The Instigator
shakuntala
Pro (for)
Losing
10 Points
The Contender
nordmarj
Con (against)
Winning
13 Points

Irrationality is no hindrance for something being true

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Post Voting Period
The voting period for this debate has ended.
after 5 votes the winner is...
nordmarj
Voting Style: Open Point System: 7 Point
Started: 7/12/2013 Category: Science
Updated: 3 years ago Status: Post Voting Period
Viewed: 1,780 times Debate No: 35546
Debate Rounds (3)
Comments (21)
Votes (5)

 

shakuntala

Pro

This scholar points out Irrationality is no hindrance for something being true

http://www.scribd.com...

I will give one mathematics and one science example

Mathematics

For 100 years after its invention calculus was shown to be irrational ie contradictory but it still worked if working is a sign of being true then Irrationality is no hindrance for something being true

""Newton and Leibniz developed the calculus". Their ideas were attacked for being full of paradoxes." Newton"s formulation of calculus was self-contradictory yet it worked. Newton worked with small increments going of to a zero limit. Berkeley showed that this leads to logical inconsistency. The main problem Bunch notes was "that a quantity was very close to zero, but not zero, during the first part of the operation then it became zero at the end." B, Bunch , Mathematical Fallacies and Paradoxes Dover, 1982, p.192. "instead of having demonstrations justify results, results were used to justify demonstrations.I. Gratten-Guinness, From the Calculus to set theory 1630-1910, Duckworth, 1980, p.296.

Science

Now even though quantum mechanics no experiment has contradicted quantum theory predictions and quantum theory is the most successful that has ever existed in science.

but quantum mechanics is irrational yet it works
again
if working is a sign of being true then Irrationality is no hindrance for something being true

"Wick state the orthodox view when he says ", ...The belief concealed is that Nature has been found in a contradiction. But quantum physicists are not simpletons. In their hearts they know such a claim is philosophically unacceptable and would be rejected in other sciences."
Wick notes " I believe orthodox quantum theorists [slates] reason, ... The microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it." A. Wick, The Infamous Boundary, Birkhauser, Berlin, 1995, p.184
nordmarj

Con

Hello. I accept the challenge and look forward to debating this topic with you. I am Con and thus i will argue that the proposition "Irrationality is no hindrance for something being true" is wrong. Specifically, i interpret the proposition to mean that a proposition and its negation can both be true at the same time. My argument then will make the case that any proposition must be either true or false but not both true and false. This is generally taken as an axiom and thus cannot be proven, so I will make some quite informal statements to begin with then let Pro choose which level he wishes to debate on, either specific axamples or general motivations for accepting or refuting the axiom of noncontradiction.

The examples given in the opening argument and in the text linked to are very vague and some of them seem to be based on misconceptions. Quantum mechanics, which I will assume refers to the standard model, is not known to be either consistent or inconsistent. It is however widely believed to be internally consistent. It is in certain conditions (where both GR and QFT effects are non-negligible simultaneously) inconsistent with general relativity, but their respective domains of validity have been restricted precisely because of the contradiction. That is the reason it is said that neither theory has the correct description of the phenomena where they contradict each other. Then, what if we where to ignore the contradiction? Well, we would have two different descriptions of a single underlying reality. When we measure the true values of whatever physical observable we choose to model, it would probably differ from both the calculated values.

In general, the fact that a theory gives correct results in any finite number of cases does not excuse a contradiction, because if there is a contradiction there will be cases where the theory does not work to predict reality. It will be possible to make a lot of statements contradicting the observed reality that the theory was supposed to describe, if one finds and exploits a contradiction.

The impossibility of contradiction is embedded in the very concepts of truth and falsehood. Although there are nonclassical logics that allow other truthvalues than these, the ones that are actually useful tend to have some form of law of noncontradiction.

I find the statements on mathematics in Deans text to be examples of a widespread postmodernist misconception, probably related to Gödels incompleteness theorems. I will not go into more detail about that here unless my opponent wishes to do so. A collection of patient explanations of why postmodern relativist statements on the contradictions of science are gibberish is given in Alan Sokals and Jean Bricmonts book Fashionable nonsense which seems to be freely available here: http://emilkirkegaard.dk...

There are also books on misuse of Gödel specifically since that is very widespread but i will leave that topic for now.

I have assumed the existence of one underlying reality since communication between different subjective minds would be impossible otherwise. I believe that the core of the debate actually lies here.

GR = General Relativity
QFT = Quantum Field Theory / Standard Model
Debate Round No. 1
shakuntala

Pro

you say
", ...I will make some quite informal statements to begin with then let Pro choose which level he wishes to debate on,

The examples given in the opening argument and in the text linked to are very vague and some of them seem to be based on misconceptions. Quantum mechanics, which I will assume refers to the standard model, is not known to be either consistent or inconsistent. "

", ...I will make some quite informal statements to begin with then let Pro choose which level he wishes to debate on, "

all I have to do is what I have done that is to show at least one or two examples of Irrationality being no hindrance for something being true

i gave an example from mathematics which showed calculus was irrational at its conception
but produced results

""Newton and Leibniz developed the calculus". Their ideas were attacked for being full of paradoxes." Newton"s formulation of calculus was self-contradictory yet it worked. Newton worked with small increments going of to a zero limit. Berkeley showed that this leads to logical inconsistency. The main problem Bunch notes was "that a quantity was very close to zero, but not zero, during the first part of the operation then it became zero at the end." B, Bunch , Mathematical Fallacies and Paradoxes Dover, 1982, p.192"

I gave statements from scientist that quantum mechanics is irrational but produces results
thus Irrationality being no hindrance for something being true

Wick notes " I believe orthodox quantum theorists [slates] reason, ... The microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it." A. Wick, The Infamous Boundary, Birkhauser, Berlin, 1995, p.184"

note a whole book has been written on irrationality in quantum mechanics
F. Selleri, Quantum Paradoxes and Physical Reality, Kluer Academic Publishers, 1990

one clear example is the dual nature of light ie both wave and particle
to which
Heisenberg notes that " the strangest experience of those years was that the paradoxes of quantum theory did not disappear during this process of clarification; on the contrary they have become even more marked and exciting."F. Selleri, Quantum Paradoxes and Physical Reality, Kluer Academic Publishers, 1990, p.v111

that is all I have to do
what you have to do is argue those example are wrong

so go ahead
nordmarj

Con

"For 100 years after its invention calculus was shown to be irrational ie contradictory but it still worked if working is a sign of being true then Irrationality is no hindrance for something being true"

Bishop Berkeleys allegations are disputed and several modern mathematicians consider the formulation of Leibniz to be free of contradiction[1], but that really doesn't matter. Even if a mathematical theory seems to produce true results, it obeys aristotelian logic. In aristotelian logic contradictions always imply that the theory can prove any statement. If one could find an explicit contradiction then one could use it to prove that the true results obtained are actually false, or vice versa. Then the theory fails to be useful. The proof that one contradiction implies that all statements are true is quite simple:

1: assume A AND NOT A
then
2: A
and
3: NOT A
then introduce an arbitrary statement B, and make a disjunction introduction
4: A OR B
but from (3), A is false so B must be true, by (4):
5: B
then we have seen that the assumption that bot A and NOT A are true, implies ANY statement!

Applied to calculus, this means it is possible to prove any result, not just the correct ones.

"I gave statements from scientist that quantum mechanics is irrational but produces results
thus Irrationality being no hindrance for something being true"

There are two widespread meanings of the word paradox. One is the logical definition, that incompatible statements are true simultaneously. But another one commonly used is to call results that are incompatible with intuition paradoxes, sometimes referred to as apparent paradoxes. It is in this sense the word is used in the twin paradox [2] for instance. It is not a logical paradox, just an unintuitive result. The same applies to most uses of the word paradox by scientists, since a theory containing an actual logical paradox would be considered worthless by them and there is thus not much said about such theories.

Your citations about quantum mechanics do not exactly specify which paradoxes they are talking about. The specific example you mention is:

"one clear example is the dual nature of light ie both wave and particle"

This is not a logical paradox, it is a result that contradicts intuition. The duality disappears in a rigorous mathematical formalism, where particles are replaced by wave packets or excitations of fields. The information on both wavelike and particlelike properties is encoded in the wavefunction even in early quantum mechanics. Even in a less rigorous formalism, the wave- and particle interpretations are used for studying different aspects of a phenomenon and are thus not really contradicting each other. When postmodern thinkers cite scientists they usually do not differentiate between logical paradoxes and paradoxes in the sense of nonintuitive results.

Also mentioned in the text by Dean is superposition. But this is again only an intuitive paradox. Superpositions of states is a mathematical construct used to predict the world, they can never be directly observed and thus no contradiction with measurements arise. As mathematical objects, they follow all laws of mathematics. Schrödingers cat will always be observed as either dead or alive, not both. The superposition is only a mathematical construct to calculate the probabilities of the two outcomes.

[1] http://arxiv.org...
[2] http://en.wikipedia.org...
Debate Round No. 2
shakuntala

Pro

you say

"Bishop Berkeleys allegations are disputed and several modern mathematicians consider the formulation of Leibniz to be free of contradiction[1], but that really doesn't matter Even if a mathematical theory seems to produce true results, it obeys aristotelian logic. "

your reference flys in the face of orthodox consensus on the issue
as your reference points out

"Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning"

facts is Bunch agrees Berkeley was correct so does I. Gratten-Guinness

Newton and Leibniz developed the calculus". Their ideas were attacked for being full of paradoxes." Newton"s formulation of calculus was self-contradictory ." B, Bunch , Mathematical Fallacies and Paradoxes Dover, 1982, p.192.

"instead of having demonstrations justify results, results were used to justify demonstrations.I. Gratten-Guinness, From the Calculus to set theory 1630-1910, Duckworth, 1980, p.296.

"Even if a mathematical theory seems to produce true results, it obeys aristotelian logic. "

yes it does but the early formulation of calculus violates the law of non-contradiction
"Newton"s formulation of calculus was self-contradictory yet it worked

"one clear example is the dual nature of light ie both wave and particle"

This is not a logical paradox, it is a result that contradicts intuition."

wrong to say a thing is both a wave at the same time it is a particle violates Aristotelian logic
law of excluded middle and it is a contradiction

quote from wiki which agrees it is a paradox

http://en.wikipedia.org...
"Wave"particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects. Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe,"

note it says
"Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe"

again
"Wave"particle duality is an ongoing conundrum in modern physics. Most physicists accept wave-particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy. Alternative views are also presented here. These views are not generally accepted by mainstream physics, but serve as a basis for valuable discussion within the community."

note it says "Most physicists accept wave-particle duality "

you say
"There are two widespread meanings of the word paradox. One is the logical definition, that incompatible statements are true simultaneously"

thus proving my point a thing is simultaneously a wave and particle- paradox irrationality

again
you say

"The duality disappears in a rigorous mathematical formalism, where particles are replaced by wave packets or excitations of fields

that is an alternative view

http://en.wikipedia.org...
"At least one scientist proposes that the duality can be replaced by a "wave-only" view. In his book Collective Electrodynamics: Quantum Foundations of Electromagnetism (2000), Carver Mead"

but as the wiki entry above stated

"Alternative views are also presented here. These views are not generally accepted by mainstream physics,"
but

"Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe"

you say
"Your citations about quantum mechanics do not exactly specify which paradoxes"

nevertheless there is a whole book written on the irrationality of GM "F. Selleri, Quantum Paradoxes and Physical Reality, Kluer Academic Publishers, 1990,

and wick even states the orthodox view
"Wick notes " I believe orthodox quantum theorists [slates] reason, ... The microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it." A. Wick, The Infamous Boundary, Birkhauser, Berlin, 1995, p.184"

I have backed up my question with quote from books and scientists and mathematicians who point out the irrationality of mathematics and science
con has given sources but it can also back up my claim- on mathematics

con gives an alternative view in physics denying wave-particle duality-paradox but as shown this view is not accepted by the majority of physicists

thus I have given evidence about irrationality in mathematics evidence from the orthodox view -con gives a reference which can back up my claim about calculus being irrational

i gave evidence about irrationality in quantum mechanics -the orthodox view
con gives an alternative view but as shown this alternative view is not accepted by most physicists

so I win
as con has not adequatfuted my claims
nordmarj

Con

"yes it does but the early formulation of calculus violates the law of non-contradiction
"Newton"s formulation of calculus was self-contradictory yet it worked."

I have shown you why it actuay doesn't, which is the widely accepted reason for demanding noncontradiction. While the theory can produce true results, the presence of a contradiction mes it can actually prove any result, including wrong ones. This has been known for millenia and I gave you the proof which is included in any basic course on formal logic.

"wrong to say a thing is both a wave at the same time it is a particle violates Aristotelian logic
law of excluded middle and it is a contradiction"

No, it is not a logical contradiction but an apparent contradiction, i.e. it contradicts intuition. The claim of quantum mechanics is that certain properties of the particle are best described as wavelike while others are described as particlelike. In quantum field theory there is one unified description that deals only with fields. Apparent paradoxes is what is usually meant when scientists talk of paradoxes.

"thus proving my point a thing is simultaneously a wave and particle- paradox irrationality"

An apparent paradox is not irrational, it does not break the laws of logic. particle-wave-duality is not a logical paradox. Neither do physicists in general claim that their theories as such are real, only that they are true in the sense of giving correct prediction of the observable results they produce. Instrumentalism is the most widespread view of science in modern physics, since Einstein.

"I have backed up my question with quote from books and scientists and mathematicians who point out the irrationality of mathematics and science
con has given sources but it can also back up my claim- on mathematics"

Your quotes do not specify whether the contradictions are apparent or logical. Neither do you seem to acknowledge that apparent paradoxes are not in any way irrational.

"con gives an alternative view in physics denying wave-particle duality-paradox but as shown this view is not accepted by the majority of physicists"

It is widely accepted that quantum field theory (modern QM that is) has rendered the duality irrelevant by a more stringent mathematical formalism (still QFT is not really mathematically rigorous, but widely believed to be internally consistent). In classical QM the duality is not a logical but an apparent contradiction. The underlying theory is described by a wavefunction evolving a described by the Schrödinger equation. This theory is not contradicting itself. Only when translating it into natural (or classic mechanical) language an apparent contradiction appears.


Debate Round No. 3
21 comments have been posted on this debate. Showing 1 through 10 records.
Posted by nordmarj 3 years ago
nordmarj
As suggested by the latest vote, it might be a good idea to take this to the forum for a more public discussion.
Posted by shakuntala 3 years ago
shakuntala
you are just completely unable to see deans point

con says
"You might be confusing irrationality with counterintuitivity."
no
when calculus was invented it was irrational[ Robinson even admits that and you have as well] but it was taken to be true so at the time Irrationality was no hindrance for calculus taken to be true
later on a reformulation was done to make it consistent

con says
"There is nothing making wave-nature and particle-nature inconsistent except human prejudice: "

wrong it is a contradiction in Aristotelian logic
as most physicists agree

it is a real paradox of nature- not an apparent one

you seem to think dean is saying mathematics and QM are irrational -he is not saying that here
what he is saying that based on the mathematics physicists say nature is a paradox ie irrational -but dean is not saying QM is not true

he is saying that even though QM says nature is irrational this no hindrance for QM being true
Posted by nordmarj 3 years ago
nordmarj
You might be confusing irrationality with counterintuitivity.
Posted by nordmarj 3 years ago
nordmarj
"what he is saying is quantum theory comes up with a paradox in describing nature"

How is it a paradox? It is not a paradox in the logical sense of the word. It is only contrary to intuition. You do not to specify how you use the word paradox. I assume you wish to prove there is a logical paradox, but now you say something different. There is nothing making wave-nature and particle-nature inconsistent except human prejudice: we are not used to the microsocpic world. But no logical inconsistency arises just because macroscopic concepts are not applicable.
Posted by shakuntala 3 years ago
shakuntala
con says
"i suggest you take it up with those physicists who say the wave-particle is a paradox -not apparent but real because it violates Aristotelian logic as law of excluded middle and non- contradiction"

As I have said, it is an apparent paradox. It only contradicts intuition, the paradox is not logical. That both natures of particles are physically true at the same time does not make it contradictory. One does not arrive at contradictory results when applying the theory. Physicists speak of apparent paradoxes as well as logical ones and those two concepts cannot be interchanged freely as you are doing."

"As I have said, it is an apparent paradox. "

wrong it is a real property of nature- not apparent
"Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe"

"That both natures of particles are physically true at the same time does not make it contradictory.

point 1
we are not talking about particles
we are talking about a "thing" that is both a particle and wave simultaneously

and
based on Aristotelian logic that makes it contradictory as physicists agree on
"Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe" not apparent but real

"One does not arrive at contradictory results when applying the theory."

thats not the point
dean is not talking about the mathematics being irrational-you cant seem to see this
what he is saying is quantum theory comes up with a paradox in describing nature
".... in the best theory describing it."quantum theory says nature is a wave-particle duality -and thus nature is a paradox

but this paradox-irrationality- does not hinder QM from being true
you are not able to see what dean is saying

"Wick says he microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it." A. Wick, The Infamous Boundary, Birkhauser, Berlin, 1995, p.184"
Posted by nordmarj 3 years ago
nordmarj
"i suggest you take it up with those physicists who say the wave-particle is a paradox -not apparent but real because it violates Aristotelian logic as law of excluded middle and non- contradiction"

As I have said, it is an apparent paradox. It only contradicts intuition, the paradox is not logical. That both natures of particles are physically true at the same time does not make it contradictory. One does not arrive at contradictory results when applying the theory. Physicists speak of apparent paradoxes as well as logical ones and those two concepts cannot be interchanged freely as you are doing.
Posted by shakuntala 3 years ago
shakuntala
con says
""you dont know your logic you have stated the law of non-contradiction
law of excluded middle is about it must be either A or NOT A only one"

Yes, that is correct. However it doesn't matter since wave is not the negation of particle so there is no violaion of either law"

"wave is not the negation of particle"

rather than get into Aristotelian logic has 3 laws law of identity law of excluded middle and law of non-contradiction

i suggest you take it up with those physicists who say the wave-particle is a paradox -not apparent but real because it violates Aristotelian logic as law of excluded middle and non- contradiction

and people like Wick
Wick notes " I believe orthodox quantum theorists [slates] reason, ... The microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it." A. Wick, The Infamous Boundary, Birkhauser, Berlin, 1995, p.184
Posted by nordmarj 3 years ago
nordmarj
"look it is clear at first calculus was irrational but worked"

No. It does not work since the presence of a contradiction makes it prove any statement. It's as simple as that.
Posted by nordmarj 3 years ago
nordmarj
"you dont know your logic you have stated the law of non-contradiction
law of excluded middle is about it must be either A or NOT A only one"

Yes, that is correct. However it doesn't matter since wave is not the negation of particle so there is no violaion of either law.
Posted by shakuntala 3 years ago
shakuntala
con says
""you admit at first calculus was irrational that is all dean is pointing out
so at the time it worked so they used it
thus
pointing out deans claim
Irrationality is no hindrance for something being true"

I have shown that a inconsistent theory does not work"

look it is clear at first calculus was irrational but worked-you admitt that
thus at the time Irrationality is no hindrance for something being true
that is deans point
what happens later is no concern for this point

you go on about it having to have been consistent fine
but again at the time it irrational -that is the point of dean

you say
"No, nothing is being sidetracked. The nature of contradiction is the heart of the debate. The law of the excluded middle is: "There cannot be a statement A for which it hols that A AND NOT A is true". But the wave nature is not the negation of the particle nature. Thus it has nothing at all to do with the law of excluded middle."

The law of the excluded middle is: "There cannot be a statement A for which it hols that A AND NOT A is true"

you dont know your logic you have stated the law of non-contradiction
law of excluded middle is about it must be either A or NOT A only one

""There cannot be a statement A for which it hols that A AND NOT A is true
a thing is a wave A and a particle NOT A
thus violating law of non-contradiction

my point is physicist agree it is a paradox because it violates Aristotelian logic

yo
but then they reformulated it to make it consistent
5 votes have been placed for this debate. Showing 1 through 5 records.
Vote Placed by johnlubba 3 years ago
johnlubba
shakuntalanordmarjTied
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Reasons for voting decision: Counter inductiveknowlde's invalid RFD.
Vote Placed by Inductivelogic 3 years ago
Inductivelogic
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Reasons for voting decision: the only thing I can really judge this by is that Con had better grammar and structure.
Vote Placed by Ragnar 3 years ago
Ragnar
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Reasons for voting decision: CVB ModusTollens: Sources not explained. Spelling & Grammar not explained. Also we refrain from voting for the comments section, as much as they probably should take that to the forums (it scares off voters, heck I probably would have voted for con, instead I was going to turn away before I spotted this votebomb).
Vote Placed by ModusTollens 3 years ago
ModusTollens
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Total points awarded:07 
Reasons for voting decision: Pro had no clue what paradoxes actually are, or what they mean in logical terms. Con explained this misunderstanding very clearly, yet Pro kept asserting s/he was right. Conduct to Con b/c Pro continued the debate in the comments.
Vote Placed by rross 3 years ago
rross
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Reasons for voting decision: What an interesting topic. By the end, though, I was still confused about what Pro means exactly by "irrational", and I agree with Con that Pro failed to prove that apparent paradoxes are irrational. But I I think Pro's original idea is very interesting. I'd love to see it argued out more.