## Science and the principle of noncontradiction

Discussions on the philosophical foundations, assumptions, and implications of science, including the natural sciences.

### Science and the principle of noncontradiction

There are certain things that need to be assumed to do science; e.g., it is assumed that events will unfold in the same patterns in the future as they appear to have unflolded in the past and unfold in the present (that formulation probably needs some clarification). Mathematics is essential to science - quantification of observations and quantification of patterns inferred from those observations is central to science. Different "realms" of math operate by different postulates and science is about "finding" the right math to fit the observed patterns of quantified data. But what about logic? Of course, mathematics has a logic (or logics) to it, but there are other formal logics. Should science be constrained by any formal logic other than logic found in mathematics?

A basic principle adhered to in most formal logics is the principle of noncontradiction - two contradictory statements cannot both be true (or a statement cannot be both true and false). Should the principle of noncontradiction be assumed in science? How would science operate if it allowed contradictory statements to be considered true? Are there examples found in science as it is practiced (by most scientists) now where contradictory statements are both considered to be true (or where a statement is said to be both true and false)?

Here is a little background on the question:

http://www.math.wichita.edu/history/topics/logic.html

One area of mathematics that has its roots deep in philosophy is the study of logic. Logic is the study of formal reasoning based upon statements or propositions. (Price, Rath, Leschensky, 1992) Logic evolved out of a need to fully understand the details associated with the study of mathematics. At the most fundamental level, mathematics is a language and it is a language of choice and must be communicated with great precision. (Wheeler, 1995) The idea of logic was a major achievement of Aristotle. In his effort to produce correct laws of mathematical reasoning, Aristotle was able to codify and systemize these laws into a separate field of study. The basic principles of logic center on the law of contradiction, which states that a statement cannot be both true and false, and the law of the excluded middle, which stresses that a statement must be either true or false. The key to his reasoning was that Aristotle used mathematical examples taken from contemporary texts of the time to illustrate his principles. Even though the science of logic was derived from mathematics, logic eventually came to be considered as a study independent of mathematics yet applicable to all reasoning. (Kline, 1972)

TLK
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### Re: Science and the principle of noncontradiction

TLK » January 9th, 2017, 5:09 pm wrote:I only asked about the principle of noncontradiction (law of contradiction or law of noncontradiction), but the same question applies to the law of the excluded middle.

LEM may not last another century. Intuitionism is making a comeback through, of all things, computer science. After all there are sets of natural numbers such that neither the set nor its complement are computable. In math, modern intuitionism is expressed via Homotopy type theory (HoTT), which lends itself to proof by computer.

Aristotelian logic is under attack not by anti-rationalists, but by science itself. If everything meaningful is computable (a common belief these days), you cannot have the law of the excluded middle.

https://en.wikipedia.org/wiki/Homotopy_type_theory

https://en.wikipedia.org/wiki/Intuition ... ype_theory

Indeed even in classical math we have the same problem. 20th century independence proofs show that in any axiomatic system of sufficient power, there are propositions that can neither be proven nor disproven. Just because you can't prove something true, does not necessarily mean it's false.
someguy1
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### Re: Science and the principle of noncontradiction

someguy1 » Mon Jan 16, 2017 2:11 pm wrote:
TLK » January 9th, 2017, 5:09 pm wrote:I only asked about the principle of noncontradiction (law of contradiction or law of noncontradiction), but the same question applies to the law of the excluded middle.

LEM may not last another century. Intuitionism is making a comeback through, of all things, computer science. After all there are sets of natural numbers such that neither the set nor its complement are computable. In math, modern intuitionism is expressed via Homotopy type theory (HoTT), which lends itself to proof by computer.

Aristotelian logic is under attack not by anti-rationalists, but by science itself. If everything meaningful is computable (a common belief these days), you cannot have the law of the excluded middle.

https://en.wikipedia.org/wiki/Homotopy_type_theory

https://en.wikipedia.org/wiki/Intuition ... ype_theory

Indeed even in classical math we have the same problem. 20th century independence proofs show that in any axiomatic system of sufficient power, there are propositions that can neither be proven nor disproven. Just because you can't prove something true, does not necessarily mean it's false.

If I understand intuitionistic logic correctly, I can see in empirical sciences where it is possible that there are situations where truth values of propositions may be unknown and such a logic may be more useful than a bivalent logic. I'm not sure I of that, though. Can you give some examples in empirical sciences where intuitionistic logic is widely used and accepted? Or examples in empirical sciences where intuitionistic logic could be used effectively.

Again if I understand it correctly, accepting the use of an intuitionistic logic would strengthen the requirement to retain the law of noncontradiction even more than in classic logics. I am still very curious if anyone can give an example of an empirical science where contradictory statements are both accepted as true (or a single statement is said to be both true and false).
TLK
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### Re: Science and the principle of noncontradiction

If anyone is interested in these questions and has a few minutes to read what appears to be an informed argument, I think this paper is worth a read:

http://www.scielo.br/scielo.php?script= ... 1000100013

I'm not sure I agree with his conclusions and I don't have enough background to judge the accuracy of some of his claims, but he does say some provocative things; e.g.:
ABSTRACT

Any inconsistent theory whose underlying logic is classical encompasses all the sentences of its own language. As it denies everything it asserts, it is useless for explaining or predicting anything. Nevertheless, paraconsistent logic has shown that it is possible to live with contradictions and still avoid the collapse of the theory. The main point of this paper is to show that even if it is formally possible to isolate the contradictions and to live with them, this cohabitation is neither desired by working scientists not desirable for the progress of science. Several cases from the recent history of physics and cosmology are analyzed.

Keywords: Consistency. Cosmology. Contradiction. Logic. Physics. Relativity.

INTUITIONISTIC LOGIC

Intuitionistic logic is weaker than classical logic. Everything that can be deduced in an intuitionistic system can also be deduced classically. Of course, the interpretation is not the same in both cases (it is constructive in the first case, structural in the second).

The system of classical logic is obtained from intuitionistic logic by adding some new axiom, like Excluded middle (φ∨¬φ) or Double negation (¬¬φ→ φ).

Intuitionists were afraid of inconsistency. In fact, they were much more afraid of contradiction than classical mathematicians were. From that point of view, intuitionism is more strongly opposed to paraconsistent logic than classical logic is.

A great advantage of intuitionistic logic was supposed to be that it was safer than its classical counterpart. But Gödel proved in 1932 that intuitionistic logic is not safer than classical logic. Any classical formula can be translated into an intuitionistic one in such a way that any classical contradiction would immediately produce an intuitionistic contradiction.

Newton da Costa and other logicians have shown us that it is possible to build consistent systems of paraconsistent logic, systems that allow us to isolate the found contradictions and so preserve the inconsistent theory from collapse or "explosion". Paraconsistent logics are weaker than classical logic, they allow for fewer inferences to be drawn. It is this weakness that makes it possible to contain the deleterious effects of contradictions. But here lurks a problem. Many domains of science -from physics to economics- are extensions of underlying mathematical theories, and it is not clear that all the power of the underlying mathematics can be preserved under a paraconsistent reconstruction.
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### Re: Science and the principle of noncontradiction

Sorry - instead of revising the original post when I edited it, the forum put up the edited version as a new post
TLK
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### Re: Science and the principle of noncontradiction

TLK » January 17th, 2017, 1:09 pm wrote:Can you give some examples in empirical sciences where intuitionistic logic is widely used and accepted? Or examples in empirical sciences where intuitionistic logic could be used effectively.

Empirical science is a long way from the kind of philosophical considerations I mentioned. My only point was to indicate that intuitionism and the rejection of LEM are making a comeback these days through the influence of computer science and contemporary work on mathematical foundations.

I don't understand intuitionism or constructive mathematics in the sense that I don't understand any system of math in which the intermediate value theorem is false. But a lot of smart contemporary thinkers are going in this direction. I'm not qualified to address developments in empirical science that relate to these issues. I did link to the Wiki articles on Homotopy type theory and Intuitionist type theory. I don't think this kind of thinking has filtered to experimental science yet (if that's what you mean by empirical science). But we live in the age of computers, and computational thinking is going to become more and more important going forward. And as I understand it, you can't hold both LEM and the belief that everything important is computable.
someguy1
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### Re: Science and the principle of noncontradiction

Since you are interested in empirical science, I wanted to add an observation about the distinction between falsification and refinement.

To answer your original question, "Should the principle of noncontradiction be assumed in science?" I would say that this is pretty standard. If I am trying to prove X, and professor so-and-so proves not-X, then my research project is pretty much toast unless I can find an error in professor so-and-so's work. In that sense, the law of contradiction is operative in standard science.

But there's another sense in which the notions of true and false are too blunt to describe what's really going on. Suppose Newton proposes his theory of gravity, which we'll called X. Then professor Einstein comes along and falsifies X. But Newtonian gravity is not wrong; it's simply been refined and extended.

In other words if I say, "Newtonian gravity is true," and "Things fall up!" those statements are both technically false. But the second statement is false in a very different way than Newtonian gravity is false.

Point being that there is some subtlety involved. When professor so-and-so shows that theory X is false, it might be that X is flat out wrong. Or it might be that X is still correct, but only under restricted circumstances; and the "not-X" theory reduces to X under these circumstances. That's the case with Newtonian and Einsteinian gravity.

In that sense, the law of contradiction isn't absolute in science. Newtonian gravity is false in an absolute sense. But then again since scientific theories are merely models that fit experiments and are never the ultimate truth of reality, every scientific theory is false. In science, truth and falsity are nuanced and relative.

From Asimov's essay:
My answer to him [someone who'd written Asimov a letter] was, "John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together."

The basic trouble, you see, is that people think that "right" and "wrong" are absolute; that everything that isn't perfectly and completely right is totally and equally wrong.

However, I don't think that's so. It seems to me that right and wrong are fuzzy concepts, and I will devote this essay to an explanation of why I think so.

I hope my post has at least the virtue of being relevant to your question. My excursion into neo-intuitionism was off the mark.
someguy1
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### Re: Science and the principle of noncontradiction

Most science is based on assuming the three main laws of logic. (1) Law of Identity, (2) Law of Non-contradiction, and (3) Law of Excluded Middle.

Without delving into the specific depths of all the different interpretations, these three are actually just forms of one that demands "consistency". A "law" is about those things that are consistent or that have patterns or rules that are consistent. So most of science has defaulted to these traditionally.

I think that a partial divorce and confusion came about with quantum mechanics though because much of the interpretation of things like superposition HAVE to abandon these laws or prove inconsistent with other areas of science.

I've already argued before on this site that a non-consistent logic must be assumed prior since they can be closed over all logic and reality. But it would have to be such that it diverges into places (worlds) that have consistency versus those without consistency. I doubt any world could be completely ever closed consistently without becoming 'dead'. I personally believe that 'contradiction' acts as a function of force in its own right. If reality is inconsistent as a whole, reality competes to try to be consistent deriving our kind of world but motivated perpetually because it cannot possibly meet that goal.
Scott Mayers
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### Re: Science and the principle of noncontradiction

someguy1 » Tue Jan 17, 2017 2:43 pm wrote:
TLK » January 17th, 2017, 1:09 pm wrote:Can you give some examples in empirical sciences where intuitionistic logic is widely used and accepted? Or examples in empirical sciences where intuitionistic logic could be used effectively.

Empirical science is a long way from the kind of philosophical considerations I mentioned. My only point was to indicate that intuitionism and the rejection of LEM are making a comeback these days through the influence of computer science and contemporary work on mathematical foundations.

I don't understand intuitionism or constructive mathematics in the sense that I don't understand any system of math in which the intermediate value theorem is false. But a lot of smart contemporary thinkers are going in this direction. I'm not qualified to address developments in empirical science that relate to these issues. I did link to the Wiki articles on Homotopy type theory and Intuitionist type theory. I don't think this kind of thinking has filtered to experimental science yet (if that's what you mean by empirical science). But we live in the age of computers, and computational thinking is going to become more and more important going forward. And as I understand it, you can't hold both LEM and the belief that everything important is computable.

I hadn't realized that intuitionistic logic had an important role to play in computation. I appreciate you sharing that. I must admit that I don't understand what you mean by "belief that everything important is computable", though.
TLK
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### Re: Science and the principle of noncontradiction

someguy1 » Tue Jan 17, 2017 10:26 pm wrote:Since you are interested in empirical science, I wanted to add an observation about the distinction between falsification and refinement.

To answer your original question, "Should the principle of noncontradiction be assumed in science?" I would say that this is pretty standard. If I am trying to prove X, and professor so-and-so proves not-X, then my research project is pretty much toast unless I can find an error in professor so-and-so's work. In that sense, the law of contradiction is operative in standard science.

But there's another sense in which the notions of true and false are too blunt to describe what's really going on. Suppose Newton proposes his theory of gravity, which we'll called X. Then professor Einstein comes along and falsifies X. But Newtonian gravity is not wrong; it's simply been refined and extended.

In other words if I say, "Newtonian gravity is true," and "Things fall up!" those statements are both technically false. But the second statement is false in a very different way than Newtonian gravity is false.

Point being that there is some subtlety involved. When professor so-and-so shows that theory X is false, it might be that X is flat out wrong. Or it might be that X is still correct, but only under restricted circumstances; and the "not-X" theory reduces to X under these circumstances. That's the case with Newtonian and Einsteinian gravity.

In that sense, the law of contradiction isn't absolute in science. Newtonian gravity is false in an absolute sense. But then again since scientific theories are merely models that fit experiments and are never the ultimate truth of reality, every scientific theory is false. In science, truth and falsity are nuanced and relative.

From Asimov's essay:
My answer to him [someone who'd written Asimov a letter] was, "John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together."

The basic trouble, you see, is that people think that "right" and "wrong" are absolute; that everything that isn't perfectly and completely right is totally and equally wrong.

However, I don't think that's so. It seems to me that right and wrong are fuzzy concepts, and I will devote this essay to an explanation of why I think so.

I hope my post has at least the virtue of being relevant to your question. My excursion into neo-intuitionism was off the mark.

The important notion of falsification in science is definitely one of the things I was thinking about when I asked the question about the role of the principle of noncontradiction in science. I think your distinction between falsification and refinement is an important one - although in a very strict sense a refinement could be seen as being based on falsification of at least some crucial aspect of a theory opening up an avenue to a theory that doesn't have the same flaw(s). Falsification is a test of a theory and the theory may not pass. That does not imply that the "falsified" theory doesn't provide a fairly good approximation of how some patterns of events in nature unfold. The history of science is full of examples of theories that are good approximations giving way to theories that are better approximations - a process of refinement.

This gets into another question I have. "Findings" in science are always tentative - open to revision with new information. In that sense, in science can we really comfortably use a logic that "works" based on assessing the truth or falsity of statements? Can we express scientific notions in true or false statements and yet still maintain the inherent contingency of scientific statements?

- As I said in my earlier post, I found the information about intuitionistic logic to be really interesting so I'm glad you posted it.
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### Re: Science and the principle of noncontradiction

Scott Mayers » Wed Jan 18, 2017 12:16 am wrote:Most science is based on assuming the three main laws of logic. (1) Law of Identity, (2) Law of Non-contradiction, and (3) Law of Excluded Middle.

Without delving into the specific depths of all the different interpretations, these three are actually just forms of one that demands "consistency". A "law" is about those things that are consistent or that have patterns or rules that are consistent. So most of science has defaulted to these traditionally.

I think that a partial divorce and confusion came about with quantum mechanics though because much of the interpretation of things like superposition HAVE to abandon these laws or prove inconsistent with other areas of science.

It does seem like assuming consistency is crucial to at least some aspects of science. The assumption that events will unfold in the future in patterns that have been observed in the past is an example of something very basic about science that is about consistency.

As long as a scientist isn't making any ontological claims about the nature of things like waves and particles, I'm not sure that we have to abandon the idea of consistency with respect to QM. The Schrodinger equation can be used to predict the probabilities of quantum level events and do so very consistently. The Schrodinger equation has no necessary ontological implications, though. I can see the problem of consistency in the notion of superposition in the Copenhagen interpretation (ontology) of QM but I'm not sure that the many-worlds interpretation (ontology) of QM has a problem with consistency with respect to the concept of superposition. Could you explain what you mean somewhat more? I'm not sure I understand.

I've already argued before on this site that a non-consistent logic must be assumed prior since they can be closed over all logic and reality. But it would have to be such that it diverges into places (worlds) that have consistency versus those without consistency. I doubt any world could be completely ever closed consistently without becoming 'dead'. I personally believe that 'contradiction' acts as a function of force in its own right. If reality is inconsistent as a whole, reality competes to try to be consistent deriving our kind of world but motivated perpetually because it cannot possibly meet that goal.

I guess I'd have to see the arguments you have presented previously because, unfortunately, I am not understanding what you are saying here.
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### Re: Science and the principle of noncontradiction

I agree on the question of stating "ontological" claims but this is still hard NOT to do because implicit in the productive capacity of science to be accepted is that it is literally understood to be 'true' if it is to mean anything when it comes to political actions.

You wouldn't think that we treat nuclear bomb technology as being something we can't treat real or not. It is still ontologically 'true' that if you push someone off a cliff, it would reasonably be determined that they would die.

I'm not dismissing that we NEED some logic of 'consistency'. But it would be a subset of a more complete logic based on an absence of 'consistency' as a necessity. It may seem that because we can't make a fixed 'rule' to begin with that its variability makes anything follow everywhere. But this is not so. If everything is possible, even based on non-consistency, this must include even limitations. But to be resolved, totality would have to be 'split'. There would be perpetually places (worlds) that allow for consistent reality as well as inconsistent ones.

The 'unsettling' nature of lacking closure is itself what causes reality.

Normally, we treat Contradiction as a place where we STOP, as a sort of dead end. But if we treat such conclusions as a 'split', while it remains true that contradiction cannot exist in one space, it justifies a 'new' place where it CAN be true. There is still a kind of 'consistency' in this but is more DYNAMIC.

Example. If we deem that George Washington is both alive and dead, while this is contradictory of some proof that might deem this conclusion valid, a solution (of many), may be to interpret this as valid if we treat the "universal" condition of this 'truth' to be based on a time span of 1500 A.D. to 2017 A.D. . That is we discover a 'place' where it IS 'true' that remains rational by finding a dimension (the universal here) in which such an apparent contradiction is true and sound.

I don't approve of QM's treatment of assuming a weirdness because it precisely gives up BEING rational (where it speaks ontologically) when it pretends something that doesn't fit in with our ordinary experience. That is why a multiworld interpretation at least has a more rational justification, for instance. This is what I mean by using a form of logic based external to a law of non-contradiction. You treat the 'third' middle factor (being both true and false) as true consistently if we find a novel dimension where it can fit is some balanced way that still allows each possibility to persist in some greater universal.
Scott Mayers
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### Re: Science and the principle of noncontradiction

Scott,

Yep, we seem to be psychologically predisposed to apply scientific "information" with some (probably implicit) ontological predisposition with respect to the "stuff" that is being manipulated when we apply that information to actual tasks. I think it's even difficult to think of the observation "side" of science without thinking of observations from some kind of physical realist point of view. I imagine that most scientists most of the time think they are observing real physical stuff.

With respect to consistency I think we have to be very careful of the semantics of the statements we are assessing for consistency, but I wouldn't dismiss the possibility of some aspect of science basically "accepting as true" statements that are inconsistent with one another. I would just like to see a concrete example of how that would work.

It seems as though you might be advocating a type of paraconsistent logic:

https://en.wikipedia.org/wiki/Paraconsistent_logic

http://philsci-archive.pitt.edu/1566/1/CosKraPATTY.pdf

Here is a link to a paper (synopsis) on the possible use of paraconsistent logic to tackle the issues around quantum superposition.

https://arxiv.org/abs/1306.3121

I have seen a couple of examples like that where there are proposals to use paraconsistent logic in science but so far I haven't come upon any that appear to be widely accepted yet.
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### Re: Science and the principle of noncontradiction

TLK » January 21st, 2017, 12:42 pm wrote:... I wouldn't dismiss the possibility of some aspect of science basically "accepting as true" statements that are inconsistent with one another. I would just like to see a concrete example of how that would work.

For most of the 20th century, physics accepted quantum theory and relativity, though nobody's been able to make them consistent with each other. Doesn't bother anyone. People keep working on integrating the two theories, and physics proceeds as long as the grant money flows.

Consistency is a technical condition in mathematical logic that doesn't even apply to physical theories. And if the axioms of math were found inconsistent tomorrow morning, it wouldn't bother anyone. The experts in foundations would get busy patching the problems, and nobody else would even notice. After all, there wasn't any foundation of math at all before the twentieth century and geniuses like Archimedes, Euler, Newton, and Gauss got along just fine.
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### Re: Science and the principle of noncontradiction

someguy1 » Sat Jan 21, 2017 3:03 pm wrote:
TLK » January 21st, 2017, 12:42 pm wrote:... I wouldn't dismiss the possibility of some aspect of science basically "accepting as true" statements that are inconsistent with one another. I would just like to see a concrete example of how that would work.

For most of the 20th century, physics accepted quantum theory and relativity, though nobody's been able to make them consistent with each other. Doesn't bother anyone. People keep working on integrating the two theories, and physics proceeds as long as the grant money flows.

Consistency is a technical condition in mathematical logic that doesn't even apply to physical theories. And if the axioms of math were found inconsistent tomorrow morning, it wouldn't bother anyone. The experts in foundations would get busy patching the problems, and nobody else would even notice. After all, there wasn't any foundation of math at all before the twentieth century and geniuses like Archimedes, Euler, Newton, and Gauss got along just fine.

My statement in bold above was too vague. That both quantum mechanics and relativity theories are "basically accepted as true" - as you point out - even though they are not consistent with one another in important ways is what I take to be a good example of interpreting "basically accepted" in a utilitarian way. Quantum mechanics works extremely well for certain kinds of events that we identify and relativity theories work extremely well with other kinds of events that we identify. In that sense, both of them are basically accepted as true even though they are not consistent with each other.

I can understand how my statement could be construed in a utilitarian way but that wasn't my intent. My intent wasn't utilitarian. When I was talking about inconsistent notions both being accepted as true, I meant something like that the explanatory inconsistency of the theories being basically accepted as okay. The problems with the results of applying both sets of theories to singularities of black holes may show that the inconsistencies between the two sets of theories could suggest that there is a "deeper" theory that needs to be created/found that explains away the inconsistencies. I think the quest to resolve the inconsistencies is a lot of the motivation to find a "unified" theory.
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### Re: Science and the principle of noncontradiction

TLK » January 21st, 2017, 4:56 pm wrote:... there is a "deeper" theory that needs to be created/found that explains away the inconsistencies. I think the quest to resolve the inconsistencies is a lot of the motivation to find a "unified" theory.

People are psychologically driven by a need for consistency, but there's no reason to think absolute truth or logical consistency in scientific theories are achievable. The history of science consists of new approximations refining (hence falsifying) the previous ones. Some think this process will end and we'll have the "theory of everything" that can be written on a t-shirt. It hasn't happened yet, but the desire for such a theory drives much of science.
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### Re: Science and the principle of noncontradiction

someguy1 » Sat Jan 21, 2017 5:36 pm wrote:
TLK » January 21st, 2017, 4:56 pm wrote:... there is a "deeper" theory that needs to be created/found that explains away the inconsistencies. I think the quest to resolve the inconsistencies is a lot of the motivation to find a "unified" theory.

People are psychologically driven by a need for consistency, but there's no reason to think absolute truth or logical consistency in scientific theories are achievable. The history of science consists of new approximations refining (hence falsifying) the previous ones. Some think this process will end and we'll have the "theory of everything" that can be written on a t-shirt. It hasn't happened yet, but the desire for such a theory drives much of science.

I think having brains with good pattern recognition ability has given us a survival advantage. Pattern recognition requires that events happen in a consistent manner. I suspect that that may be one of the biggest reasons why we seem to have such an innate sense of "looking" for consistency in our experiences. And expecting consistency in our statements about our experiences.

There is kind of a funny tension in science. It is well established that "conclusions" in science are tentative - which is a recognition that what we think we know may not be consistent with the way the world actually is. And yet it seems like one of the central goals of science is to try to get as "close" as we can to seeing the way the world actually is. It's like we seek absolute truth about the way the world works but, based on plenty of previous experience, we need to stay humble and accept that we may never know the truth of the way the world actually works.
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### Re: Science and the principle of noncontradiction

For some thoughts, I’m not sure, but like the consideration about truth and also the LEM considerations mentioned, but perhaps, of the laws, identity may be defended where contradiction is arguably contextual, relative, etc., for an example, violation of non-contradiction with entropy resolved with entropy as relative, Marolf, 2003.

Or there have been expressions like, “…Presumably I would give up the principle of contradiction if I ever had a sense datum which was both red and not red, for example.” (Putnam 1983a, p. 110) (Also adds, “…. I think it is right to say that, within our present conceptual scheme, the minimal principle of contradiction [i.e. the claim that not every statement is both true and false] is so basic that it cannot significantly be ‘explained’ at all. But that does not make it an ‘absolutely a priori truth’, in the sense of an absolutely unrevisable truth”.

There were some notions perhaps like this mentioned in another thread, e.g., not regarding the colour red, but blue and black/ white and gold perhaps by considering the image in different contexts, but even so, https://en.wikipedia.org/wiki/The_dress , what do you think of examples rather like this?

Anyway, such notions may involve how the world may be divided up. There are other considerations but, Aristotle argued something to the effect that if taken to an extreme, the observer could be relative to the observer. There might be other means to similar effect, but this is about relative identity, https://plato.stanford.edu/entries/identity-relative/ and properties, https://plato.stanford.edu/entries/properties/ .
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