While many assumed an absolute grid in space to which every motion could be absolutely referenced, this was contradicted by the Michelson-Morley experiment that showed that the speed of light was exactly the same in every direction. Einstein didn't follow the 'bedrock logic' of the time but adopted the results from the Michelson-Morley experiment as true and Special Relativity was born as a direct consequence. This shows that the absolute belief in bedrock logic inhibits breakthrough in our thinking about nature, about existence.

See also: http://vm.uconn.edu/~wwwphil/logic.pdf

As a philosopher you are aware that there are serious questions as to whether self-evident is logically valid at all.

These are non-questions. It doesn't mean anything to ask whether logic is logically valid.

How are you gonna prove that statement deductively? Let's begin with the uniformity of nature, how do you rigorously infer that all of nature, even the farthest regions not observable to us or unknown dimensions of existence will always abide to your choice of logic? You feel it in your guts, right?

[Trevor Salyzyn]

Fujaro, could you please give an example of a type of logic without self-identity?

[Fujaro]

]You must rely on deductive logic only and then there is only 'now' as you suggested yourself. Inferring a timeflow from the comparison of adjacent snapshots is an inductive reasoning.

Firstly, we don't "infer a timeflow". Rather, we experience time, which is a completely different thing.

But that's worse! Experiencing relies on appearances through our senses. It's pretty basic that such won't suffice as a logical argument.

[Trevor Salyzyn]

As a side-note, logic without self-identity is different than logic without non-contradiction.

For instance, logic without non-contradiction might say that:
1. A
2. B
does not imply
3. A & B

Whereas, without self-identity:
1. A
2. B
does not imply
3. A
4. B

[clyde]

Kevin;

Due to Carl, my attention was drawn to this,

Logic never says "the boy is outside", but rather "That which appears to be a boy, appears to be outside" (which may be shortened for convenience).

Science too, when it is logical (which happens rarely), only says "That which appears to be a boy, appears to be outside".

In the same way, wouldn’t it have been more accurate to write,

“That which appears to be logic does not appear to say “"the boy is outside", but rather appears to say"That which appears to be a boy, appears to be outside"”

and

“That which appears to be science, when it appears to be logical (which appears to happen rarely), appears to say “"That which appears to be a boy, appears to be outside".”

As I have noted previously, logic is a phenomena like boy, outside, science, etc.

clyde

[Fujaro]

There is an experience of the "now" and an experience of something other than now, which we call "the past", which we define as being prior to the present. The present must, logically be caused by the past, since there's nothing else that could cause the present.

You are not making sense. It is illogic to conclude from your statement that there is only experience in the now from appearances alone (about a past), that there has to be a prior. Maybe the appearance of the past in the now is a false one, maybe it's somehow an appaerance from the now. How can you deductively decide on that?

I'm curious to know in what way this helps the 'I' to escape from the snapshot logic.

The "I", as a logical entity, does not occur in time, and therefore it is not a snapshot.

Does the appaerance of "I" not exist? If so, how is it possible that there appears an appaerance of a logical "I"?

We can imagine a category which contains all unknown things (ie, all things not as yet consciously experienced). In this manner, all the things that we are not consciously aware of, exist.

But what about the categories you can't imagine?

The observation of 'I' in the first part of the sentence is still in another snapshot than the observation of 'I' in the last part.

It is an observation of the same "I", at different times, just as the number "1" is always the same "1", no matter when you observe it.

There you go, you call it the obervation of "I". Following your terminology so far this means it is an appearance, as I suggested to you. And since the appaerances are within snapshots you demolish your own argument with this.

[Fujaro]

Fujaro, could you please give an example of a type of logic without self-identity?

To my knowledge there are only inductive types of logic that can do without A=A. I have provided the example already:

Furthermore I do think that I can point to a thing in reality without referring to rigorous A=A. I simply restrict myself to a limited set of properties to define that the thing is A. I can do that logically, and I can do that empirically. So I allow that I might discover empirically that this table in the ninth dimension that I yet can't investigate in no way is the table I thought it was. I would from it suggest another way of dealing with A=A. And I also allow that I might discover empirically that this table has ome proprties in the second spatial dimension I had overlooked up till then. I would allow my own fallible judgement.

[Trevor Salyzyn]

Do two inductive arguments, with the same set of premises and margins of error, lead to the same conclusion?

[Fujaro]

Do two inductive arguments, with the same set of premises and margins of error, lead to the same conclusion?

Does the abiding of the circuits in your PC/Mac to the quantum tunneling effect constitute a succes of induction and deduction together or to deduction alone?

[Trevor Salyzyn]

Hey, I'm simply trying to establish if two identical inductive arguments lead to identical conclusions, since a possible logic without self-identity would be one where two absolutely identical arguments lead to entirely different conclusions. It should be obvious why I'm doing this in the first place: if there were a single type of logic without A=A, then that would be a sufficient counter-example to an earlier claim (by David, I believe?) that logic is self-identity. This is actually to your benefit, since even one counter-example refutes a universal claim.

I'm not disputing the utility of inductive logic.

[Diebert van Rhijn]

At some point one must accept the foundations of logic as true, or no logic will emerge at all.

Isn't that in a nutshell where you were arguing against before?

What happens if no logic would emerge? What are the consequences? Unknown for sure!

[clyde]

Kevin;

Due to Fujaro, my attention was drawn to this,

A thing is said to "exist" when it is observed or imagined.

We can imagine a category which contains all unknown things (ie, all things not as yet consciously experienced). In this manner, all the things that we are not consciously aware of, exist.

Are you positing that the appearance of a thing creates the thing?! Isn’t it more accurate to say that the appearance of a thing is the appearance of a thing (You know, A=A.) and that one can say that the appearance of a thing exists.

And from the appearance of “a category which contains all unknown things” one could say that the category exists, but one could not say that any thing in that category exists, otherwise the thing would not be unknown.

clyde

[David Quinn]

Well, I really don't think that logic (or philosophic logic as you call it) isn't compatible with science. My statement would be that they need each other as in symbiosis. And I have stated such several times before. But I do think that you and Kevin are using the word 'logic' as a trojan horse into the arguments presented. There is a real issue here in your perception of deductive logic versus inductive logic. Only the former leads to truths in a strict sense and at least Kevin also agrees on this. In the above reply you become very fuzzy about the actual logical rules you are using to infer that A=A is true. All you say about it is that it is a logical step, that it is not just assuming. But you don't provide rigorous logical evidence you demand from your opponents.

I did, but you're not seeing it.

Surely you can't fail to understand that in order to construct any kind of proof or dispoof at all, identifiable evidence must be called upon. And surely you can't fail to understand that evidence which is identifiable necessarily conforms to the principle of A=A. If it didn't, we wouldn't be able to observe it, let alone identify it.

It is clear, then, that "refuting A=A" falls into the same category as a "square circle". It is a contradiction in terms.

Although I do acknowledge that from experience A=A is pretty hard to deny, there is no logical evidence for it. Russell once proposed to test it empirically, but that ran into obvious problems with the lack of aboluteness about empirical measurement.

I've long known Russell to be an idiot of the highest order, but he never fails to surprise me with the scope of his idiocy.

Are you seriously saying that he thought A=A could be proven or dispoven through empirical testing? And worse, that after setting out to perform this task, he eventually realized that it was not feasible due to the lack of absoluteness in empirical observation?

Words fail me.

Everything I read on the subject denies very strongly that a logical proof for it exists.

Perhaps you should stop reading for awhile and resolve the matter properly in your own mind. The logica proof is there if you're willing to find it.

Finally Kevin comes forward with an appeal to knowledge a priori ("logic is automatically built-in to the conscious mind") and thus all hinges on the truth of this statement. Well the statement has had a strong proponent in Kant, but ever since Kant it has been heavily debated among philosophers. To claim this direct link to The Absolute, you should be able to give a detailed account of how this is supposed to come about or it should be distrusted.

The proof lies in the fact that it impossible to be conscious and have coherent thoughts without being conscious of forms (i.e. distinguishable appearances that have identity). Consciousness without forms is no consciousness at all.

As I see it, you are in a dilemma. Allowing inductive reasoning removes rigour from your deductive stance and opens the door to other inductive axiomas as more promising guiding principles, prohibiting inductive logic is the end of the application of A=A to existence.

A=A can be applied either inductively or deductively - and just as meaningfully in each case. Currently, you are only open to the possibilities of the former. That's understandable, this is how we have all been taught.

Furthermore I do think that I can point to a thing in reality without referring to rigorous A=A. I simply restrict myself to a limited set of properties to define that the thing is A. I can do that logically, and I can do that empirically. So I allow that I might discover empirically that this table in the ninth dimension that I yet can't investigate in no way is the table I thought it was. I would from it suggest another way of dealing with A=A. And I also allow that I might discover empirically that this table has ome proprties in the second spatial dimension I had overlooked up till then. I would allow my own fallible judgement. From this I'd like to suggest another way of dealing with A=A. The central problem from reality that is adressed with the A=A is the problem of identity. Not the A=A as a logical statement is the real issue at hand, but the meaning of identity in the real world. When can we be sure about the identity of a thing in a reality that may have hidden properties at the moment?

None of this is relevant.

To illustrate, consider a pyramid in 3-D space being inserted perpendicularly into a 2-D plane where the flatlanders live (I trust you are familiar the flatlander analogy). From the flatlander's perspective, the pyramid presents as a square. That is all they know of the object. To them, it is a square and nothing else. And yet a being in 3-D space can see that it is a pyramid.

Now, how is the principle of A=A affected by all of this? It isn't affected at all. The flatlanders observe a square and can realize that they are not seeing a circle or some other shape. Likewise, the 3Ders observe a pyramid and can realize that they are not seeing a cylinder or some other object. A=A is in full operation here.

Is the object really a square or a pyramid? The question has no meaning because objects are always observed in context. Is the object both a square and a pyramid at the same time, thus violating A=A? No, it isn't. It is simply an object that presents as a pyramid in 3-D space and as a square in 2-D space. So again, A=A is not violated.

If the object truly violated A=A no one would be able to experience it. It wouldn't be able to exist in the first place.

-

[Kevin Solway]

Are you positing that the appearance of a thing creates the thing?

Appearance (where its boundaries are) is one of the main causes of a thing.

Isn’t it more accurate to say that the appearance of a thing is the appearance of a thing (You know, A=A.) and that one can say that the appearance of a thing exists.

A thing is actually an appearance.

And from the appearance of “a category which contains all unknown things” one could say that the category exists, but one could not say that any thing in that category exists, otherwise the thing would not be unknown.

The category appears to contain countless things because it can be mentally divided up endlessly.