When reality contradicts logic and reason

[Magical Realist]

What does science do when the math dictates illogical states? What does it do when the empiricle evidence defies the rational? For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical? Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? Where would the hope of understanding lie THEN?

 

[river]

What does science do when the math dictates illogical states? What does it do when the empiricle evidence defies the rational? For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical? Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? Where would the hope of understanding lie THEN?

By being far more open minded than we are nowadays

 

[river]

Mainstream science is caught between the paradox of wanting to investigate a particular ology , out of natural curiosity , and the ridicule of doing so and the funding to be able to do so

It more than unfortunate , it is a crime really

Knowledge not gained , right or wrong is huge , for Humanity

 

[spidergoat]

It's not illogical, it just points to the incomplete nature of our understanding.

 

[river]

It's not illogical, it just points to the incomplete nature of our understanding.

Agreed

But in order to do so requires an opening of minds , and truth as well

 

[C C]

[...] What does it do when the empiricle evidence defies the rational? [...] Do we accept it as true even though it is illogical?

No problem for the raw, actual process of science itself, as Simanek elaborates below. Individual scientists, OTH, might personally / privately favor particular schools of philosophical thought outputted over the history of PoS, that fixate with "proper formal accounts" of research activity and method which might differ somewhat from this. But the "concrete" work proceeds in its more loose manner.

Donald Simanek: The bottom line is that logic alone can tell us nothing new about the real world. Ditto for mathematics, as Albert Einstein observed: "Insofar as mathematics is exact, it does not apply to reality; and insofar as mathematics applies to reality, it is not exact."
[...]
Scientists do not arrive at models and theories by application of logic. They arrive at them by many processes lumped under the name 'induction'. Induction cannot be reduced to a set of logical rules (though many have tried). To see patterns (sometimes subtle and hidden ones) in data and observations requires creative ability. This is the ability to think ahead and say, "What model, set of statements (laws) or theoretical construct could I devise from which these observations and data might be deduced?"

We can't find, discover, or construct scientific laws and theories by mathematics and logic alone. But we can derive testable and useful results by application of mathematics and logic to laws and theories, and if those deduced results pass experimental tests, our confidence in the validity of the theory from which they were derived is strengthened.

In this context, logic and mathematics are reliable and essential tools. Outside of this context they are instruments of error and self-delusion. Whenever you hear a politician, theologian or evangelist casting verbal arguments in the trappings of logic, you can be pretty sure that person is talking moonshine.
[...]
Scientists speak in a language that uses everyday colloquial words with specialized (and often different) meanings. When a scientist says something has been found to be 'true', what is meant isn't any form of absolute truth. Likewise scientists' use of 'reality' and 'belief' don't imply finality or dogmatism. But if we inquire whether a scientist believes in an underlying reality behind our sense impressions, we are compounding two tricky words into a philosophical question for which we have no way to arrive at a testable answer. I'd be inclined to dismiss the entire question as meaningless, and not waste time discussing it, or any other such questions. Yet a few scientists and philosophers disagree, and wax eloquent in writing and speaking about such questions.

The notion that we can find absolute and final truths is naive, but still appealing to many people, especially non-scientists. If there are any underlying "truths" of nature, our models are at best only close approximations to them—useful descriptions that "work" by correctly predicting nature's behavior. We are not in a position to answer the philosophical question "Are there any absolute truths?" We can't determine whether there is an underlying "reality" to be discovered. And, though our laws and models (theories) become better and better, we have no reason to expect they will ever be perfect. So we have no justification for absolute faith or belief in any of them. They may be replaced someday by something quite different in concept. At least they will be modified. But that won't make the old models "untrue". All this reservation and qualification about truth, reality, and belief, doesn't matter. It isn't relevant to doing science. We can do science quite well without 'answering' these questions, questions that may not have any answers. Science limits itself to more finite questions for which we can arrive at practical answers. --Uses and Misuses of Logic [in regard to science]

Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? [...]

This cuts to the matter of contradiction (illogical). Whereas the non-philosophical scientist may not expect or pre-conditionally anticipate the empirical, natural realm to perfectly conform to the demands of correct, formal human thinking... her more a priori / law-abiding or "nomological realist" counterparts may at best only confine allowance of such (deviation from coherence) to the possibility of the "Absolute or transcendent" as referenced below. At any rate, it is descriptions of the world that are amenable to being judged by bivalent or two-value systems (the former just "is and does" as it "is and does", regardless of interpretations).

Approaches of reason that are putatively "inconsistency-tolerating"...

Laurence R. Horn: Beyond the Western canon, the brunt of the battle over LNC [Law of Non-Contradiction] has been largely borne by the Buddhists, particularly in the exposition by Nagarjuna of the catuṣkoṭi or tetralemma, also known as the four-cornered or fourfold negation. Consider the following four possible truth outcomes for any statement and its (apparent) contradictory:

(1) S is P
(2) S is not P
(3) S is both P and not-P
(4) S is neither P nor not-P

For instances of the positive tetralemma, on Nagarjuna's account, all four statement types can or must be accepted:

"Everything is real and not real.
Both real and not real.
Neither real nor not real.
That is Lord Buddha's teaching."

Such cases arise only when we are beyond the realm to which ordinary logic applies, when “the sphere of thought has ceased.” On the other hand, much more use is made of the negative tetralemma, in which all four of the statements in can or must be rejected. Is this tantamount, as it appears, to the renunciation of LEM [Law of Excluded Middle] and LNC, the countenancing of both gaps and gluts, and thus--in Aristotle's view--the overthrow of all bounds of rational argument?

It should first be noted that the axiomatic status of LNC and LEM is as well-established within the logical traditions of India as it is for the Greeks and their epigones. Garfield (1995) and Tillemans (1999) convincingly refute the claim that Nagarjuna was simply an “irrationalist”. In the first place, if Nagarjuna simply rejected LNC, there would be no possibility of reductio arguments, which hinge on the establishment of untenable contradictions, yet such arguments are standardly employed in his logic. In fact, he explicitly prohibits virodha (contradiction). Crucially, it is only in the realm of the Absolute or Transcendent, where we are contemplating the nature of the ultimate, that contradictions are embraced; in the realm of ordinary reality, LNC operates and classical logic holds. (Recall Freud's dichotomy between the LNC-observant conscious mind and the LNC-free unconscious.) In this sense, the logic of Nagarjuna and of the Buddhist tradition more generally can be seen not as inconsistent but paraconsistent. Indeed, just as Aristotle ridiculed LNC-skeptical sophists as no better than vegetables, the Buddhists dismissed the arch-skeptic Sanjaya and his followers, who refused to commit themselves to a definite position on any issue, as “eel-wrigglers” (amaravikkhepa). Sanjaya himself was notorious for his periodic lapses into the extended silence Aristotle described as the last refuge of the LNC-skeptic. --Contradiction; SEP

 

[Baldeee]

What does science do when the math dictates illogical states?

It doesn't, if the maths is correct.
All it means is that our understanding is flawed / incomplete, or that the maths, while correct, is improperly being applied.

What does it do when the empiricle evidence defies the rational? For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical?

I think your understanding of what it is to be logical or not is flawed.
Just because we accept or consider something to be logical does not make it so, especially in light of new evidence.
Logic leads one from propositions to conclusions.
If the conclusion appears counter-intuitive, as in your example, it remains logically valid if the propositions are valid.
If new evidence is unearthed that put the validity of the existing propositions in doubt then they can no longer be held to be valid, and thus previous conclusions are no longer valid.
And our understanding of what we are observing changes.
[/Quote]Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? Where would the hope of understanding lie THEN?[/QUOTE]Reality conforms only to itself.
Hopefully our reason conforms to reality, through sound logic applied to valid propositions.
Where the two differ will either be in the soundness of the logic, or in the validity of the propositions.
But since reality provides the validity to any proposition, any understanding that deviates from reality can not be considered valid, and so our understanding needs to change.

 

[Pete]

What does science do when the math dictates illogical states? What does it do when the empiricle evidence defies the rational? For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical? Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? Where would the hope of understanding lie THEN?

"Unintuitive" does not mean "illogical" or "irrational"

 

[LaurieAG]

What does science do when the math dictates illogical states? What does it do when the empiricle evidence defies the rational? For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical? Does this mean that reality may not necessarily even conform to our reason or logic?

Light paths from rotating galactic sources can be captured as points in the discrete instance of the observation while their paths can also be waves that exist in real time between the rotating sources and the observer.

The only questions of logic and reason that comes into play are assumptions about gravity curving light paths as opposed to the gravity required to keep sources rotating around fixed galactic centers causing the light paths being emitted in straight lines from the sources, as they rotate and flow directly to the relatively stationary observer, being physically curved in the real time it takes them to go from source to observer.

 

[Magical Realist]

The Problem of Induction:

"The original problem of induction can be simply put. It concerns the support or justification of inductive methods; methods that predict or infer, in Hume's words, that “instances of which we have had no experience resemble those of which we have had experience” (THN, 89). Such methods are clearly essential in scientific reasoning as well as in the conduct of our everyday affairs. The problem is how to support or justify them and it leads to a dilemma: the principle cannot be proved deductively, for it is contingent, and only necessary truths can be proved deductively. Nor can it be supported inductively—by arguing that it has always or usually been reliable in the past—for that would beg the question by assuming just what is to be proved.

A century after Hume first put the problem, and argued that it is insoluble, J. S. Mill gave a more specific formulation of an important class of inductive problems: “Why,” he wrote, “is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a little way towards establishing an universal proposition?” (Mill 1843, Bk III, Ch. III). (Compare: (i) Everyone seated on the bus is moving northward. (ii) Everyone seated on the bus was born on a prime numbered day of the month.)

In recent times inductive methods have fissioned and multiplied, to an extent that attempting to define induction would be more difficult than rewarding. It is however instructive to contrast induction with deduction: Deductive logic, at least as concerns first-order logic, is demonstrably complete. The premises of an argument constructed according to the rules of this logic imply the argument's conclusion. Not so for induction: There is no comprehensive theory of sound induction, no set of agreed upon rules that license good or sound inductive inference, nor is there a serious prospect of such a theory. Further, induction differs from deductive proof or demonstration (in first-order logic, at least) not only in induction's failure to preserve truth (true premises may lead inductively to false conclusions) but also in failing of monotonicity: adding true premises to a sound induction may make it unsound."----http://plato.stanford.edu/entries/induction-problem/

 

[leopold]

What does science do when the math dictates illogical states?

most probably re-evaluate the assumptions made.

What does it do when the empiricle evidence defies the rational? For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical?

we MUST accept it as true because it is EXACTLY how light behaves.
reality trumps everything else, regardless of the math.
the assumption i would make is that we do not understand the nature of light.

Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? Where would the hope of understanding lie THEN?

you must remember that reality and our interpretation of said reality are 2 different things.

 

[wynn]

What does science do when the math dictates illogical states? What does it do when the empiricle evidence defies the rational? For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical? Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? Where would the hope of understanding lie THEN?

How come a person doesn't like Quine ...

 

[Magical Realist]

How come a person doesn't like Quine ...

Go ahead then and summarize what Quine taught. No urls. In your own words. We're all ears..

 

[Russ_Watters]

What does science do when the math dictates illogical states?

That makes no sense. Math is logic so the results of math cannot be illogical.

 

[Magical Realist]

That makes no sense. Math is logic so the results of math cannot be illogical.

Can you tell us how the Axiom of Infinity is derived from the rules of formal logic then?


"...∊ 2 if and only if X = 0 or X = 1, where 0 is the empty set and 1 is the set consisting of 0 alone. Both definitions require an extralogical axiom to make them work—the axiom of infinity, which postulates the existence of an infinite set. Since the simplest infinite set is the set of natural numbers, one cannot really say that arithmetic has been reduced to logic...."----http://www.britannica.com/EBchecked/topic/46225/axiom-of-infinity

 

[Russ_Watters]

Can you tell us how the Axiom of Infinity is derived from the rules of formal logic then?

Do you know what the word "axiom" means?

 

[Magical Realist]

Do you know what the word "axiom" means?

This is the definition of axiom: "Logic or Mathematics . a proposition that is assumed without proof for the sake of studying the consequences that follow from it."

The Axiom of Infinity is not based on logic. I just showed you that. Obviously not all math is based on logic then.


I would also remind you of Godel's Incompeteness Theorems:

"Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem.

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency."----http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems

 

[Russ_Watters]

Correct, an axiom is an assumption. Logic starts with assumptions, then you make deductions from them. This does not make math illogical any more than it does any other logic that starts with an assumption.

An axiom, or postulate, is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy.[1] The word comes from the Greek ἀξίωμα 'that which is thought worthy or fit,' or 'that which commends itself as evident.'[2][3] As used in modern logic, an axiom is simply a premise or starting point for reasoning....

In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Within the system they define, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow otherwise they would be classified as theorems. However, an axiom in one system may be a theorem in another, and vice versa.

http://en.wikipedia.org/wiki/Axiom

Take Special Relativity, for example. Evidence suggests very strongly that the speed of light is constant, but since all knowledge is tentative due to the inability to test absolutely every case, it has to be considered an assumption as a basis for starting a mathematical/logical analysis of the issue.

As suggested above, you appear to be making the mistake of believing that what is counter-intuitive is illogical. That's wrong. Humans perceive the world mostly on Newtonian time and distance scales and prior to 1900 assumed that the universe worked in a Newtonian way on all scales. It is not an unreasonable assumption, but it happens to be wrong. But since we go through life perceiving the world in that way, it is difficult to accept that it is wrong. That's why we consider Relativity and QM counter-intuitive when we are first exposed to them, even though logic shows us that they are more correct than the Newtonian view.

Starting with the assumption that the universe is Newtonian because we don't know any better is a fine assumption, but hanging on to that assumption when it is proven to be wrong because experience makes it intuitive is most decidedly illogical.

Going back to the OP:

For example, light is, illogically enough, modelled as both a particle and a wave. Do we accept it as true even though it is illogical?

That isn't illogical. Light displays traits of both waves and particles and therefore is modeled that way. That's completely logical! Similarly, water displays both bulk fluid properties and discrete particle properties. It can be modeled as either depending on what you are trying to investigate.

 

[Pete]

Does this mean that reality may not necessarily even conform to our reason or logic? That there could be an irrational basis behind what happens? Where would the hope of understanding lie THEN?

The Problem of Induction:

Both of these problems have the same solution - acknowledge their existence, then ignore them as useless, because they make no difference to any choice we make.

We assume that reality conforms to the dictates of deductive logic, because what's the use of assuming the alternative?
We assume that reality conforms to the dictates of inductive logic for the same reason.

 

[Magical Realist]

Correct, an axiom is an assumption. Logic starts with assumptions, then you make deductions from them. This does not make math illogical any more than it does any other logic that starts with an assumption.

http://en.wikipedia.org/wiki/Axiom

Take Special Relativity, for example. Evidence suggests very strongly that the speed of light is constant, but since all knowledge is tentative due to the inability to test absolutely every case, it has to be considered an assumption as a basis for starting a mathematical/logical analysis of the issue.

As suggested above, you appear to be making the mistake of believing that what is counter-intuitive is illogical. That's wrong. Humans perceive the world mostly on Newtonian time and distance scales and prior to 1900 assumed that the universe worked in a Newtonian way on all scales. It is not an unreasonable assumption, but it happens to be wrong. But since we go through life perceiving the world in that way, it is difficult to accept that it is wrong. That's why we consider Relativity and QM counter-intuitive when we are first exposed to them, even though logic shows us that they are more correct than the Newtonian view.

Starting with the assumption that the universe is Newtonian because we don't know any better is a fine assumption, but hanging on to that assumption when it is proven to be wrong because experience makes it intuitive is most decidedly illogical.

Going back to the OP: That isn't illogical. Light displays traits of both waves and particles and therefore is modeled that way. That's completely logical! Similarly, water displays both bulk fluid properties and discrete particle properties. It can be modeled as either depending on what you are trying to investigate.

Why is it ok to posit an axiom based on no evidence whatsoever if it only makes your equations work? If the axiom "Unicorns exist." made everything in the universe explainable in a consistently logical way it still wouldn't make that axiom one bit more true. Or are we less concerned with the truth of the axioms and more interested in how they allow theories to explain things?

As for light being a particle and a wave at the same, no that is not logical. By all standards of aristotlean logic, something cannot be in two opposite states at the same time. It's like saying the figure is both a square and a triangle. It's just not rational. Thus not only is the duality of light illogical, but quantum superpositions are too. The math may support it. The evidence may support it. But reason and logic do not support it.