2021-07-04

39: Please State the Major Premise, Explicitly and Honestly

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A dream that talking it over with each other will bring an agreement is unenlightened and rather harmful. To agree to disagree is the way, but how?

Topics


About: truth
About: argument

The table of contents of this article

Starting Context


  • Nothing particularly.

Target Context


  • The reader will understand that to agree to disagree is the way and the requisites to accomplish that.

Orientation


Absolute truths exist.

What we are supposed to do is to maintain the unboundedly consistent hypotheses system.

To establish the unbounded consistency is the only way to near truths.

Main Body

Stage Direction
Hypothesizer 7 soliloquizes.

1: "Insights into Mathematics" Is Great, When It Is Not a Logical Bottomless Swamp


Hypothesizer 7
 These days, I am binge-watching a YouTube channel, "Insights into Mathematics", which is several years old, but I found it recently.

I first found a series, "Differential Geometry", in the channel, and was fascinated by its fresh viewpoints (projective geometry, tangent conics, etc.) and clear (mostly) descriptions.

Well, I did not understand the real intention of the professor's refusal to use irrational numbers, but I was not much worried about it because the issue was not so obtrusive in the series. I rather thought "As someone who can be so clear is insisting so, he must have a good reason.".

Finding out that the channel contained more series, I expectantly began to watch "Math Foundations". . . . Wow, the construction of the numbers system (natural numbers, integers, fractions, rational numbers, and corresponding polynumbers) is lucid and beautiful, and some information introduced there (Ford circles, etc.) is interesting and thought-provoking.

Well, I was perplexed by the video titled "MF 16: Why infinite sets don't exist", because the title suggested explaining the reason, but I did not see any in it. . . . Did the professor think that the contents of the video constituted a reason? . . . If so, he must have had an untold major premise I did not share.

And I was repulsed by its arguments on functions (refer to the video named "MF 42: The problem with `functions'"): the "Riemann (n)" function is not legitimate because humans do not know the truth or falsehood of the Riemann hypothesis? . . . It seems blaming the function just because humans are ignorant (the argument that someone's proving the hypothesis or finding a crack in the proof changes the nature of the function seems as amiss as an argument that an underachieving student's miscalculating '1 + 1' changes the nature of the arithmetic: the nature of the arithmetic did not change at all; it is just that student made a mistake). . . . I could not help but begin to suspect that there was an unacceptable mentality underlying the channel.

However, I did not leave the channel, partly because I still hoped that my suspicion would turn out to be wrong, partly because the channel contained much benefit still, and partly because I felt compelled to find out the professor's real intention on irrational numbers.

And by and by, the series began to relentlessly denounce irrational numbers, but I have to say that the arguments are a logical bottomless swamp: they are like "Humans can't do calculations on irrational numbers; so, irrational numbers don't exist!", but that sounds as awry (and arrogant) as a blind person's argument "I can't see any light; so, light doesn't exist!". . . .

2: State the Major Premises Explicitly, Please


Hypothesizer 7
 The main reason why some of the channel's arguments are a logical bottomless swamp is that the major premises are untold.

The professor is insisting that there is not any infinite set, and his ground for the nonexistence of the natural numbers infinite set is, as far as I can fathom, only that humans do not understand well about extremely big numbers (refer to the video titled "MF 17: Extremely big numbers").

In order for that ground to logically lead to the nonexistence, I cannot help but suspect that he has an untold major premise: each element of any set has to be well understood by humans.

Logically speaking, the major premise must be there, but I hesitate to decide so, because it is too absurd.

It is absurd because, for example, when I have picked up 3 random stones on a field and have formed (at least, I claim to have done so) a set, does the set not exist, because I (or anybody) do not understand the 3 stones well? . . . I certainly do not know their weights, their composition, where and how they have been created, how they have come there, etc., but so what? . . . For me, the criterion for the set to be legitimate is that it is clear what belong and what do not belong to the set.

As another example, the set of a single black hole does not exist, because humans do not understand the black hole well?

I have to say that such a notion of 'set' is not shared by most people.

As another major claim, he is insisting that there is not any irrational number, and his ground for the nonexistence of the square root of 2 is, as far as I can fathom, only that humans cannot handle it well (to be exact, do calculations on it, check whether another algorithm generates the same infinite decimal or not, find a canonical algorithm (refer to the video titled "MF 92: Difficulties with real numbers as infinite decimals")).

To explain more, he argues against 'Cauchy sequence' and 'Dedekind cut', but they are attempts to generally define irrational numbers, and failures of the generalization attempts (although I myself do not agree that they are failures) does not prove the nonexistence of the single irrational number of the square root of 2. And he argues against irrational numbers as infinite decimals by infinite choices (refer to the video titled "MF 92: Difficulties with real numbers as infinite decimals"), but that does not prove the nonexistence of irrational numbers by algorithms. As for irrational numbers that can be defined by algorithms (the square root of 2 is one of them), his ground is, as far as I fathom, only that humans cannot handle them well ("What is the square root of 2 + pi + 'e'?" is his usual challenge). . . . Remember that he has to prove that not any single irrational number exists.

To be sure, his claim that "any information that cannot be written finitely does not exist because the universe cannot contain the expression" cannot be used to prove the nonexistence of the square root of 2, because the square root of 2 can be written finitely as an algorithm.

In order for that ground to logically lead to the nonexistence, his untold major premise must be: "Whatever humans can't handle well doesn't exist!".

It must be so, logically speaking, but I tend to harbor a doubt, because it is too absurd.

It is absurd because, it is just about human incompetence; does the reality consider human incompetence and vanish some things just because they cannot be handled by humans? . . . What a selfish world view!

The professor is blaming that pretending to be able to do what humans cannot do is arrogance, but what is far more arrogant is deciding that something does not exist just because humans cannot do something with it.

Anyway, whatever his true major premises are, they are not shared by most people, so, they have to be explicitly stated, because otherwise, most people cannot see any logic in the arguments.

3: I Mean, Honestly Please: Major Premise Is Not a Luxury


Hypothesizer 7
 I mean, honestly please, because most people do not disclose their true major premises in most cases.

Why? That is because the major premises are too absurd or too selfish, I guess.

A critical test for being a true major premise is that it is unconditional. In other words, major premise is not a luxury shown off only on sunny days.

For example, if someone can be fair only when he or she is happily satiated, being fair is not his or her major premise; probably, "My welfare precedes others'!" is the one, which he or she will not disclose because otherwise, also other people would say "OK, then, likewise, we will let our welfare precede yours!".

If someone is wobbly about his or her claimed-to-be-major-premise, usually, that is because it is not his or her true premise, and he or she is really being driven by a clandestine major premise.

4: Then, Please Make a Consistent Explanation


Hypothesizer 7
 Once the major premises are honestly clarified, you should be able to make a consistent explanation of your theory.

Some one may say "Everyone has the right to have his or her opinion.", but I have to supplement it like this: "Everyone has the right to have his or her opinion, only if the opinion is a consistent one.".

You know, what is inconsistent is absolutely wrong, and I do not think that there is any necessity to permit the right to claim wrong theories.

I mean, almost all the opinions are hypotheses, and there can be many possible hypotheses at a time, and all of them have to be permitted to be claimed. However, any inconsistent hypothesis is just wrong, and has to be modified to eradicate the inconsistencies, or should be entirely disposed.

5: I Mean, an Unboundly Consistent One Please


Hypothesizer 7
 I mean, an unboundedly consistent one please.

Some people adamantly keep insisting that their theories are consistent, by shutting out inconvenient facts.

You know, if inconvenient facts are just shut out, any absurd theory can be claimed to be consistent in its bounded territory.

As the universe is one, all the facts really fit together, and when any new fact is found, any hypothesis, which should be a model of the reality, should be checked and be modified if necessary. . . . That is the scientific way.

6: It Is Not That Any Major Premise Cannot Be Disproved, but . . .


Hypothesizer 7
 It is not that one can adopt any arbitrary major premise.

Any major premise that is against a fact is just wrong.

Any major premise that contains a contradiction is just wrong.

Such major premises can be flatly disproved, logically.

But there can be many possible suppositions that cannot be disproved, at least, for the time being.

7: Why a Prevalent Dream Is Harmful


Hypothesizer 7
 Some people express the belief that talking it over with each other will bring an agreement, but it is an unenlightened and rather harmful (even if beautiful) dream.

It is generally impossible because the opposing parts have different major premises and the major premises cannot be generally disproved.

Certainly, some major premises can be logically disproved (as is mentioned in the previous section), but it is an undeniable fact that people who have conceived absurdly wrong major premises in the first place usually adamantly stick to their wrong major premises.

So, anyway, major premises cannot be or are very unlikely to be overturned by talking over.

With incompatible major premises, agreement is generally impossible, and encouraging to try such impossibility does no good than cause frustration.

8: To Agree to Disagree Is the Way


Hypothesizer 7
 To agree to disagree is the way.

What to do is 1) let the opponent state the major premises explicitly and honestly 2) let the opponent explain the theory unboundedly consistently 3) admit that the theory is a viable hypothesis, even if it is not one that you adopt.

It is possible even if the opponent has the major premises you do not accept.

9: Why to Agree to Disagree Is Prevalently Difficult


Hypothesizer 7
 It is possible and is even simple, but does seem to be difficult prevalently.

Why? Well, 1st, the opponent will not disclose the major premises honestly, probably because they are absurd or selfish. And 2nd, the opponent insists on the consistency of his or her theory by shutting out inconvenient facts.

The opponent displays untrue major premises and with inconsistencies being pointed out, he or she eternally wobble the displayed major premises and logic, trying to defend the conclusions in any way. The inconsistencies most inevitably sneak in, because the conclusions are not really driven from the displayed major premises, but from some clandestine major premises, so, the displayed major premises and the conclusions do not logically fit together in the first place.

Thus, the argument becomes a bottomless swamp.

Such an argument is meaningless, because the theory being argued about is just a decoy that is not adopted even by the opponent.

10: Of Course, One Can Change Major Premises, but . . .


Hypothesizer 7
 I said that any argument in which major premises are wobbled is meaningless, which does not mean that one should not change his or her major premises.

In fact, to change one's true major premises is a quite noble, laudable act, which is rarely seen.

What is prevalently seen is not that, but clandestine major premises are adamantly unchanged, while decoy major premises are put out, tweaked this way and that way, pulled back, and put out again, and so on, patching up an inconsistency creating a new inconsistency elsewhere, never reaching a wholly consistent theory.

If one changes his major premises, that is very good, but he or she has to do that explicitly and make a wholly (unboundedly, of course) consistent explanation based on the new major premises, that is what I mean.

11: "Insights into Mathematics" Is Very Thought-Provoking, Anyway


Hypothesizer 7
 The channel is a very peculiar phenomenon: sometimes, it is really educative; sometimes, it is impressively beautiful; sometimes, it is absolutely unacceptable; anyway, it is very thought-provoking.

Watching it, I have thought about the relationship between the reality and a human-made model, the limitation of digitization (at least, of finite digitization), anthropocentrism, arrogance, argument, etc., mainly from standpoints that oppose to the channel.

An interesting fact is that just because something is not agreeable does not mean it is not valuable.

I want to talk more concerning the channel, in some future articles.

References
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