The necessary truth of mathematics (?)

[Write4U]

"Vixens are female foxes" might be invoked to explain the meaning of the word vixen, to a child or a foreigner perhaps. A gap in their knowledge of the English language has thus been filled. Meanwhile, they have learned precisely nothing new about how the world is. Tautologies -- by definition -- have no empirical content, therefore they cannot possibly increase our understanding of empirical matters (cf. science).

We are way off in lala-land here.

What is vacuous is this:
Mathematical axioms, for example, are statements of logic and not fact. They can't be falsified. There are no possible circumstances in which 2 + 2 ≠ 4.

"Therefore the mathematical statement, 2 + 2 = 4 is not scientific."

This conclusion is stupid and untrue. All our science rests on Mathematics, not on an Intelligent Designer.

Interestingly, it is a comedian who put this in proper perspective.

Watch this and comment on the observation of which story contains durable truth, regardless of any falsification or other sophistry.

 

[Gawdzilla Sama]

I imagine that faux pas comes from knowing as much about mathematics as they do about science.

 

[DaveC426913]

Mathematical axioms, for example, are statements of logic and not fact. They can't be falsified. There are no possible circumstances in which 2 + 2 ≠ 4.

"Therefore the mathematical statement, 2 + 2 = 4 is not scientific."

I am not sure who is disagreeing with whom here, but what Ricky says is pretty simplistic (I'm being generous and not saying it's wrong - after all it's just a sound bite).

Mathematical axioms, for example, are statements of logic and not fact

True. That what an axiom is. We define the rules of our number system.

Although I think the only axiom required is 0+1=1. I believe all the rest follow from that one, and can be mathematically proven.


"There are no possible circumstances in which 2 + 2 ≠ 4. "

Of course there are.
2+2 = 11 in base 3.
2+2 = 10 in base 4.
2+2 = "22" in JavaScript.

One must be specific about what one's system is, before one can say what is true or not.

 

[axocanth]

"There are no possible circumstances in which 2 + 2 ≠ 4. "

Of course there are.
2+2 = 11 in base 3.
2+2 = 10 in base 4.
2+2 = "22" in JavaScript.

One must be specific about what one's system is, before one can say what is true or not.

Dave, once again, commits the fallacy of equivocation. It's been pointed out to him before. I don't think he likes me much lol. Someone else tell him.

 

[axocanth]

P.S. There are 10 kinds of people: those who understand binary and those who do not.

 

[axocanth]

P.P.S. In the Malay language, the word "air" means water. Is it true, then, that people breathe water in Kuala Lumpur?

 

[axocanth]

Just one more thing . . .

This conclusion is stupid and untrue. All our science rests on Mathematics, not on an Intelligent Designer.

No doubt mathematics plays a major role in science. Just to name one (among many) counterexample, though, I'm pretty sure you'll find that Darwin's Origin contains not a single mathematical equation. Thus, we must conclude either:

(i) Not all science rests on mathematics, or

(ii) Darwin wasn't doing science.


Take your pick!



You might also consider Einstein's insight . . .

"In my opinion the answer to this question is, briefly, this:- As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Pure mathematics brings us certainty, then. But this certainty comes at the price of describing the real world - which is what we normally take science to be doing.

Edit: And precisely the same considerations apply to a vacuous necessary truth such as the theory of natural selection. Insofar as we can be certain of its truth, we can be certain that it tells us nothing about how the world really is.

 

[axocanth]

"There are no possible circumstances in which 2 + 2 ≠ 4. " [ -- Write4U ]

Of course there are.
2+2 = 11 in base 3.
2+2 = 10 in base 4.
2+2 = "22" in JavaScript.

One must be specific about what one's system is, before one can say what is true or not.

Just in case what I said above isn't clear to some readers . . .

Write4U tells us that there are no possible circumstances in which 2 + 2 ≠ 4. Barring abstruse philosophical considerations (cf. W. V. O. Quine and semantic holism) what Write4U asserts is generally regarded to be correct. It's a necessary truth - true "in all possible worlds" if you will. Almost nobody except oddball philosophers with a Quinean bent would disagree.

But Dave does disagree, and I think we can safely assume he does not have a Quinean bent.

Dave disagrees because in another language (other than base ten), 2 + 2 might equal something else.

But Write4U is not speaking another language. He/she is speaking the standard base 10, which we can confirm by simply asking him/her. Presumably he/she is not speaking Malay either, which could be as easily confirmed by asking him/her.

 

[Write4U]

Although I think the only axiom required is 0+1=1. I believe all the rest follow from that one, and can be mathematically proven.

Exactly and 1 + 1 = 2 can also be mathematically proven it is mathematical "fact".

"There are no possible circumstances in which 2 + 2 ≠ 4. "

Of course there are.
2+2 = 11 in base 3.
2+2 = 10 in base 4.
2+2 = "22" in JavaScript.

One must be specific about what one's system is, before one can say what is true or not.

That is anthropomorphizing mathematics into different symbolic human DIALECTS and does not affect the Universal mathematical guiding principle.
Try the Fibonacci Sequence in any of those dialects. 0, 1, 1, 2, 3, 5, 8, etc...... see how that works out.

The Universe knows only one UNIVERSAL mathematical language where the symbolic representation of 2 + 2 = 4, logically, always, everywhere.

But Write4U is not speaking another language. He/she is speaking the standard base 10, which we can confirm by simply asking him/her. Presumably he/she is not speaking Malay either, which could be as easily confirmed by asking him/her.

True, the key phrase is "standard base 10" on which all derivative mathematics are based

 

[Write4U]

No doubt mathematics plays a major role in science. Just to name one (among many) counterexample, though, I'm pretty sure you'll find that Darwin's Origin contains not a single mathematical equation. Thus, we must conclude either:

(i) Not all science rests on mathematics, or

(ii) Darwin wasn't doing science.

If mathematics play a major role in explaining "some" of the universal processes, why not in "all" processes?

Darwin was presenting a narrative of the fundamental processes. The scientific mathematics came later as the evolutionary chronology became known through fossil remains and their genetic properties.

Even if evolution were, hypothetically, rejected, contested by new data, scientists would have to study hard to find an alternative natural explanation that was able to explain everything that evolution explains today plus the new data that contested it.
Evolution is a fact and a well-supported scientific theory. Feb 28, 2019

Seems like a mathematical pattern to me.

Evolution is both a fact and a theory. Evolution is widely observable in laboratory and natural populations as they change over time. The fact that we need annual flu vaccines is one example of observable evolution. At the same time, evolutionary theory explains more than observations, as the succession on the fossil record. Hence, evolution is also the scientific theory that embodies biology, including all organisms and their characteristics.

more....... https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6428117/#

 

[axocanth]

He [Darwin] was presenting a narrative of the fundamental processes. The scientific mathematics came later.

So, before the mathematics were added, no science had been done? Darwin's work was at a pre-scientific stage?

You won't make many friends around here by saying that lol.

 

[Write4U]

So, before the mathematics were added, no science had been done? Darwin's work was at a pre-scientific stage?

You won't make many friends around here by saying that lol.

Do tell.... (Some of it is deserved)

Darwin wasn't a scientist. He was a naturalist, an observer who had a keen eye and mind.

Darwin received his BA from Christ's College, Cambridge, but the undergraduate degrees awarded by Oxford and Cambridge weren't then specialized by field. He didn't have a degree "in" zoology, botany, or geology because no British university graduate of that era did.Feb 25, 2021

Was Darwin not a formally trained scientist?

Answer (1 of 3): No, there was hardly anyone who could be called “a formally trained scientist” in his day (Michael Faraday comes to mind as a possible exception if one isn’t too technical about the terminology), but his advanced formal education was particularly far from that, being aimed at pro...

www.quora.com

 

[axocanth]

Do tell.... (Some of it is deserved)

Darwin wasn't a scientist. He was a naturalist, an observer who had a keen eye and mind.

Funny, if we were to invite members here to compose a list of the ten greatest scientists of all time, I'd expect to see Darwin's name on the list.

Is it possible you're excluding him for . . . er . . . ad hoc reasons?

Oh well, neither of us is in danger of being overwhelmed by fan mail at least lol.

 

[Write4U]

Funny, if we were to invite members here to compose a list of the ten greatest scientists of all time, I'd expect to see Darwin's name on the list.

Is it possible you're excluding him for . . . er . . . ad hoc reasons?

Oh well, neither of us is in danger of being overwhelmed by fan mail at least lol.

Of course Darwin was a brilliant scientist. He was just not "certified".
I consider Robert Hazen as Darwin's evolved and "certified" scientific progeny.

Robert Miller Hazen (born November 1, 1948) is an American mineralogist and astrobiologist. He is a research scientist at the Carnegie Institution of Washington's Geophysical Laboratory and Clarence Robinson Professor of Earth Science at George Mason University, in the United States. Hazen is the Executive Director of the Deep Carbon Observatory.

Robert Hazen - Wikipedia

en.wikipedia.org

He went further back than Darwin and demonstrated the high probability of abiogenetic processes that eventually evolved and produced living organisms.

 

[DaveC426913]

Dave disagrees because in another language (other than base ten), 2 + 2 might equal something else.

Projection much? You commit the very error you think I made. You use the word "language" with an ambiguous meaning in an attempt to conceal the truth.

Base 10 is not a langauge. Neither is base 3 or base 4. (Now there's some equivocation for you.)

They are all perfectly valid counting systems, base 10 merely being the one most people typically use by convention.

Furthermore, it wouldn't matter if the example did use different languages. The statement made was broad and unconditional; it did not specify "in X circumstances".

The statement "There are no circumstances where 2+2 does not equal 4" is demonstrably false.


You really ought not use words you don't fully understand. It makes you look foolish.

 

[axocanth]

@ Dave above

This is all very silly. You continue to make an extremely elementary mistake -- you did it in my own thread too -- that would have been easily avoided had you bothered to educate yourself in a little of that much maligned (around here anyway!) "philosophical claptrap".

The mistake you are making is this: failing to distinguish between a word or a name or a symbol and its referent.

"Frank Sinatra" is a name, a linguistic entity. Frank Sinatra is neither a name nor a linguistic entity. He is (or was) a flesh-and-blood American singer, as I'm using the name now.

My assertion "Frank Sinatra was born in Hoboken, New Jersey" is potentially refutable. If it can be shown that Frank Sinatra was not born in Hoboken, then my assertion has been shown to be false.

It is certainly not refuted by you naming your cat "Frank Sinatra" and announcing "Frank Sinatra was not born in Hoboken."

The name as used by myself, and the name as used by yourself -- though identical -- has a different referent. You refer to a cat; I refer to Old Blue Eyes.



Likewise with Write4U. When he/she asserts "2 + 2 = 4", the name, or the symbol if you prefer, "4" -- as he/she uses it -- refers to the number four (in English, not Malay or Chinese!).

You do not refute the assertion by invoking a case where the name or symbol "4" refers to something else. This is known as equivocation. You do not refute it either by naming your cat "4" or protesting that "four" means warthog in Swahili.


I will not waste any more time on your stupidity, especially since it is compounded by a very distasteful arrogance, condescension, and spite. Ask around at your local university!

 

[axocanth]

"There are no possible circumstances in which 2 + 2 ≠ 4. "

Of course there are.
2+2 = 11 in base 3.
2+2 = 10 in base 4.
2+2 = "22" in JavaScript.

One must be specific about what one's system is, before one can say what is true or not.

To put an end to this, here's the precise "refutation".

Write4U asserts the following, as he/she is using the symbols -- 2 (two) + 2 (two) = 4 (four). This is necessarily true, we are told.


Dave demurs. It is not always true, he insists. His first attempt at refutation takes the following form: 2 (two) + 2 (two) = 11 (four)

Dave, then, is asserting precisely what Write4U is asserting, thus no refutation has occurred.


And what's Dave's mistake? Ans: Failing to see that his "11" and Write4U's "4" co-refer - two different symbols refer to the same thing. (cf. "Frank Sinatra" and "Old Blue Eyes").

To repeat, one does not refute "Ava Gardner was married to Frank Sinatra" by protesting "No, she wasn't! She was married to Old Blue Eyes!!"

 

[DaveC426913]

The assertion "there is no circumstance in which 2+2 does not equal 4" is demonstrably false. Nothing you have said changes that. No one is fooled by your prestidigitations.

You've got a hammer and everything to you seems to be an equivocation nail. The word does not have the broad power you pretend it does. You're just trolling.

 

[axocanth]

re above . . . I'm off to listen to Frank. It's a lot more pleasant than listening to an abject moron.

 

[axocanth]

Oh, but for all you Chinese scholars out there. Consider the following true statement:

" 2 + 2 = 四 "

"Look!", Dave exclaims jubilantly, "2 + 2 doesn't always equal 4. You are refuted!!! In the above statement it equals a weird squiggle!!"

Would that it were so easy to violate the basic laws of arithmetic! The mistake Dave makes time and time again is not to ask himself what that weird squiggle refers to.