Differences between Facts and Theories!

[Sha'irullah]

My sorry mistake. I meant to write "buy." As in . . .

"So evidently you don't buy the claim of science that Homo sapiens evolved. Hmmmm . . . ."​

Oh I understand .

Well why would I not accept evolution?

There is no belief in evolution just acceptance. It is a fact that many have issues accepting.

What makes you think I do not accept evolution?

If I did not then I would not be a very great non-theist as I have no motive to not accept it

 

[metis]

Theorems and axioms aren't so much used in the sciences themselves (more by the sciences I would say) as they belong to the language of mathematics. Theories in the sciences, theorems in mathematics. Axiom doesn't really have a corresponding term in the sciences, for precisely the reason that proofs only exist in mathematics (logic being included): the discourse realm is closed.

Actually we do use these terms in anthropology at times, and I've also seen them used in cosmology. Check these definitions of "axiom" out from Dictionary.com:

1.a self-evident truth that requires no proof.
2.a universally accepted principle or rule.
3.Logic, Mathematics . a proposition that is assumed without proof for the sake of studying the consequences that follow from it.

It's the latter that you're undoubtedly referring to, but the other to are not in the mathematics area.

 

[LegionOnomaMoi]

Actually we do use these terms in anthropology at times, and I've also seen them used in cosmology. Check these definitions of "axiom" out from Dictionary.com

I have access to the OED online, so I really don't need Dictionary.com to find out how the term is commonly used. The Sage Dictionary of Social Research Methods doesn't have either "axiom" or "theorem" anywhere but is littered with "theory" and "hypothesis". There's no entry for either in The SAGE Dictionary of Cultural Studies either. They're not even in the two-volume Encyclopedia of Medical Anthropology. I've no doubt that in computational anthropology the terms are used, just like in cosmology. That's because mathematics is the language of the sciences. I have a few university level anthropology textbooks, such as the basic Anthropology: The Human Challenge (2011 edition), and not one has either term (except the occasional colloquial use of "axiom"). Although the two-volume 21st Century Anthropology: A Reference Handbook uses "axiom" in the colloquial sense, the only use of "theorem" I found was on p. 603 in the construction "mathematical theorems". I think it's safe to say that if "axiom" & "theorem" are used in anthropology, they are either used non-technically or used in reference to mathematics.

 

[Skwim]

There is no belief in evolution just acceptance. It is a fact that many have issues accepting.

Well, I, for one, believe it. Although I'm curious as to what you see as the meaningful difference between "belief in" and "acceptance."

What makes you think I do not accept evolution?

Not that you don't accept evolution, but the evolution of man. First you said "When using the scientific concept it is preferred to use the word principle and not fact," which implies that "principle" and "fact" are pretty much synonyms---If they differ significantly you never explained it. Then you said,

"Evolution is a principle but the evolution of man is a theory which is based upon multiple principles and fulfillment of a hypothesis."
​

So, you're saying that while evolution is a fact of sorts, evolution of man, in contrast, is only a theory. I say this because theories don't have the certitude of facts (your principles). Hence my observation that you seem to think the evolution of man doesn't rise to the level of certainty you grant other organisms, which you see as a fact. Therefore my, "So evidently you don't buy the claim of science that Homo sapiens evolved."

 

[metis]

I have access to the OED online, so I really don't need Dictionary.com to find out how the term is commonly used. The Sage Dictionary of Social Research Methods doesn't have either "axiom" or "theorem" anywhere but is littered with "theory" and "hypothesis". There's no entry for either in The SAGE Dictionary of Cultural Studies either. They're not even in the two-volume Encyclopedia of Medical Anthropology. I've no doubt that in computational anthropology the terms are used, just like in cosmology. That's because mathematics is the language of the sciences. I have a few university level anthropology textbooks, such as the basic Anthropology: The Human Challenge (2011 edition), and not one has either term (except the occasional colloquial use of "axiom"). Although the two-volume 21st Century Anthropology: A Reference Handbook uses "axiom" in the colloquial sense, the only use of "theorem" I found was on p. 603 in the construction "mathematical theorems". I think it's safe to say that if "axiom" & "theorem" are used in anthropology, they are either used non-technically or used in reference to mathematics.

Even though it is not a scientific source, you might be interested in this:

Axioms play a key role not only in mathematics, but also in other sciences, notably in theoretical physics. In particular, the monumental work of Isaac Newton is essentially based on Euclid's axioms, augmented by a postulate on the non-relation of spacetime and the physics taking place in it at any moment.

In 1905, Newton's axioms were replaced by those of Albert Einstein's special relativity, and later on by those of general relativity.
Another paper of Albert Einstein and coworkers (see EPR paradox), almost immediately contradicted by Niels Bohr, concerned the interpretation of quantum mechanics. This was in 1935. According to Bohr, this new theory should be probabilistic, whereas according to Einstein it should be deterministic. Notably, the underlying quantum mechanical theory, i.e. the set of "theorems" derived by it, seemed to be identical. Einstein even assumed that it would be sufficient to add to quantum mechanics "hidden variables" to enforce determinism. However, thirty years later, in 1964, John Bell found a theorem, involving complicated optical correlations (see Bell inequalities), which yielded measurably different results using Einstein's axioms compared to using Bohr's axioms. And it took roughly another twenty years until an experiment of Alain Aspect got results in favour of Bohr's axioms, not Einstein's. (Bohr's axioms are simply: The theory should be probabilistic in the sense of the Copenhagen interpretation.)...

Regardless, the role of axioms in mathematics and in the above-mentioned sciences is different. In mathematics one neither "proves" nor "disproves" an axiom for a set of theorems; the point is simply that in the conceptual realm identified by the axioms, the theorems logically follow. In contrast, in physics a comparison with experiments always makes sense, since a falsified physical theory needs modification. -- Axiom - Wikipedia, the free encyclopedia

 

[LegionOnomaMoi]

In 1905, Newton's axioms were replaced by those of Albert Einstein's special relativity, and later on by those of general relativity.
Another paper of Albert Einstein and coworkers (see EPR paradox), almost immediately contradicted by Niels Bohr, concerned the interpretation of quantum mechanics.

The relationship between mathematics and physics has never been stronger, particularly in the case of quantum physics. Quantum mechanics is basically mathematics:

"In classical physics, the notion of the “state” of a physical system is quite intuitive...there exists a one-to-one correspondence between the physical properties of the object (and thus the entities of the physical world) and their formal and mathematical representation in the theory...With the advent of quantum theory in the early twentieth century, this straightforward bijectivism between the physical world and its mathematical representation in the theory came to a sudden end. Instead of describing the state of a physical system by means of intuitive symbols that corresponded directly to the “objectively existing” physical properties of our experience, in quantum mechanics we have at our disposal only an abstract quantum state that is defined as a vector (or, more generally, as a ray) in a similarly abstract Hilbert vector space.
The conceptual leap associated with this abstraction is hard to overestimate. In fact, the discussions regarding the 'interpretation of quantum mechanics' that have occupied countless physicists and philosophers since the early years of quantum theory are to a large part rooted precisely in the question of how to relate the abstract quantum state to the 'physical reality out there.' (pp. 14-15)
from Schlosshauer's Decoherence and the Quantum-to-Classical Transition (from Springer's monograph series The Frontiers Collection; 2007)

This was in 1935

1) They aren't just his words. EPR isn't an abbreviation for some procedure or a serious neurological condition, it's the standard way of referring to the 1935 paper that Einstein, Podolsky, and Rosen published (Phys. Rev. 47, 777-780).

However, thirty years later, in 1964, John Bell found a theorem

Again:
"Because quantum mechanics violates Bell’s inequality, it is in empirical disagreement with the family of local physical theories.
Thus, we have that if the quantum predictions are correct, then there is no way to explain the experimental results using any local theory. And indeed, experiments have supported quantum mechanics in this regard, so that we may conclude also that nature is nonlocal."

Bell's theorem is called a theorem because it is mathematical. It is not a theory. Violating does not prove that it is wrong or right. It is there to show what the implications are if certain conditions hold or fail to hold.

And it took roughly another twenty years until an experiment of Alain Aspect got results in favour of Bohr's axioms, not Einstein's.

One of the most famous mathematical proofs in physics is Bell's inequality, which is (trivially) a proof that if particular measurements on a physical system are made such that particular correlations between particle spins are found, then either locality or realism must be sacrificed to explain it. Such results were found first by Aspect et al. in 1982

In mathematics one neither "proves" nor "disproves" an axiom for a set of theorems

Odd. Under "axioms" we find Euclid's fifth postulate. "Euclid's fifth postulate cannot be proven as a theorem, although this was attempted by many people. Euclid himself used only the first four postulates ("absolute geometry") for the first 28 propositions of the Elements, but was forced to invoke the parallel postulate on the 29th. In 1823, Janos Bolyai and Nicolai Lobachevsky independently realized that entirely self-consistent "non-Euclidean geometries" could be created in which the parallel postulate did not hold. (Gauss had also discovered but suppressed the existence of non-Euclidean geometries.)"
Axioms (also called postulates) in physics, logic, and mathematics are propositions that are self-evidently true. However, what is self-evidently true can, and has been, shown to be incorrect or to not hold in particular cases. This was true of Euclid's fifth axiom, which everybody who was anybody in mathematics tried to prove as a theorem only to find that it was possible to have geometries in which it did not exist. Minkowski space, the geometry of spacetime, is a non-Euclidean geometry that depends upon a rejection of Euclid's axioms. The difference between the use of postulates/axioms in mathematics vs. physics is that there is only one way to show an axiom need not be true in mathematics (using reasoning), and two ways in physics (reasoning and/or empirical results).

In contrast, in physics a comparison with experiments always makes sense, since a falsified physical theory needs modification

Bell's 1964 paper can't be falsified by experiments. It's mathematical. The nearly a century of debate over the interpretation of quantum mechanics is due to our inability to know how experiments correspond with our mathematical representation of them. Physical systems in quantum mechanics are described as abstract mathematical entities in an abstract mathematical space (Hilbert space) with no one-to-one correspondence between the mathematical representation and whatever the physical system actually "is". QM is essentially (and, some would argue, actually) a statistical mechanics.

 

[metis]

The relationship between mathematics and physics has never been stronger, particularly in the case of quantum physics. Quantum mechanics is basically mathematics:...

Thanks for what you wrote. After I posted last, one of the things that dawned on me was that I don't remember the word "theorem" being used in my studies in anthrpology and biology, past and present. "Axiom", yes; "hypothesis", yes; "theory", yes; "theorem", I don't think so. Hmmmmmm.

 

[Iti oj]

.....im sad

 

[ruffen]

In my view, fact is the way the world really is, regardless of whether we understand it or not. For example, the truth about the age and origin of our universe is a fact that we may gradually uncover over time.

A hypothesis is what most people refer to as a "theory" - it's an idea of how something is

A scientific theory is a hypothesis that has been tested and retested and for which there is much evidence, so that it is widely accepted in the scientific community.

A theory can be "proved wrong", but any new hypothesis will need to account for every experiment that has both confirmed and disproved the previous theory. This means that if someone is to disprove the Big Bang Theory, they will have to account for the expansion of the Universe, the Cosmic Microwave Background radiation, and every other piece of evidence that exists.

For example, Newton's theory of gravity started out as a hypothesis, but after thorough checks and research, attempts to disprove it and using the hypothesis to predict positions of planets etc., it became the theory of gravity and remained that way for over 300 years.

Then, it was discovered that the orbit of Mercury didn't quite follow Newton's theory - the point farthest away from the Sun precessed ever so slightly so that the orbit changed over time (due to relativistic effects because of Mercury's orbital speed and position in the Sun's gravity well). Einstein's theories of special and general Relativity "disproved" Newton's laws and replaced our understanding of how gravity and space and time work. They successfully predicted Mercury's motion as well as lots of other observed and confirmed phenomena. They will remain the current theories until some tiny inconsistencies might be observed that need explaining - but they may well be close enough to reality (fact) that they accurately describe the actual Universe good enough for the theory to remain.

There is however a know discrepancy or gap between the Theory of Relativity and Quantum Mechanics that needs to be solved with some sort of theory of Quantum Gravity. Does that mean that the Theory of Relativity is "just a theory" or just a guess? Nope - it just means it does not provide a complete description of reality, but the parts it does describe seem to be accurate and correct.

So a theory is our current best understanding of a subject, while a fact is the way it really is independent of our understanding.

 

[gnostic]

Theorems and axioms aren't so much used in the sciences themselves (more by the sciences I would say) as they belong to the language of mathematics. Theories in the sciences, theorems in mathematics. Axiom doesn't really have a corresponding term in the sciences, for precisely the reason that proofs only exist in mathematics (logic being included): the discourse realm is closed.

When I was studying physics and chemistry, and any other fields in science, I didn't come across words like "theorem" or "axiom", in lectures, classrooms or textbooks (from what I can recall). Whenever I came across these words, they were always in mathematics.

So I'd agree.

 

[ImprobableBeing]

A fact is something that has to be proven and can be repeated threw scientific experimentation. Meaning the results do not change.
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A theory is something that relies on (or is a result of) scientific experimentation, but the results are not dependent on the experiment itself.

How do you view the differences between "FACTS" and "THEORIES"?

Well for one fact isn't an established scientific term, a theory in science is as good as it gets.

Theories don't graduate and become laws or facts, they are always theories with less or more evidence and will remain so for all time.

Now, if we are talking about observable phenomena (which i assume you mean to be facts) then evolution and gravity would be examples of such and both have theories that describe HOW these phenomena operate.

Of course, we know that the theory of gravity is wrong while the ToE is next to germ theory the strongest supported theory that we have, so strongly supported that it's findings are actually used every day to make predictions in evolution of bacteria and viruses so we have a vaccine and an atibiotic before there even is a virus or bacteria to innoculate for or treat for. It's incredibly accurate but not without it's faults since we cannot always predict the exact environment where the evolution takes place.

 

[Skwim]

Well for one fact isn't an established scientific term, a theory in science is as good as it gets.

Sure it is. Pure and simple, in science a fact is an objective and repeatedly verified observation. Of course, in science facts sometimes get changed a bit, but this is an understood possibility, so no scientific fact is ever assumed to be an inviolate truth.

 

[ImprobableBeing]

Sure it is. Pure and simple, in science a fact is an objective and repeatedly verified observation. Of course, in science facts sometimes get changed a bit, but this is an understood possibility, so no scientific fact is ever assumed to be an inviolate truth.

No, that would be empirical evidence for something (usually a theory).

In the example of evolution, the empirical evidence would be observation of evolution and the Theory is then based on these empirical evidences to describe how the process works.

Of course, i agree that everything needs to be falsifiable which always makes it "to the best of our current knowledge".