Math And Objective Existence

Continued from ValueExistenceProofTwo

{Can you give a "clear enough" definition of what a function returns?}

I don't want to define stuff if I don't have to. Based on past experience, I should try to avoid attempting rigorous IT definitions. It seems we can only say concrete things about explicit implementations, not general concepts. But I will say that in D1 languages (dynamic with explicit types), functions return at least a type indicator of some kind, and a value/literal/data-item-like thingy. The packaging of these two concepts differs per model, and as long as these two things are "kept" for a while in some manner and are accessible to the model's guts, the models have sufficient info to "do their job". --top

[No. You just refuse to learn how to say concrete things about general concepts. The rest of us have been doing so for thousands of years.]

You just think they are concrete because you mistake your personal head model as universal/external truths. You have a mental block problem in that area and don't recognize subjectivity. Your alleged concrete statements just define vague terms in OTHER vague terms, creating FractalVagueness.

{So you say.}

[Primes are a general concept. What's subjective about them? Is there something that's a prime for one person but not another? Or how about something that's a prime for me today, but might not be tomorrow?]

Some argue that integers are a UsefulLie approximation and don't reflect reality. We can count "people", but people are full of many different life-forms such that a biological definition won't settle anything. And cancer and mutations rule out using DNA alone as the cut-off between human and non-human or "belonging" to the same individual versus not belonging. The bottom line is that two parties will agree on one or more UsefulLie and then build to the next step based on that set of agreement. If my acceptance or rejection of UsefulLie's does not match that of the reader, then they will probably disagree with my conclusions. But I don't think my stated assumptions are abnormal or unreasonable to most readers, or at least "regular programmers", who the target model is designed for.

[Whether or not integers reflect reality is immaterial. Please answer the questions instead of dodging them.]

Primes ARE subjective: they don't exist in reality. They are a head model. We have various notations for math that result in physical markings, but these are just a projection of mental ideas; a mutually-agreed-upon representation of them with mutually-agreed-upon rules. Math is not science. If there is a dispute over claims about primes, two or more parties use the agreed-upon representation/notation and related rules to work out the differences. We even have machines (software) that can successfully (agreeably) process math because almost everybody agrees with the notation and related transformation rules.

Contrast this with politics. While both sides ("left" and "right" here) agree that "we should improve the economy", both sides don't agree on the process/transformation to do that.

[Whether or not integers reflect reality is immaterial. Please answer the questions instead of dodging them.]

I'm sorry, I thought I did, with explanation.

[No, you just repeated your earlier rant using different words.]

I'm sorry, it looks answered to me. I don't know what else to add. Try different or more specific questions or specific scenarios/examples/cases perhaps.

[Try answers to the questions I asked. Subjective doesn't mean "does not reflect reality". Subjective doesn't mean "not real". (And how can I get more specific than asking for a number that is prime for one person and not another?)]

Are you asking me to estimate the likely responses to a survey about primes given to multiple people?

[No. I'm asking you to show me something that meats the definition of prime when considered by one person, but doesn't when considered by another. They must be using the usual definitions and rules for such things yet come up with different results. That's what it would take for primes to be subjective.]

"Using the usual"? Isn't that ArgumentFromPopularity? (Also see above re "fuzzy primes".) As far as agreeing to the reference notation and agreeing to certain transformations, but not further results based on those transformations is fairly rare and not the kind of problem that we usually encounter here. Our usual problem here is agreeing that some specific notation or "root" rules about such notations reflect "common notions" as originally given in English. Our problems are usually translating English into agreeable base notations and/or transformation rules, NOT subsequent steps based on that base set. Even something as seemingly simple as "values have types" get into a big disagreement on how to represent/process "have" and when this have-ness is active or not in a model that attempts to mirror human notions.

[No, it's not an ArgumentFromPopularity. It's not even an argument. Please quit dodging and answer the questions.]

PageAnchor ET-Apple

I'm honestly not dodging your questions. I believe the problem is, based on years of trying to read your material, is that you are a poor writer and don't realize it. Part of this is that what you write in English is a lossy version of your head model, but you don't realize this is the case because when YOU read it back to yourself to check it, you unconsciously re-inject into it the "lost" pieces by filling in the gaps with your existing head models. See TheMartianAndTheApple for an analogy. I believe you to be unconsciously making a similar mistake. My interpretation of your English statements does not match yours, despite not being "wrong".

{I don't think that's it. You don't appear to have made any attempt to answer what are very straightforward questions. This has all the appearance of evasion. If you don't know what prime numbers are, just say so.}

You really think they are "straightforward"? "What they are" is simple English, but "is" and derivatives are not "straightforward". Classification or equivalency is quite often a source of contention. It's only "clear" (rarely disputed) where an agreed-upon notation and related base rules exists. There are probably multiple formal definitions of "primes". However, that does not necessarily mean a given person "runs" that formal definition in their head. For example, a security technician who uses prime numbers for their work may not care about how they are generated, but views them as something akin to "list of funny numbers I get from an online table that I use to manage security tools". To him/her, it's merely a "source" of certain kind of numbers useful for a given purpose. If you probe them, they may be able to give you a typical-sounding definition of having no non-one divisors, but his PRIMARY mental model does not revolve around their "generation" criteria.

Reminds me of this story:

National Geographic Writer: "Okay you gays, can you describe to me what a bison is?"

Human: "A large, powerful, fury grazing mammal."

Elephant: "A small furry animal that keeps muddying up my favorite watering spots."

Mouse: "That big brown shadow that squashed my brother!"

Lion: "The best food!"

To most humans, primes would probably be described as something like, "A number that satisfies that annoying paper process [algorithm] I learned in school to pass the test".

{You appear to be conflating personal feelings about mathematics with mathematics. How odd.}

Are you asking me for a formal mathematical definition of "prime numbers"? Otherwise, "is" is relative; Classification (set membership) and equivalence is based on perspective.

[Of course not. We are asking for you to answer the questions instead of dodging them.]

Well I do agree with that. The few times I have thrown anything into the discussion, what I have thought I was saying somehow changes when he replies. It is as if he is trying to avoid being clear in his answers. I really dunno. I look in regularly to see if there is any progress, and there is none. Just more pedantic (IMHO) argument. I still don't know what a tag offers, and where it may be used. --AnonymousDonor

Well, I tried my best to answer the questions and explain the design tradeoff choices as carefully as I can. I don't know where the communication breakdown is happening. Your criticisms are usually at the summary level, and not the detail level (choice weighing considerations) such that I cannot apply them to anything concrete. My variable/value is less characters than the other "nested" equivalent; that has to at least give it some objective points. And "is" is relative. There is no known central classification force in the universe. A bison "is" food to a lion's primary classification system. And most rigorous proofs come after a notation and its base rules are vetted and agreed upon. Until such is formed for "semantics", you are in foggy territory where few if any other fields have done well in as far as good science. Your claims and questions ofen assume canonical/central objective standards that have not been clearly established or measured.

One may have multiple definitions in multiple notations for "primes" that can produce or qualify numbers as expected in our tests; and intuitively most feel there is a "central" concept to them even though the notations and definitions vary. However, this "central concept" has not been scientifically tamed. I'm just the messenger.

THANKYOU Top


Drifting Off Topic?

What does this topic have to do with language semantics being measurable or objective? If there's no connection, I should probably abandon my participation; it's growing into a LaynesLaw snake-pit. We have tests for primes that almost everybody agrees with (regardless of whether they are subjective or not), but we don't have the same kind of tests for "semantics". It smells like a false equivalency is being set up here. -t

[It's a counter to one of your arguments. One of your arguments is that semantics can't be objective because it's a general notion. The bit about primes shows that you can talk objectively about general notions, and in fact, humans have been doing so for thousands of years.]

You are putting words in my mouth. I did NOT say it "can't be", and I did not say semantics "are" a notation. They may be able to be proven objective, but YOU have not done such so far. And one can only talk "objectively" about them within the framework of notation. Math allows us to create fake worlds, UsefulLies, and we can make objective statements within those worlds using their made up rules. The utility of a UsefulLie does not prove objectivity.

[You did indeed say, "we can only say concrete things about explicit implementations, not general concepts." This is twice now you've been caught lying about what you've said on this very page. Now quit dodging and answer the questions.]

That's not the same as your "can't be" phrase. And "concrete" is not necessarily the same as "objective". In a specific model/notation, concrete things can be said, but they are not necessarily globally objective. One can say concrete things about imaginary numbers in the imaginary model, but that model may not fit a particular external phenomena. They can be concrete relative to a model. Primes can be concrete relative to a mathematical model/notation. I don't dispute that.

[What does "globally objective" mean, and if you didn't mean "objective" when you said "concrete", what did you mean by "concrete"?]

Anyhow, I don't want to get into a general debate about the philosophy of math at the moment. There are probably many things we commonly agree on regardless of whether they are "objective" or not such that starting from square-one is probably a distraction from the original issue. There's no reason to debate the objective existence of integers, for example, because I accept their existence as a working assumption. Thus, I ask to see if we can all re-focus on the issue of measuring semantics for equivalency (or similarity) for Algol-influenced/style dynamic languages. --top

[That's fine, you can come back to this topic whenever you feel ready to answer the questions. I will point out that the topic you wish to refocus us on is off-topic on this page. If you wish to discuss that, return to the page (or, even better, create a page devoted to that topic).]


(Moved from above)

{Furthermore, what is your definition of "subjective"?}

Depends on point of view or perspective.


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