But regarding your objections to Objectivism, Objectivism summed up in a sentence is commitment to objective reality. I fail to see how a philosophy that promotes exploring the scientific world and going wherever the evidence takes one can be inconsistent with physics and mathematics.

Judith

The metaphysics is flawed. It is based on Aristotle's erroneous ideas of cause. There is only one kind of cause - efficient cause. An action of type A leads to an action of type B with some known spectrum of possible outcomes along with the probability of the outcome. Aristotelean metaphysics would lead to a rejection of quantum physics which is known (empirically) to be correct.

This is why L.P. regards quantum physics as nonsense despite its clear evidential support and the effectiveness of its applications.

How is Rand's metaphysics integrally connected to Aristotle's erroneous ideas of cause? Can you document that connection?

Objectivism summed up in a sentence is commitment to objective reality.

Judith

In light of quantum mechanics there is no such thing as 'objective reality' . When the observer can have an effect on the observed the notion of 'pure objectivity' loses it's meaning.

Not true. To observe means interacting an observing system (which is physical) with the observed system. The outcome will be one of the eigenvalues associated with the Hermitian operator that characterizes the observation and the resulting state will be one of the eigenstates of the operator. You can't get more objective than that. Quantum theory is not only objective, it is the -most accurate- physical theory ever formulated since the beginning of human existence.

Observation is interaction. Interaction is governed by quantum laws. That is how the world works.

~ You clearly have a 'thing' about Aristotle and his (as most of his times) non-experimental 'science' observations. I'd say that Hawking is carrying this same tradition onward, but, this is really all irrelevent to O'ism being faulty in its metaphysics. Aristotle is not revered in O'ism for any science-observations (and why you harp on this I don't understand) but for his analysis of Logic and his application of it to a coherent system OF metaphysics.

The problem is that Aristotles's so-called 'laws of thought' do not work in modern science. They work in mathematics and they will remain a valuable tool there but in 'real' life even A=A does not work, since at sub atomic levels everything is in a constant state of change.

Not so. The eigen-values and eigen-vectors of an observable are well defined and obey specific laws. While the outcomes of an observer-observed interaction are probabilistic , the set set of values of the outcome are quite well defined.

Are you saying that coins don't exist just because coin toss outcomes are governed by probabilities?

Bob Kolker

No, I'm referring to uncertainty principles. In our attempt to observe something we alter it and so this blurs the line between observer and observed. This does not, however, invalidate determinism, it mean we must adopt a different kind of 00-valued, probabilistic determinism, which is what QM does.

Not so. The eigen-values and eigen-vectors of an observable are well defined and obey specific laws. While the outcomes of an observer-observed interaction are probabilistic , the set set of values of the outcome are quite well defined.

Are you saying that coins don't exist just because coin toss outcomes are governed by probabilities?

Bob Kolker

No, I'm referring to uncertainty principles. In our attempt to observe something we alter it and so this blurs the line between observer and observed. This does not, however, invalidate determinism, it mean we must adopt a different kind of 00-valued, probabilistic determinism, which is what QM does.

All observation is interaction between an observing system and an observed system and even there the boundary is not always a Bright Line. What is observed perceptually is the outcome of the interaction. But all participating physical systems exist, and the observation has a definite spectrum of eigenstates and eigenvalues. When the interaction settles down, the value observed will be one of the eigenvalues and the state the observed system is in will be one of the eigenstates.

And yes, there is a probability associated with each outcome. It is not statistical probability, it is probability defined in terms of super-posed quantum state the observed system is in when the observation is made (i.e. when the Hermitian Operator corresponding to the observation is applied to the composite vector representing the state of the observed object.

As to the appropriate logic for resolving the well known dualities a non-distributive non-boolean logic has been suggested. See -Interpreting the Quantum World- by Jeffrey Bub (Cambridge University Press).

I hate to be obvious (not really—philosophy is the art of the obvious), but would any of this kind of method of thinking do you any good if a tiger were after you? Would you have a "quantum perceptual interaction" with it to figure out if it really exists on its own and is all there anyway? Or would you run like hell?

I have yet to see any of this kind of thinking account for the existence of entities.

~ You clearly have a 'thing' about Aristotle and his (as most of his times) non-experimental 'science' observations. I'd say that Hawking is carrying this same tradition onward, but, this is really all irrelevent to O'ism being faulty in its metaphysics. Aristotle is not revered in O'ism for any science-observations (and why you harp on this I don't understand) but for his analysis of Logic and his application of it to a coherent system OF metaphysics.

Aristotle's physics (as we have received it) was wrong and it was wrong because -he did not check his conclusions against facts-. Ayn Rand advised (on several occasions) that one ought to check his premises. Too bad Aristotle did not follow that advice.

~ You clearly have a 'thing' about Aristotle and his (as most of his times) non-experimental 'science' observations. I'd say that Hawking is carrying this same tradition onward, but, this is really all irrelevent to O'ism being faulty in its metaphysics. Aristotle is not revered in O'ism for any science-observations (and why you harp on this I don't understand) but for his analysis of Logic and his application of it to a coherent system OF metaphysics.

The problem is that Aristotles's so-called 'laws of thought' do not work in modern science. They work in mathematics and they will remain a valuable tool there but in 'real' life even A=A does not work, since at sub atomic levels everything is in a constant state of change.

However the law of non-contradiction does hold. Now and forever.

The problem is that Aristotles's so-called 'laws of thought' do not work in modern science. They work in mathematics and they will remain a valuable tool there but in 'real' life even A=A does not work, since at sub atomic levels everything is in a constant state of change.

Today's physical theories were arrived at by following the math. The investigators got to bizarre conclusions that seemed inconceivable to them, but empirical experimentation supported the conclusions. I don't see how it's possible for something to apply in math but not in "reality".

We know what we know about the subatomic world based on mathematics and observation. We know about the changes, and the changes follow certain laws. A quark doesn't randomly turn into a water molecule which then turns into a chicken. Within the world of those laws, A is A.

Today's physical theories were arrived at by following the math. The investigators got to bizarre conclusions that seemed inconceivable to them, but empirical experimentation supported the conclusions. I don't see how it's possible for something to apply in math but not in "reality".

We know what we know about the subatomic world based on mathematics and observation. We know about the changes, and the changes follow certain laws. A quark doesn't randomly turn into a water molecule which then turns into a chicken. Within the world of those laws, A is A.

Judith

Physics is applied math, not mathematics. If 'reality' obeyed the laws of mathematics we would never have to adjust our theories since each law would be true forever, but this is not the case. In physics, we cannot define the objects perfectly as we can in mathematics and so there will always be new information and so adjustments. So mathematics does apply to reality, but only in a limited fashion. Objectivism (personification) seems to want to take Aristotle's simple rules of logic and apply them to 21st century life on earth, well, good luck with that!

Physics is applied math, not mathematics. If 'reality' obeyed the laws of mathematics we would never have to adjust our theories since each law would be true forever, but this is not the case. In physics, we cannot define the objects perfectly as we can in mathematics and so there will always be new information and so adjustments. So mathematics does apply to reality, but only in a limited fashion. Objectivism (personification) seems to want to take Aristotle's simple rules of logic and apply them to 21st century life on earth, well, good luck with that!

Classical logic is what most mathematicians use in their work. Even as we speak.

You have made another error. The conclusions of applied mathematics are true a priori based on certain -mathematical- assumptions (as opposed to assumptions about the world), regardless of how they are interpreted in real world applications. Physics on the other hand is based on hypotheses and postulates that are not a priori true. For example, the second law of thermodynamics. This law does not follow from any logical postulate. It is assumed because it seems to be true in all cases observed. That is no guarantee of it general truth. That is the difference between a hypothesis (something assumed) and an a priori necessary statement.

Classical logic is what most mathematicians use in their work. Even as we speak.

Yes, this is what I have been saying in this and another thread, logic works perfectly in mathematics but not in 'real' life. If you try and apply logic in a strict manner to 'real' life you are doomed to failure. When was the last time you used a syllogism to make a decision?

[premise1] I like cheese

[premise2] This is cheese

[conclusion] I like this cheese

(he then eats it and finds that he hates blue cheese) Damn this logic!

Classical logic is what most mathematicians use in their work. Even as we speak.

Yes, this is what I have been saying in this and another thread, logic works perfectly in mathematics but not in 'real' life. If you try and apply logic in a strict manner to 'real' life you are doomed to failure. When was the last time you used a syllogism to make a decision?

[premise1] I like cheese

[premise2] This is cheese

[conclusion] I like this cheese

(he then eats it and finds that he hates blue cheese) Damn this logic!

"I like cheese" means he likes any kind of cheese (since there was no limitation or qualification in the sentence). He finds he does not like blue cheese. Ergo premise 1 is false. Do you know what a universally quantified proposition is? Apparently not.

Sloppy thinking could be bad for your health. Consider that.

Returning to Putnam, in 1968 he published the essay "Is Logic Empirical?" which was renamed "The Logic of Quantum Mechanics" in a later collection of his papers. He proposed a quantum-logical interpretation of quantum mechanics to give an example of how we might have an empirical reason for revising logic.

Reichenbach had attempted an interpretation of quantum mechanics in 1944 using a three-valued truth-functional logic. (Our standard logic is a two-valued truth-functional logic.) The Reichenbach quantum-logical interpretation of quantum mechanics has no adherents today.

"Far more important than artificial many-valued logics are the quantum logics that arise naturally in the Hilbert space formalism. The strongest of these logics---strongest in the sense of most closely approximating to classical logic---is the logic which mirrors the structure of the set of closed subspaces of Hilbert space. This quantum logic was first studied by the mathematicians Garrett Birkoff and John von Neumann in a classic paper of 1936. By quantum logic we mean Birkoff and von Neumann's quantum logic and the various ways in which it may be formulated as a logic.

"A lattice of propositions is of course not quite a logic, whatever a logic is. But a lattice of propositions has a structure which is at least very much like the structure of a logic. So if quantum logic really is a logic, we should first make it look like a logic. Then we will be in a position to discuss whether it really is a logic.

//

"Quantum logic can in fact be fairly easily transcribed as a logic in the usual logical styles---as an axiomatic system, as a sequent calculus, and as a natural deduction system. . ." (127-28).

Particles and Paradoxes: The Limits of Quantum Logic

Peter Gibbins (1987)

Quantum logics utilize algebraic accounts of quantum theory. They make use of Boolean algebras, partial Boolean algebras, and orthomodular lattices. These structures can be found embedded in Hilbert spaces, those complex topological vector spaces appropriate to quantum mechanics. [see Chapter 7 of The Structure and Interpretation of Quantum Mechanics R.I.G. Hughes (1989).]

The basic idea is to supercede the classical logical constants of AND, OR, and NOT with the lattice-theoretic (algebraic) operations of MEET, JOIN, and ORTHOCOMPLEMENT. Recall the distribution equivalences for AND and OR that we learn in elementary logic, such as {[p AND (q OR r)] Equiv [(p AND q) OR (p AND r)]}. Corresponding equivalences of distributions do not obtain for MEET and JOIN in the algebra appropriate to quantum mechanics.

It seems to me as to most philosophers of physics today that the word supercedes in the first sentence of the preceding paragraph gets it wrong. The very Hilbert spaces and algebraic structures embedded in them from which some would draw a new logic are themselves deductively certified as sound mathematics using simply classical logic.

I would like to add some further thought to my old remarks quoted in the preceding post.

It is possible, for all I know at this time, that the mathematics required for quantum theory can be rederived using the quantum logic I described. If that proved not possible, then the quantum logic would not do as a revised general logic. If such a rederivation of the necessary mathematics were executed, there would be the further question of whether other interpretations of quantum mechanics---say the transactional interpretation or sum-over-histories interpretations---were superior to an interpretation requiring a revision of general logic.

So I don't mean to give the impression that revisions and improvements in the discipline that is logic are not possible. It should be noticed, however, that adoption of the quantum logic as more fundamental than our classical logic would not require any loosening of the law of non-contradiction. Rand's conception of logic as the art of non-contradictory identification would still stand.

In the collection The Law of Non-Contradiction edited by Priest, Beall, and Armour-Garb (Oxford 2004), I recommend especially the following:

"What is a Contradiction?" by Patrick Grim

"In Defense of the Law of Non-Contradiction" by Edward Zalta

~~~~

Greg and Bob,

I haven't forgotten the promise over on the Analytic-Synthetic thread. Will deliver shortly.

Some more, this from Michael Friedman in Dynamics of Reason (CSLI 2001):

In the 1930s the mathematician John von Neumann, who had worked intensively on both the current situation in the foundations of logic and mathematics and on the mathematical foundations of quantum mechanics, suggested that a revision of classical logic, wherein the distributive law for disjunction and conjunction is not longer universally valid, might be the best way for rigorously comprehending the radically new conceptual situation Bohr had attempted to address through the idea of complementarity. From this point of view, the logical space governing quantum mechanical quantities or properties is a non-distributive or non-Boolean algebraic structure, consisting of a system of distributive or Boolean sub-structures than cannot simultaneously be realized or embedded within a single comprehensive Boolean structure. And this yields a precise algebraic interpretation of the idea of complementarity (a non-orthodox one, of course) in so far as quantum-mechanical quantities or properties are indeed individually classical (within a particular Boolean sub-structure), and the underlying source of quantum-mechanical "weirdness" is simply that they do not fit together within a single classical (or Boolean) logical structure. This interpretive suggestion, to my mind, represents the right kind of intervention from the philosophical or meta-scientific level . . . . It remains to be seen, however, whether von Neumann's interpretive suggestion can yield a full and satisfying resolution of the deep conceptual difficulties still afflicting the theory [QM]. (122-23)

However the law of non-contradiction does hold. Now and forever.

Ba'al Chatzaf

Is that the one that states that something can both be and not be something? Like something can not be a wave AND a particle? Oh wait, yes it can!

Wave and Particle are metaphors. The quantum wave and particle can be subsumed under a -single- mathematical model. In short, no contradiction. The "contradiction" lies in your misunderstanding of quantum field theory. Dirac showed in 1928 there is no contradiction.

Wave and Particle are metaphors. The quantum wave and particle can be subsumed under a -single- mathematical model. In short, no contradiction. The "contradiction" lies in your misunderstanding of quantum field theory. Dirac showed in 1928 there is no contradiction.

The original premise was that if something is a particle, it cannot be a wave and vice versa. Experimental evidence has shown that this premise was wrong, even if it seemed obvious according to our intuition. Our intuition isn't always reliable, however. As the premise is wrong, there is no contradiction.

Wave and Particle are metaphors. The quantum wave and particle can be subsumed under a -single- mathematical model. In short, no contradiction. The "contradiction" lies in your misunderstanding of quantum field theory. Dirac showed in 1928 there is no contradiction.

The original premise was that if something is a particle, it cannot be a wave and vice versa. Experimental evidence has shown that this premise was wrong, even if it seemed obvious according to our intuition. Our intuition isn't always reliable, however. As the premise is wrong, there is no contradiction.

I agree, Dragonfly. The problem is (again ) 2-valued logic. It works absolutely in mathematics but only partially in any other language, like physics. Korzybski said "whatever you say something IS, it isn't", so the problem begins when we say "it IS a particle" or "it IS a wave". Speaking about what something IS is a result of applying an epistomology which is about 2000 years old and sadly out of date. There is no need to say what it is, we only need to describe how it behaves, how to measure it's effects, it's structure, etc. This is the goal of science, to create symbolic maps similar in structure to 'reality'.

I agree, Dragonfly. The problem is (again ) 2-valued logic. It works absolutely in mathematics but only partially in any other language, like physics. Korzybski said "whatever you say something IS, it isn't", so the problem begins when we say "it IS a particle" or "it IS a wave". Speaking about what something IS is a result of applying an epistomology which is about 2000 years old and sadly out of date. There is no need to say what it is, we only need to describe how it behaves, how to measure it's effects, it's structure, etc. This is the goal of science, to create symbolic maps similar in structure to 'reality'.

Try again. It goes more like this: I observe a particle-like manifestation of the object or I observe a wave-like manifestation of the object. That intransitive verb "is" is tricky.

~ I understand 'some' of your perplexity, but am perplexed by most. Primarily because of my lack of understanding your main point in your post #169 adjuncting #168 (copied/beamed from "Metaphysics-Schrodinger's Cat..." post #121.)

~ Indeed, I am most perplexed by your quoting (mainly, to what point?) someone, and, it's not clear here as to who said such..."So if quantum logic really is a logic [!?], we should first make it look like a logic[!!??]. Then we will be in a position to discuss whether it really is a logic." Huh?--- At this point, I found further reading...logically speaking...pointless (though I attempted to slough through, and found it...not worthwhile.)

~ Your followup (169) post speaks of "...using the quantum logic I described," but, I can't say you gave a clear and distinct 'description' of such, ergo, I know not (as the previously quoteds) of what you speak, in *your* (nm *their*) use of the term 'logic.'

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## Judith

How is Rand's metaphysics integrally connected to Aristotle's erroneous ideas of cause? Can you document that connection?

Judith

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## John Dailey

Baal:

~ While you're responding to Judith, I'd appreciate a response to my last query also.

LLAP

J:D

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## BaalChatzaf

Not true. To observe means interacting an observing system (which is physical) with the observed system. The outcome will be one of the eigenvalues associated with the Hermitian operator that characterizes the observation and the resulting state will be one of the eigenstates of the operator. You can't get more objective than that. Quantum theory is not only objective, it is the -most accurate- physical theory ever formulated since the beginning of human existence.

Observation is interaction. Interaction is governed by quantum laws. That is how the world works.

Ba'al Chatzaf

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## tjohnson

The problem is that Aristotles's so-called 'laws of thought' do not work in modern science. They work in mathematics and they will remain a valuable tool there but in 'real' life even A=A does not work, since at sub atomic levels everything is in a constant state of change.

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## tjohnson

No, I'm referring to uncertainty principles. In our attempt to observe something we alter it and so this blurs the line between observer and observed. This does not, however, invalidate determinism, it mean we must adopt a different kind of 00-valued, probabilistic determinism, which is what QM does.

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## BaalChatzaf

All observation is interaction between an observing system and an observed system and even there the boundary is not always a Bright Line. What is observed perceptually is the outcome of the interaction. But all participating physical systems exist, and the observation has a definite spectrum of eigenstates and eigenvalues. When the interaction settles down, the value observed will be one of the eigenvalues and the state the observed system is in will be one of the eigenstates.

And yes, there is a probability associated with each outcome. It is not statistical probability, it is probability defined in terms of super-posed quantum state the observed system is in when the observation is made (i.e. when the Hermitian Operator corresponding to the observation is applied to the composite vector representing the state of the observed object.

As to the appropriate logic for resolving the well known dualities a non-distributive non-boolean logic has been suggested. See -Interpreting the Quantum World- by Jeffrey Bub (Cambridge University Press).

Ba'al Chatzaf

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## Michael Stuart Kelly

Guys,

I hate to be obvious (not really—philosophy is the art of the obvious), but would any of this kind of method of thinking do you any good if a tiger were after you? Would you have a "quantum perceptual interaction" with it to figure out if it really exists on its own and is all there anyway? Or would you run like hell?

I have yet to see any of this kind of thinking account for the existence of entities.

Michael

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## BaalChatzaf

Aristotle's physics (as we have received it) was wrong and it was wrong because -he did not check his conclusions against facts-. Ayn Rand advised (on several occasions) that one ought to check his premises. Too bad Aristotle did not follow that advice.

Failure to check is a major fault.

Ba'al Chatzaf

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## BaalChatzaf

However the law of non-contradiction does hold. Now and forever.

Ba'al Chatzaf

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## Michael Stuart Kelly

Bob,

Oh my God!

Is that positively true?

Michael

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## Judith

Today's physical theories were arrived at by following the math. The investigators got to bizarre conclusions that seemed inconceivable to them, but empirical experimentation supported the conclusions. I don't see how it's possible for something to apply in math but not in "reality".

We know what we know about the subatomic world based on mathematics and observation. We know about the changes, and the changes follow certain laws. A quark doesn't randomly turn into a water molecule which then turns into a chicken. Within the world of those laws, A is A.

Judith

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## tjohnson

Physics is

appliedmath, not mathematics. If 'reality' obeyed the laws of mathematics we would never have to adjust our theories since each law would be true forever, but this is not the case. In physics, we cannot define the objects perfectly as we can in mathematics and so there will always be new information and so adjustments. So mathematicsdoesapply to reality, but only in a limited fashion. Objectivism (personification) seems to want to take Aristotle's simple rules of logic and apply them to 21st century life on earth, well, good luck with that!## Link to comment

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## tjohnson

Is that the one that states that something can both be and not be something? Like something can not be a wave AND a particle? Oh wait, yes it can!

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## BaalChatzaf

Classical logic is what most mathematicians use in their work. Even as we speak.

You have made another error. The conclusions of applied mathematics are true a priori based on certain -mathematical- assumptions (as opposed to assumptions about the world), regardless of how they are interpreted in real world applications. Physics on the other hand is based on hypotheses and postulates that are not a priori true. For example, the second law of thermodynamics. This law does not follow from any logical postulate. It is assumed because it seems to be true in all cases observed. That is no guarantee of it general truth. That is the difference between a hypothesis (something assumed) and an a priori necessary statement.

Ba'al Chatzaf

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## tjohnson

Yes, this is what I have been saying in this and another thread, logic works perfectly in mathematics but not in 'real' life. If you try and apply logic in a strict manner to 'real' life you are doomed to failure. When was the last time you used a syllogism to make a decision?

[premise1] I like cheese

[premise2] This is cheese

[conclusion] I like this cheese

(he then eats it and finds that he hates blue cheese) Damn this logic!

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## BaalChatzaf

"I like cheese" means he likes any kind of cheese (since there was no limitation or qualification in the sentence). He finds he does not like blue cheese. Ergo premise 1 is false. Do you know what a universally quantified proposition is? Apparently not.

Sloppy thinking could be bad for your health. Consider that.

Ba'al Chatzaf

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## Guyau

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## Guyau

I would like to add some further thought to my old remarks quoted in the preceding post.

It is possible, for all I know at this time, that the mathematics required for quantum theory can be rederived using the quantum logic I described. If that proved not possible, then the quantum logic would not do as a revised general logic. If such a rederivation of the necessary mathematics

wereexecuted, there would be the further question of whether other interpretations of quantum mechanics---say the transactional interpretation or sum-over-histories interpretations---were superior to an interpretation requiring a revision of general logic.So I don't mean to give the impression that revisions and improvements in the discipline that is logic are not possible. It should be noticed, however, that adoption of the quantum logic as more fundamental than our classical logic would not require any loosening of the law of non-contradiction. Rand's conception of logic as the art of non-contradictory identification would still stand.

In the collection

The Law of Non-Contradictionedited by Priest, Beall, and Armour-Garb (Oxford 2004), I recommend especially the following:"What is a Contradiction?" by Patrick Grim

"In Defense of the Law of Non-Contradiction" by Edward Zalta

~~~~

Greg and Bob,

I haven't forgotten the promise over on the Analytic-Synthetic thread. Will deliver shortly.

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## Guyau

Some more, this from Michael Friedman in

Dynamics of Reason(CSLI 2001):## Link to comment

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## BaalChatzaf

Wave and Particle are metaphors. The quantum wave and particle can be subsumed under a -single- mathematical model. In short, no contradiction. The "contradiction" lies in your misunderstanding of quantum field theory. Dirac showed in 1928 there is no contradiction.

Ba'al Chatzaf

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## Dragonfly

The original premise was that if something is a particle, it cannot be a wave and vice versa. Experimental evidence has shown that this premise was wrong, even if it seemed obvious according to our intuition. Our intuition isn't always reliable, however. As the premise is wrong, there is no contradiction.

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## tjohnson

I agree, Dragonfly. The problem is (again ) 2-valued logic. It works absolutely in mathematics but only partially in any other language, like physics. Korzybski said "whatever you say something IS, it isn't", so the problem begins when we say "it IS a particle" or "it IS a wave". Speaking about what something IS is a result of applying an epistomology which is about 2000 years old and sadly out of date. There is no need to say what it is, we only need to describe how it behaves, how to measure it's effects, it's structure, etc. This is the goal of science, to create symbolic maps similar in structure to 'reality'.

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## BaalChatzaf

Try again. It goes more like this: I observe a particle-like manifestation of the object or I observe a wave-like manifestation of the object. That intransitive verb "is" is tricky.

Ba'al Chatzaf

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## John Dailey

Stephen:

~ I understand 'some' of your perplexity, but am perplexed by most. Primarily because of my lack of understanding your main point in your post #169 adjuncting #168 (copied/beamed from "Metaphysics-Schrodinger's Cat..." post #121.)

~ Indeed, I am most perplexed by your quoting (mainly, to what point?) someone, and, it's not clear here as to who said such..."So if quantum logic really is a logic [!?], we should first make it look like a logic[!!??]. Then we will be in a position to discuss whether it really is a logic." Huh?--- At this point, I found further reading...logically speaking...pointless (though I attempted to slough through, and found it...not worthwhile.)

~ Your followup (169) post speaks of "...using the quantum logic I described," but, I can't say you gave a clear and distinct 'description' of such, ergo, I know not (as the previously quoteds) of what you speak, in *your* (nm *their*) use of the term 'logic.'

LLAP

J:D

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