Yet they don't — LuckyR

yet they don't what?

They fret about making "wrong" decisions (making mistakes) — LuckyR

yes, that's certainly part of the process.

let me rephrase: it doesn't match MY intuition, and many other people. To many of us, (2+2=4) implies (Kamala Harris is a presidential nominee) makes no sense even if the classical logic truth table comes out as true, because the left side of the implication at least seemingly has nothing to do with the right side.

Maybe it matches your intuition, and I'm sorry for trying to speak for you. My mistake.

A→B is somewhat straightforward, A implies B. And logic here agrees with our intuition. — Lionino

I'd push back against this - this is one of the most egregious examples of logic disagreeing with our intuitive use of implication.

In classic symbolic logic, a -> b is true, according to its truth table, if, for example, a is true and b is true.

(2+2=4) implies (Kamala Harris is a presidential nominee). These is true in classical logic. But it doesn't really match our intuition at all.

The point being, of course everyone should deliberate on important questions, therefore the deterministic worldview leads to imprudent decisions — NotAristotle

But if you know that determinists do deliberate, despite being determinists, then you know that that's not an example of determinism leading to imprudent decisions.

Even putting compatibilism aside, I have spoken with many determinists in my life, and not a single one of them came to the conclusion that "determinism is true, so I should never deliberate" - so if that's the argument you have that determinism leads to imprudent decisions, it seems empirically that that's just simply not true.

In my experience, the kind of thought process that leads to things like "determinism is true, so I should never deliberate" isn't generally a thought process determinists usually think, it's usually a thought process non-determinists imagine determinists think. I don't know where I'm going with that train of thought, but I think it's interesting nonetheless. Non-determinists think, "If I was a determinist, I would think this", but determinists themselves almost never actually think this...

But I didn't — I like sushi

You didn't ... make an op in which you talk about determinists and what they think and what their ideas are? Come on dude.

Your op talks about determinism as if compatibilism isn't a type of determinism. It's not off topic to point out, hey, compatibilism actually is a type of determinism! And a compatibilist determinist would answer some of the questions of the op differently from how a non compatibilist determinist would.

Not interested in that discussion whatsoever. — I like sushi

You made an op in which you talk about determinists and what they think and what their ideas are, and the consequences of their ideas - whether you like it or not, some determinists are compatibilists. You don't have to reply to me if you don't like what I'm saying.

Let me put it this way:

There's these apparently competing ideas of how the world works. One idea is, we are "agents", and agents have minds and make decisions and use the bodies they're commented to to enact those decisions in the world.

The other idea is, the world chugs along via physical causality.

And then there's the compatibilist approach, and one way to frame it is as a combination of both of those statements. There are agents who are enacting their decisions in the physical world, but the implementation of an "agent" is also entirely physical and happens in brains. So you have the agential view of the world simultaneously with the physically-casual view of the world.

There is a very real difference as outlined in the OP. — I like sushi

Just because some person wrote that there's a difference in some OP doesn't make it so

the alternative is that there isn't a real difference between those things.

Between a series of specific brain states, compared to pondering and weighing the options in ones mind.

Who is to say that the entire experience of pondering and weighing ones options in the mind doesn't emerge from, and is entirely supervenient on, a sequence of brain states, pushed forward by physical causality?

Then why not reference that in the OP? — Bob Ross

Because I wanted to talk about the question of their contradictoriness without the baggage of the riddle. I think most people got the correct answer, and understood the question, anyway.

why? He's acting exactly as he's determined to. What's the line of reasoning that ends with "therefore I shouldn't deliberate?"

yes, he keeps talking like you can just skip straight to the end, but... that's not how determinism works in principle.

You can't just cut out deliberation if deliberation is part of the determined process.

you talk about it as if they could choose not to

The way I've stated it is relevant to this:

https://en.wikipedia.org/wiki/Barbershop_paradox

The way I stated it was no more or less vague than it needed to be for it's relationship to that.

I think it should be worded as "Elvis is a man DOES imply that elvis is NOT simultaneously immortal and mortal".

It positively implies something, rather than "does not" imply something.

Elvis is a man does not imply that Elvis is both mortal and immortal – (A → ¬(B and ¬B)) — Lionino

Is that the right English translation of that?

Keep in mind that ¬(B and ¬B) is equivalent to B or ¬B - would you say A → (B or ¬B) can be worded as "Elvis is a man does not imply that Elvis is both mortal and immortal"?

Depending on circumstances, it might make more sense to say something like "A can't be proven to imply a contradiction" rather than "A doesn't imply a contradiction". Classic symbolic logic is very constraining, and it's hard to express certain things that seem simple in natural language.

the goal anyway is to translate "A does not imply a contradiction", not any other phrase. — Lionino

This might seem crazy to you, but I would translate that as just A, or in other words, A is true. If you are stating, for a fact, in classical logic, A definitely doesn't imply any contradictions, and we also know that false statements necessarily do imply contradictions, then the only way to say "A definitely implies no contradiction" is to say "A is true"

https://www.umsu.de/trees/#~3a~5(a~5~3(b~1~3b))


https://www.umsu.de/trees/#~3a~5(a~5(b~1~3b))

I would reword it from "a does not imply a contradiction" to "a implies this particular non-contradiction".

And when a is false, it implies everything, contradictions and non contradictions.

What's the general beliefs here regarding Trump's culpability for the infamous events of January 6?

The two main takes are:

he incited what happened
he didn't incite what happen

each of those takes usually has two subtakes, ...and it was good/acceptable, or ...and it was bad.

I have a kind of in-between take when it comes to the two main takes - I'm not convinced he did incite it, but I am convinced his actions after it started make him ethically culpable for it anyway. His actions after it started, reportedly, are he watched it unfold on TV, just sitting there watching it, and people around him kept asking him to make an announcement to stop it, an announcement that would hopefully reach the people at the capitol somehow, a request for them to stop and go home. And when he was requested to do that, repeatedly, he refused.

This makes me think that one of the two situations is the case:
1) he did deliberately incite what happened, even if his literal words allow for some plausible deniability
2) he didn't deliberately incite what happened, but *he was perfectly happy to see it unfold anyway*

There's not a good argument to be made that he didn't want it to happen, because he's a Leader, allegedly, and as a leader if he didn't want it to happen, and he didn't lift a finger to stop it, then... that's no leadership at all. If you want to excuse his lack of action, you cannot simultaneously believe he's a good leader. So either he wanted it to happen, or he's an exceptionally poor leader, not both. And it's clear to me that he IS able to get people to follow him, so if it was his will to stop what happened, he absolutely could have. He didn't want to stop it.

But is that criminal? If he has (a) plausible deniability in the words that led to the riot, and (b) just failed to do anything to stop it, is that criminal? Should it be?

Obviously if you think storming the capitol was good or ethically neutral, then that question doesn't really matter. But if you think it was bad, what happened at the capitol, then the obligation of a person to stop something bad from happening does matter. Some people don't beleive in obligations like that - some people believe you don't have to stop anything bad from happening if you didn't directly make it happen, and his plausible deniability in his words at the rally that preceded the storming arguably give the defense that he didn't directly make it happen.

So, how much plausible deniability does he have for what happened?
And, regardless of that deniability, was what happend *bad*?
And what kind of responsibility does he have given his refusal to lift a finger to stop it?

One way of approaching the problem might be thinking about the fact that wars are fought - some wars - ostensibly over freedom. Which means that a huge portion of humanity thinks it's sensible to take and give lives in exchange for freedom. So this seems to be an example of people valuing freedom over some other things.

So the challenge is, I guess, proving it.

I don't think the challenge is in principle possible to provably solve, because value doesn't seem to be a universally objective measure. In other words, I don't think there's an objective answer to "How many lives are worth exchanging for how many peoples freedom?" just like there's no objective answer to "How many scoops of chocolate are worth 5 scoops of vanilla?"

Since one entails the other but other does not entail one, we may say that everytime «A implies a contradiction» is false, «A does not imply a contradiction» is true; but it is not everytime «A does not imply a contradiction» is true that «A implies a contradiction» will be false. Therefore there is an assymetrical relationship between the two statements quoted.
The prover confirms my intuition:
(a→¬(b∧¬b)) does not entail ¬(a→(b∧¬b))
¬(a→(b∧¬b)) entails (a→¬(b∧¬b)) — Lionino

Which one of the above phrases are you saying is the english translation of (a→¬(b∧¬b))?

It's either «A implies a contradiction» is false
or «A does not imply a contradiction» is true, right?

But consider this:
((a → ¬(b∧¬b)) ∧ ¬a) → (a → (b∧¬b)) is valid

(a→¬(b∧¬b)) doesn't actually stop a from implying a contradiction - it can be assumed true, and still be the case that a implies a contradiction.

¬(b∧¬b) just means (b v ¬b)

It seems plausible that:

(φ^~φ) takes on the meaning of <explosion> as the antecedent of a modus ponens
(φ^~φ) takes on the meaning of <reductio-rejecton> as the penultimate step of a reductio
(φ^~φ) takes on the meaning of <false> as the consequent of a modus tollens

Weren't you mocking me earlier in the thread for relating this side of logic to the principle of explosion? Or was that someone else?

Assuming contraposition and MP is the same as assuming MT. — Lionino

This of course makes the argument you brought up for MT circular. That's fine, we can move past that and find one that obeys the rules presumably.

so there are more rules to the game then, apparently.

Rule 1. Don't assume mt.
Rule 2. Don't simultaneously assume contraposition and MP

Can I assume MP if I don't also assume contraposition? Can I assume contraposition if I don't also assume MP? Are there any more rules you haven't explicitly stated yet?

Are there any proofs of MT that obey the rules of the game we're playing? Obviously the one you've been talking about doesn't obey .

My proof did not assume mt, it did assume contraposition and MP.

If you believe that's the same as assuming mt, then that means the proof of mt that uses those two assumptions is circular.

yes, using MP, not mt.

If it's circular, fine, give me one that isn't circular. I assumed, perhaps wrongly, that when I asked you for a proof of mt that you like, that you wouldn't like an explicitly circular one.

Give me a proof of mt you like that isn't circular.

so you believe the MP+contraposition argument is circular? It's just using mt to prove mt?

You want a proof of some argument Y that doesn't assume modus tollens.

You presumably have a proof of Modus tollens that you like, that doesn't itself assume modus tollens.

Whatever format of argument that proof takes - that argument that doesn't assume modus tollens, but proves Modus tollens - I can use that exact same format of argument to prove Y similarly without assuming Modus tollens.

I've already done it above, but I can do it again

if you give it to me I will show you how it makes perfect sense

you want a proof of ρ→(φ^~φ) , therefore ~ρ that doesn't assume modus tollens, if you give me your preferred proof of Modus tollens I can give that to you.

didn't really talk about proving MT at any point, so I don't know why you are asking that. — Lionino

You don't know why I'm asking what?

MT can be derived from MP and contraposition — Lionino

Ok, I'm going to assume you mean this proof (the one wikipedia lists as "Via contraposition"):

1
P→ Q (Given)
2
¬ Q (Given)
3
¬Q →¬P (Contraposition (1))
4
¬ P (Modus ponens (2,3))

This is the proof of modus tollens that you like - it proves modus tollens without assuming it, correct?


So it's pretty straight forward to use the same format, I'll take my previous argument which assumes Modus Tollens:

ρ→(φ^~φ) (premise)
~(φ^~φ) (law of non contradiction)
:. ~ρ (modus tollens)

And reformat it to be in the style above, the proof that you like of modus tollens that doesn't assume modus tollens:

ρ→(φ^~φ) (premise)
~(φ^~φ) (law of non contradiction)
~(φ^~φ)→ρ (contraposition)
:. ~ρ (modus ponens)

I'm asking you what proof you like - that's not a claim that mine is a proof of that. What proof of Modus tollens do you like?

I didn't say mine was, are you reading the words I'm posting?

what proof of Modus tollens do you like? We can prove φ→(ψ^~ψ)⊢~φ without assuming Modus tollens is the case, but by instead directly using the proof of Modus tollens.

if not by modus tollens? I don't think we do. — Lionino

Ok so we're playing a game (I don't mean that pejoratively, I like games) where we have to prove the conclusion without using modus tollens, is that right?

What are the rules of the game? Are we allowed to use the rule of non contradiction?

You said before that the proof for modus tollens is easy - does that proof obey the rules of this game? If so, which proof of Modus tollens do you like? There are multiple, I want to make sure I'm using the right one.

I will play this game, if you answer my questions then we can have a solution.

This is perhaps my favorite proof for the modus tollens thus far. The question is whether that second step justifies the modus tollens. — Leontiskos

This isn't a proof of Modus tollens. This is a use of Modus tollens.

You've been asking for 12 pages for a proof of Modus tollens?