Voyager
2yr ago
No it won't.
Now you're making an unsupported assumption about my character instead of an argument. Retract it and apologize.
Obvious circular reasoning. You believe X is false, and you say it's possible for you to be convinced that X is true if X were true, but X is false, because you believe X is false.
No, I proved X is false separately. "X is false, because I believe X is false" is not an argument I've made.
Do you accept the possibility that X may be true? Yes or no.
No. X is a mathematical claim, and it's proven false.
Note that if you make a new argument I will consider the possibility again while analyzing your argument.
Voyager
2yr ago
But 0 is what we think, because 0 is 4. You're just changing the representation. It's like saying "You think 2+2 is '4', but it's actually 'four'".
Also, the claim in your post was
So there you have it: 2+2 is not necessarily 4.
which is wrong whether or not 2+2=0 can be true.
Voyager
2yr ago
Either way 2+2=0 can be true.
Only because 4=0. So 2+2=4 is true, and the central claim of your substack post is wrong.
Correct?
No. Some basic mistakes:
-
Isomorphy requires preservation of structure, in our case the structure of respective additions. This is not the case: Addition in
{0,1,2,3}works different than inℤ/4ℤ. -
We don't say an element in a structure is isomorphic to one in another.
-
(ℤ/4ℤ)*is an entirely different structure. For starters, it contains only 3 elements. (The*signifies we're excluding the 0.)
Voyager
2yr ago
In your opinion, which isn't infallible.
Is that supposed to be a counterargument?
This is not enough.
Yes it is. Listening to your case and engaging with your argument will make me change my mind if your case is convincing enough.
Therefore it's impossible for you to be convinced of anything (about Alice and even less of Bob), and there's no point in me even trying.
No, it's still possible for me to be convinced of true things.
You'e right there's no point trying to convince me of a false statement about math. Instead you should let yourself be convinced by me.
Voyager
2yr ago
Information is always missing.
Not information that is available and relevant to the argument. I already explained that to you. Stop defending your fallacious argument.
No, you are deliberately not engaging with my argument.
To the degree I am, it's because you're trying to set up a red herring.
Voyager
2yr ago
You appear to be approaching the question from a context of laws and other highly legible systems of formal rules. If I'm understanding you correctly, the idea would be that there's a clear separation between the legal rules and the justice system, and the various sorts of informal social consequences for lesser transgressions, with the idea being that the latter are perhaps less important and can more or less be ignored. If someone's not breaking the law, they should be left alone to do as they please, and we should in fact maintain a broad commons of unpoliced social space where people, generally, mind their own business and live and let live.
I don't think you understood me correctly, I made no such distinction.
My point applies equally to informal social punishment: You should punish bad actions, not "bad people". At its basis, that's an ethical principle. No one deserves punishment for existing.
It is not obvious to me that this is actually true. I know that libertarians and Enlightenment idealists of the first water think it's true, and even desperately want it to be true, but many of the arguments they present seem to me to cash out in various forms of just-world fallacy. Censoring people doesn't seem to lead to you getting censored in any sort of causal fashion.
There seems to be another misunderstanding here. By "honest people" I'm not referring to the people who want to oppress scoundrels, in fact I believe these people are very often not honest. I'm thinking people who are minding their own business, innocent people.
My point is not that oppression is shortsighted due to risk of backfiring, but ethically fraught due to risk of hurting innocent people (as well as on its own merits in a vacuum). And it does seem obviously, trivially true that if you cut down the law (or non-law principle), it can't protect people anymore.
That said, the risk of backfiring is higher than you believe. Purity spirals, the revolution eating its own children. You talk about the soviets, but "the soviets" includes many people who did not in fact win in the end. Trotsky lost the power struggle with Stalin, and suddenly Trotskyists were considered scoundrel. Yezhov led the great purge and fell to it himself. Not everyone gets to be Stalin, so even the person who doesn't care about hurting innocents might consider self-interest.
What protects honest people is a cohesive society of other honest people who share their values and their understanding of who is and is not a scoundrel, and are willing and able to punish defectors appropriately. Lacking that, all the laws in the world will not save them.
You can't sustain an understanding of who is scoundrel. As you say yourself:
The distinction does not seem sustainable at our present social scale.
The issue is that if you go after bad people and aren't fair to them, it becomes hard for supposed scoundrel to defend themselves.
This also means dishonest people gain power, because they can falsely accuse honest people of being scoundrel. The solution is to go after bad actions, and fairly, so the accused gets a chance to correct potential mistakes.
Voyager
2yr ago
Yes, but the premise of this line of thought is precisely the opposite: it's not easy to prove Bob isn't racist, other other hand it's extremely easy to prove Alice isn't racist.
That's my exact point. If you prove Alice isn't racist, you haven't proven anything relevant. You're just nitpicking. The actual relevant question of whether Bob is racist is unaddressed.
But discussing is not accepting. You are arguing that Bob is a racist, but you are nowhere near accepting the possibility that he might not be.
I'm accepting the possibility Bob might be racist to the degree I'm required to: I'm listening to the supporting case and engaging with your arguments.
Your arguments that Bob is racist just aren't convincing. You're mainly arguing he's as racist as Alice and I happen to know she isn't. And instead of leaving it at that until you make a better argument, which I could, I'm trying to work out why you think Alice is racist and how it applies to Bob, and arguing against that.
You are not willing to accept […]. Which proves my point.
No, I'm not accepting your point because it's false. You don't get to twist opposition to your argument into support for your point.
The information in English is limited too. Information is always limited.
"Tomorrow is Monday" has limited information.
Exactly. And because the information is limited, relevant information is missing, and you can't make your argument. If you include the missing information, e.g. by saying "Tomorrow is monday, calendar week [current+1]", it becomes obvious that your claim is false, your example only appears to support your claim because information is omitted. It's evidently possible to include this information. Talking about "limited information" is nothing but a smokescreen to hide your attempt to deceive by strategic omission.
The case where the week ends in Saturday is included.
I was specifically addressing the other case (because "this doesn't change if the end of the week is saturday" is obviously irrelevant when the first part 'this' refers to is wrong.)
You claim the information is available because if the week ends in Sunday "we both know" when the week ends. No, we don't, because I don't. If you want to claim you know when the week ends from the phrase "tomorrow is Monday" go ahead, I do not know.
No, I claim I know when the week ends from the phrase "the week ends in sunday", which was included in your example. You're playing obtuse.
And it doesn't seem to me you are engaging with my argument.
That's because you're not understanding (or pretending to not understand) my critique thereof.
My example was crystal clear in explaining that the day the week ends does not matter in describing what day comes after Sunday.
And this claim is simply not true. It does matter if we are interested in what week it is. Your example doesn't show that because it's just colloquial speech where (relevant for us) information is omitted, which is the opposite of crystal clear.
I showed that by giving a counterexample, where it does matter.
Voyager
2yr ago
So it's essential.
No it isn't. You will never encounter it in most math fields. Philosophy mostly is what you do when you aren't busy with concrete problems.
Depends on what you mean by "doubt".
What should an engineer do who needs to calculate 1+1 to design a bridge? I hold that anything but "answer 2 and move on" is wasting time that could be used to build a bridge.
Scoundrels should be oppressed.
Scoundrels should have justice coming to them, for the bad things they actually do, no more, no less. Doing more than that, because they're bad people who deserve being treated badly, is not justice, and it's not what the justice system is supposed do to, and it can get out of control quickly. That's not autoimmune disorder, that's leukemia.
As long as you're keeping to justice, punishing scoundrels for scoundreling, not for existing, honest people have little to fear. Once you cut down the law to get at scoundrels who "hide behind it" by abiding it, it doesn't protect honest people anymore either.
Another issue is that scoundrel can mean bad people, but it also can mean icky people. Lolicons are the latter.
Voyager
2yr ago
You can't define (or redefine) the meaning of a word in common language. It already has a meaning. What you might call a definition is a description of the meaning, and you measure it by how accurately it overlaps the usage.
Caplan notes that the "classic" description of feminism is inaccurate and offers a better one.
This shouldn't be surprising as a self-description of a political movement is unlikely to be optimized for accuracy or clarity. It's optimized for supporting a political goal, and that goal may well be furthered by deception and deliberate confusion.
(You can take a word, redefine it, and then use it throughout the scope of that definition (e.g. a book).
In math, this works fine, but in politics/political science, it takes exceeding intellectual rigor and honesty, because the words you use have connotations and it's hard to keep them out and use your definition straight.
And when you talk to other people, who don't subscribe to your definition, you have to redetermine all implications of the new concept, and that's not going to happen.)
Voyager
2yr ago
If a person says "Bob is as racist as Alice", and I show that Alice is not racist, then says, "OK. Bob is as racist as Mary", and I show Mary is not racist, "OK. Bob is as racist as Linda", Linda isn't racist. Wouldn't it make sense to doubt whether or not Bob is actually racist?
Okay, but if someone says "Bob is as racist as a KKK grand wizard", it would still make sense to doubt it. Conversely, if they say "Bob is as racist as Alice, because he's the author of the bobracial supremacy manifesto", pointing out Alice isn't racist just distracts from the point at hand. Yes, it's a bad metaphor, but the point stands.
Compare this discussion. I have refuted your argument that 2+2=4 is not unequivocally true, but I'm still willing to discuss the point you were trying to make without forcing you to come up with a new example.
It contains the congruence class 4Z (= {...-8,-4,0,4,8...}) of which the number, more so the symbol, 4 is a valid representant.
The statement remains true.
Voyager
2yr ago
Wrong. Information by its very nature is limited. Nobody is "artificially" limiting the information that can fit in one bit, one bit can only fit one bit of information. Period.
That's a red herring. We're not talking about bits. We're talking about the information we have about your example, which was given in english.
No, we don't. You are assuming where the week starts.
Liar. The end of the week being sunday was included in your description of the example.
All information is incomplete.
Not all information is incomplete in the sense that reasoning from it leads to false conclusions. Stop defending your fallacious argument.
Absolutely not. The speaker knows what the statement means, what the symbols mean, in what structure we're operating. The rest is just basic arithmetic over the natural numbers.
Voyager
2yr ago
No? So nobody in mathematics doubts the Zermelo–Fraenkel set theory axiomatic system?
Doubt about axioms is basically mathematical philosophy.
Who said an engineer should doubt 1+1=2?
So you agree doubt about everything is not reasonable in every field?
Voyager
2yr ago
I literally said "it doesn't matter if Bertrand Russell personally doubted it or not".
No one doubted it, because it wasn't actually reasonable to doubt it. Russell wanted to formalize a foundation, he wanted to prove that arithmetics derived from logic, not that arithmetics was true.
Doubt is essential in all fields.
Not doubt about math or fundamental logic. That is only reasonable in philosophy. An engineer who doubts 1+1=2 will never build any bridges, and no bridges will crash because an engineer assumed 1+1=2.
If you doubt the fundamentals, you're doing philosophy. If you want to get anything done, you need to stop doing philosophy. You need to choose some axioms, build a knowledge base and then get to work on questions that are actually in doubt.
100% certainty is extremely dangerous. And I don't see you addressing this at all.
Because right now a fallacious argument is being made for too little certainty, not too much. I'm addressing the bad arguments that are actually on the table.
Voyager
2yr ago
If the speaker who brought up 2+2=4 is using standard symbols, he's unambiguously correct, so that can't be what we're talking about.
Voyager
2yr ago
In our case, informations isn't just limited, but artificially limited, i.e. omitted. The information is indeed still available, just by deriving it from context. We both know monday after sunday is next week.
You're making an argument based on information you know is incomplete, and the missing information invalidates it. Don't do that.
Voyager
2yr ago
Not really. I can guarantee you that Russell used 1+1=2 when calculating his daily expenses even before he formally proved it. Had he failed at his attempt to prove it, he would have gone on believing and using it. I can guarantee you he didn't scold any colleagues for using 1+1=2 without proof.
He wanted a formal proof for itself, not because one was needed.
Voyager
2yr ago
If you're omitting the information of which week it is because it's not relevant, you're omitting information, and that means you can't use the result to support your argument, because it's missing information.
Voyager
2yr ago
In general? Yes. In this example? Absolutely the speaker's fault. If you're using non-standard symbols, you need to denote that.
Voyager
2yr ago
But your clock would read 01:00.
We use this concept in programming all the time. If the week ends in Sunday we don't say that the day after that is Monday the next week, it's Monday
That's merely convention, omitting information that can be derived from context for brevity. If you want to make a formal argument, you need to include that information again. Everyone is aware monday is next week, that's why you don't spell it out if it isn't relevant, but if you're e.g. scheduling business on a weekly base, you might have to say "Tomorrow is monday, which is next calendar week".
Nevertheless it is the case. We think 4, 4 is 0, therefore "0=not what you think" isn't true.
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