...

There he is again.

Basically I agree that the dialectic doesn't have "to worry" about the PNC in the sense that it's philosophically legitimate. — Moliere

The result of contradiction in classical logic is not just vague - it's quite literally anything.

(p ^ ~p)⊃q. From a contradiction, anything goes. That is, if we allow contradiction then everything is both true and false, and we cannot explain anything. There are various systems of paraconsistent logic that accomodate or mitigate explosive results, so I won't rule out some form of dialectic, but I won't rule it in, either. (see what I did there...?)

This would make more sense if we paid attention to the dichotomistic manoeuvre involved. — apokrisis

While dialectic has a certain appeal, I'm not as enamoured by it as you. I see two major issues. First, and most obviously, in classical logic asserting something and its negation leads to contradiction, not to some third option. Priest and others have addressed this wonderfully by playing with the law of non-contradiction, developing some intriguing alternatives. But it remains that the sort of contradiction seen in dialectic is not the sort of contradiction found in formal logic. What a dialectic contradiction is remains, I think, ambiguous

And secondly, even if we supose that dialectic does not breach non-contradiction, the result is not clear. Given the Principle of Explosion, anything could follow from a contradiction, so given a thesis and an antithesis, the nature of the resulting synthesis is far from fixed.

So I would rather not glorify dialectic by calling it a "logic".

The task is to build ourselves as beings with the agency to be able to hang together in an organismic fashion. — apokrisis

Why?

That "ought" thing, again.

Logic isn't a replacement for natural languages. Nor is it a set of rules for how one ought construct arguments. This was part of the subject of my thread Logical Nihilism, and the work of Gillian Russell.

in English, there is no lexical distinction between inclusive-or and exclusive-or, but A∨B is inclusive-or, meaning the result is also True if both are True. — Lionino

So what logic does in this case is to set out explicitly two ways of using "or" of which we were probably unaware. After understanding this we are able to say clearly whether we are using an exclusive or an inclusive "or". Prior to that logical analysis, we were probably unaware of the distinction, let alone which we were using.

So logic here is setting up a degree of precision that can carry over into natural languages. It's acting as a tool to make clear what it is we are doing with our sentences.

It's a mistake to think that there are laws of logic that have complete generality - and must be obeyed in all circumstances. Rather logic sets out sub-games within language, with their own specific rules. Natural languages permit the breaking of the rules of any of these sub-games.

Take a look at these examples from Russell. ϑ ⊧ ϑ and ϑ & ϒ ⊧ ϑ might seem to be candidates for logical laws one might expect to have complete generality.

Identity: ϑ therefore ϑ;: a statement implies itself. But consider "this is the first time I have used this sentence in this paragraph, therefore this is the first time I have used this sentence in this paragraph"

Elimination: ϑ and ϒ implies ϑ; But consider "ϑ is true only if it is part of a conjunction".

Logic sets up systems in which some things can be said and others are ruled out, but natural language is far broader than that, allowing for the breach of any such rule.

Logic doesn't give us a crystalline replacement for natural languages. But it can set out clearly what it is we are doing with our statements.

Thanks — Wayfarer

Cheers.

I am versed in anglo philosophy, with its emphasis on critique. It's not sufficient to learn about Buddhism or scientism, they must also be subject to analysis, which is roughly to see how consistent and complete they might be. But having said that it remains possible that any inconsistency I see is not apparent to those who are better versed. The trick then is to explain such inconsistency.

You are probably aware already of my disregard for the Kantian notion of the thing in itself. I can't see how to make sense of it in a way that enables it to be useful. If there is a way that things are that is outside of our comprehension, then it is irrelevant to that comprehension. The only practical consequence can be a nod to the mysterious, and silence. We cannot access "the world as it is in itself", not because it represents some profound fact about the world and our relation to it, but because the thing-in-itself is a useless metaphysical construct.

It is apparent that there is a distinction between what we believe and how things are. This distinction explains both how it is possible that we are sometimes wrong about how things are, and how we sometimes find novelties. In both cases there must be a difference between what we believe is the case, and what is the case. We modify what we believe so as to remove error and account for novelty; which is again to seek a consistent and complete account.

The "we" here is intentional. What is so loosely labeled "experience" only takes place in a mind and brain embedded in a community. There simply is no way to remove our communality, and any account that does not take this into consideration starts broken. It's not you looking out the window, but us. Something to be acknowledged if we would take into account the "experience of looking".

So there is a manifest difference between the way things are and the way we believe that they are. Yet we are, as you point out, "participants, moral agents, in our own lives", so to this we must add a difference between the way things are and the way we want them to be. It's this difference that is relevant to 's question. "Fair and just" is not found in the way things are so much as the way we want them to be.

I asked ChatGPT... — Wayfarer

Et tu? I can't accept GPT as authoritative. In any case, if your idealism claims that the world is inherently mental, it must respond to the three puzzles - other people, that we are sometimes wrong, and novelty. If your idealism claims only that our beliefs are mental, it misses the relation between the world and what we believe.

I can't help but contrast your response to me and your response to @Gnomon, here: . Analytical Idealism is not, so far as I can make out, a form of Epistemological idealism. So again, you seem to me to want your cake and to eat it, by answering issues I raise from the point of view of Epistemological idealism while answering issues others raise from the point of view of ontological idealism.

it is empirically true that the Universe exists independently of any particular mind.

Take this as granted.

But what we know of its existence is inextricably bound by and to the mind we have

We can grant the point that we only know things with our minds.

and so, in that sense, reality is not straightforwardly objective.

Reality is just what is the case. It is neither subjective nor objective, it just is.

It is not solely constituted by objects and their relations.

Neither here nor there.

Reality has an inextricably mental aspect, which itself is never revealed in empirical analysis.

This has not been demonstrated. What has been shown is that what we know "has an inextricably mental aspect".

Whatever experience we have or knowledge we possess, it always occurs to a subject...

What we experience and know, is about reality, but is not the whole of reality.

— a subject which only ever appears as us, as subject, not to us, as object.

Indeed, what we know is mental, but that does not imply that the world is mental...

The argument attempts to show that the world is partially mental, but only succeeded in showing that the what we say about the world is "mental".

That is, the argument presented here does not demonstrate it's conclusion.

Compare this with my own response to

Fairness is not something we come across in the world.

It's something we do in the world. — Banno

Which if nothign else has the advantage of not being dependent on collapsing wave functions.

I admire @Wayfarer's work, and that he and I agree on a great many things. In particular we both have a distrust of scientism, as well as the sort of speculative physics that is neither good physics nor good philosophy.

And I agree that there is a division here that needs acknowledgement. For Way, it is the difference between the world and mind. For me, it is the difference between how things are and how they ought be.

Perhaps an analogy will help. In a corporate body, understanding the way things are is a job for the bottom level of management. Middle management at best looks at how to get what the corporation wants. But deciding what the corporation wants happens at the top. It is a far more difficult issue than simply describing how things are.

(Unfortunately those in charge of deciding what corporations want usually grossly simplify the problem by saying "more profit", thus denying their place and rendering themselves mere Apparatchik.)

Reality "exists independently of any particular mind" yet " has an inextricably mental aspect".

Again, you mix two quite different things - the world, and what we say about it,

Yes, reality exists independently of any particular mind. But what we say about reality is inextricably dependent on us.

These are two quite different things.

"Put another way"?

Here:

Hence there is no need for me to deny that the Universe is real independently of your mind or mine, or of any specific, individual mind. Put another way, it is empirically true that the Universe exists independently of any particular mind. But what we know of its existence is inextricably bound by and to the mind we have, and so, in that sense, reality is not straightforwardly objective. It is not solely constituted by objects and their relations. Reality has an inextricably mental aspect, which itself is never revealed in empirical analysis ¹. Whatever experience we have or knowledge we possess, it always occurs to a subject — a subject which only ever appears as us, as subject, not to us, as object. — The Mind–Created World

" ...it is empirically true that the Universe exists independently of any particular mind."
yet
"...its existence is inextricably bound by and to the mind we have"

He wants his cake and to eat it.

I'll let A.C. Grayling describe this one: — Count Timothy von Icarus

Where? Citation?

This thread has strayed away from the relatively simple yes/no/maybe question of a Just World --- where your opinion is just as valid as mine --- onto the open-ended (infinite ; non-empirical ; unverifiable) question of Subjective vs Objective Reality.

To Wit : Various interpretations of Quantum "collapse" seem to split along the line of another non-empirical question : is there a truly general Objective Observer to maintain the cosmos in Potential (statistical uncertainty - probability) when no specific Subjective observer is looking (measuring) to make it locally certain (Actuality)? Is it true that, the quantum waveform, and the immaterial field within which it is waving, is a generalized mathematical abstraction (mental image), not an observed real event? — Gnomon

One might even say that the latter has little if anything to do with the former - that how things are is a different type of question to what we should do.

From A Private View of Quantum Reality.


If this were how the wave function is, unobserved, then there is a way that the wave function is, unobserved.

Or is it that there is no "way that the wave function is", unobserved?

Which goes against 's story.

Sure, all that. You want your cake and to eat it.

On the one hand there is a world that is as it is 'independent' of us.

On the other, what we say, think, know, believe, conjecture, doubt or whatever is dependent on us - not us as individuals but us as a community.

But this just means that knowing, believing, conjecturing, doubting or whatever are dependent on us; but not that the world is dependent on us.

You cannot, from your argument, reach this conclusion.

Picture a tranquil mountain meadow. Butterflies flit back and forth amongst the buttercups and daisies, and off in the distance, a snow-capped mountain peak provides a picturesque backdrop. The melodious clunk of the cow-bells, the chirping of crickets, and the calling of birds provide the soundtrack to the vista, with not a human to be seen.

Now picture the same scene — but from no point of view. Imagine that you are perceiving such a scence from every possible point within it, and also around it. Then also subtract from all these perspectives, any sense of temporal continuity — any sense of memory of the moment just past, and expectation of the one about to come. Having done that, describe the same scene.Now picture the same scene — but from no point of view. Imagine that you are perceiving such a scence from every possible point within it, and also around it. Then also subtract from all these perspectives, any sense of temporal continuity — any sense of memory of the moment just past, and expectation of the one about to come. Having done that, describe the same scene.

“Impossible!” you object. “How can I imagine any such thing?! It is really nothing at all, it is an impossibility, a jumble of stimuli, if anything — this is what you are asking me to imagine! It is completely unintelligible.”

But that is my point. By this means I am making clear the sense in which perspective is essential for any judgement about what exists — even if what we’re discussing is understood to exist in the absence of an observer, be that an alpine meadow, or the Universe prior to the evolution of h. sapiens. The mind brings an order to any such imaginary scene, even while you attempt to describe it or picture it as it appears to exist independently of the observer. — The Mind–Created World

Remember this?

SO let's go back to your meadow. I stand facing you. A butterfly flutters between us. You say "See the butterfly flutter from left to right!" I reply "Beautiful! But it went from right to left!"

"Ah," says you, "and from this we see that what is happening in this world is true or false only with reference to the perspective of some observer! For you, it is true that the butterfly went right to left, but for me it is that the butterfly flew left to right!"

But me being Banno, you know I'm going to disagree. "How can something be true for one of us and not for the other?" I ask, scratching my nose. You carefully explain again how truth, the way things are, is dependent on perspective, and that as a result mind is integral to the whole of reality; how we cannot have the "view from nowhere" required for truth to be independent of some point of view.

"Oh." says I. Then I sit quietly for a while, arms folded, staring at the ground, while you glory in the vista.

"If we swapped places, it would be you who says that the butterfly flew right to left, while I would say it flew left to right"

"Yes", you explain patiently, "The truth is dependent on one's perspective, so if we swap perspectives, we swap truths".

"But we agree that the butterfly was flying away from the river and toward the mountain", I finally offer.

"S'pose so", says you, in the hope of shutting me up.

So on we traipse, over the foothills, through the pass to the valley beyond the mountain; all the while, butterflies flitting past us, heading in the same direction.

Over a cup of coffee, I return to the topic. "Yesterday, the butterflies were going towards the mountain. Now, they are going away from the mountain. And yet they are going in the same direction. How can that be?"

"Well," you patiently begin, "both the butterflies and we are heading East, towards the rising sun. Yesterday the mountain was before us, and now it is behind us".

"Oh. So yesterday the butterfly was heading East, and today it is still heading East, and this is a way of saying which way the butterfly is heading?"

"Yes", you agree, thinking to yourself that next time you might choose a different companion.

"Yesterday we disagreed that the butterfly was heading left to right or right to left, and that this was because we each have a different perspective. But even though we had different perspectives, we agreed that for you it was left to right, while for me it was right to left - that if we swapped places, we would also swap perspectives. We agreed that the butterfly was heading towards the mountain. And now, even though the butterfly is heading away from the mountain, we agree that it is heading East. Is that right?" I puzzle.

"Yes!", your disinterest starting to show.

"So hasn't it been the case that the Butterfly was always heading East, regardless of our perspective? Isn't this a way of describing the situation that removes the need to give the perspective of the observer? And if that is so, then perspective is not an attribute of the world, but of how we say things about the world. We can rephrase things in ways that do not depend on where we are standing...."

Taking a breath, I continue "We started with butterflies moving left and right, but found ourselves disagreeing; then we said the butterflies were flying towards the mountain, but after we crossed the pass found that they are flying away from the mountain. Then we said that they are flying East. Each time, our view became broader, and where we were standing became less important. Sure, I can't talk about taking a point of view from nowhere, but it makes sense to try to talk about things in such a way that it doesn't matter were I am standing. Not a point of view from nowhere, but a point of view from anywhere. We can set out some truths in such a general way that we can agree, and it doesn't matter where we are standing. And if we do that, our personal perspective becomes irrelevant."

"Of course I can say what it is - it's mountains and poppies and butterflies... we agree on this. The thing is, you think as if you started this walk by yourself, and forgot about other people. That's the trouble with idealists - they are all of them closet solipsists."

"But you've set me another puzzle: the tent might not be where I think I left it. I might turn out to be mistaken about it's location. That'd be a puzzle for someone who understood the word as being created by the mind. If mind creates the world, how could the world ever be different to what the mind supposes - how could one ever be wrong about how things are? In order to be mistaken, there must be a difference between how things are and how one thinks they are - but how could that happen, if everything is in the mind..."

I sigh. "You know, we have followed this path each time, only to backtrack when the going gets tough. There are three problems - the puzzle of other people, the fact that we are sometimes wrong, and the inevitability of novelty - each of which points to there being meadows and butterflies and other people, despite what you have in mind. I think you know that idealism won't cut it." — Banno

The problem is that modus tollens can be proven syllogistically quite easily, but how do you prove that you may derive ~ρ from ρ→(φ^~φ)? — Lionino

Prove RAA without MT?

Interesting problem.

I have never seen a reductio that does not have multiple assumptions. — Leontiskos

:lol:

I give in.

OK. Much clearer Thanks.

(2) amounts to

2. ~(b^~b)

Nope.

Straight RAA does not require the "and elimination". It's an additional step when there are multiple assumptions.

1. a → (b ∧ ~b)
2. If b is true (b ∧ ~b) is false. If b is false (b ∧ ~b) is false, so (b ∧ ~b) is false.
3.~a → ~(b ∧ ~b) - contraposition (1)
4. ~a - modus ponens (2,3) — Count Timothy von Icarus

Modus Ponens is ρ→φ, ρ, ⊢ φ.

Not seeing it in 4.

What I have consistently said is that reductio is not valid in the same way that a direct proof is. — Leontiskos

So, what is a "direct proof"? I gather you think using MT is direct, but RAA isn't? What's the distinction here?

While you are there, what does "FALSE" mean?

To me, RAA depends on modus tollens. — Lionino

What does "depends on" do here?

Modus Tollens: ρ→φ, ~φ ⊢ ~ρ
RAA: ρ→(φ^~φ) ⊢ ~ρ

Both are equally useable rules of inference.

But my fuller position is that any inference utilizing strange senses of would-be familiar logical concepts must be used with care. I am not opposed to the Mines of Moria, but I don't think people are taking enough care in traversing them. — Leontiskos

And yet your claim that Reductio is invalid is just wrong.

The grain of truth in @Leontiskos' position is that reductio arguments need to be used with care. If we have a bunch of assumptions that lead to a falsehood, we can throw out any and all of the assumptions.

This has a place in many philosophical critiques. For example, it underpins the Duhem–Quine thesis, and greatly complicated Popper's fablsificationism.

Not quite so in formal systems. In classical logic if assumptions a,b,c,d lead to a contradiction we can only conclude that their conjunct is false.

But this allows is also to conclude certain implications. We might infer for example that a^b^c→~d. That is, if a, b, and c are true, it must be d that is false.

Worth keeping in mind

So here's the apparent problem:
A, A→¬B∧B ⊢ ¬A
A, A→¬B∧B ⊢ A
It seems we can infer both A and ~A from the same thing. But that's because the two assumptions, A and A→¬B∧B, are inconsistent.

I don't see where I require anything like that in that post. After all, it's your post.

It might help if you explained what FALSE is.

As it stands, I can't take much more of this gobble. It's clear that reductio is valid as used in classical logic.

truth incarnate... — Leontiskos

:grin:

Presumably that's TRUE? Or is it 'TRUE'?

Well, first, ρ,μ ⊢φ^~φ⊢ (ρ→~μ) ^ (μ→~ρ) is nonsense. I stuffed up. Am I allowed to edit it? :wink:

It should be
(ρ^μ) →φ^~φ⊢ (ρ→~μ) ^ (μ→~ρ)

:lol:

I think you have here managed to set out Leo's confusion far more clearly than has Leo.

Can you see the answer?

A→(B∧¬B)
¬(B∧¬B)
∴ ¬A — Leontiskos

If ¬(B∧¬B) is true, as it must be, then this is not a valid use of modus tollens.

Again, as i pointed out previously, you are comparing two very different arguments. But further your case is not helped by your not setting out the inferential steps in each case. Indeed, your new first example is not well-formed in classical logic. Why is the second line a quote? Was that in error (if so, then I suggest you edit it...). And if you were to modify it so as to be well-formed, what would it look like, if not ¬(B∧¬B)?

And how is "(B∧¬B) is false" and example of FALSE? Because of the quotes? What do they do?

What you write here is just a muddle.

The post does not show that I said I 'preferred the reductio to the modus tollens".

And what I am after is a straight forward explanation of what "FALSE" is. Referring back to old posts that do not give a clear explanation anyway is in no way helpful.

you said you preferred the reductio to the modus tollens. — Leontiskos

Rubbish.

Leo, what is "FALSE"?

So I ask again: How is it that something and its negation can both [function as the second premise of a modus tollens]? — Leontiskos

It doesn't. Explained last time you made this claim...

Oh, and what is "FALSE"?

I think Leontiskos is talking about choosing between the conjuncts, while Banno is correctly stating that reduction ad absurdum is formally valid. — Lionino

I'm glad you followed this.

, what is "FALSE"?

It's your term.

This conversation is increasingly inane. Again, I seem to have reduced you to reciting gobbledygook.

I literally said it was an interpretation, not a translation. — Leontiskos

Ok, Presenting a statement that someone has not made is not presenting an interpretation. :roll:

This does not contradict what I have been saying. — Leontiskos

Quite so. So what? It remains that RAA is a valid inference in classical propositional logic.

What is the supposed difference between "false" and "FALSE"?

Banno may speak for himself, but I don't know what difference in reference you mean by spelling 'false' without caps and with all caps. — TonesInDeepFreeze

Neither do I. This distinction between false and FALSE is not my doing. It seems to be another case of Leontiskos confabulating arguments on the part of those who disagree with him.

That was my interpretation of Banno, not Banno himself. — Leontiskos

Presenting a statement that someone has not made is not presenting a translation.

I think your charges of "misrepresentation" are all bosh — Leontiskos

I agree with Tones that you habitually misrepresent positions that are counter to your own, here and elsewhere.
_________________

Has everyone agreed by this point that ↪Banno's truth table does not fully capture what a reductio is? — Leontiskos

I'll agree with that. It is incomplete. As Tones pointed out RAA is an inference rule, not a sequent within classical propositional logic. The inference allows one to infer ~ρ given a proof of (μ ^ ~μ) with ρ as assumption, a form displayed in the truth table.

The easiest way to see this is to note that a reductio ad absurdum is not formally valid — Leontiskos

This is rubbish. Given a proof of B and ~B from A as assumption, we may derive ~A as conclusion. This is the form of reductio inferences and is quite valid.


I think that what has Leo worried is the notion that in an informal reductio with multiple assumptions, we have to have grounds for choosing which assumption we deny. So for example if we have assumption A and assumption B and assumption C, and from these we infer some contradiction, we then have the option of rejecting any or all of the assumptions, and a choice to make.

This is not the case in formal uses of reductio.

Given ρ,μ ⊢φ^~φ, we can write that ρ→~μ or we can write that μ→~ρ. (Tree proof 1; Tree proof 2)

Leo seems to think that choosing between ρ→~μ and μ→~ρ somehow involves an act of will that is outside formal logic. He concludes that somehow reductio is invalid. His is a mistaken view. Either inference, ρ→~μ or μ→~ρ, is valid.

Indeed, the "problem" is not with reduction, but with and-elimination. And-elimination has this form
ρ^μ ⊢ρ, or ρ^μ ⊢μ. We can choose which inference to use, but both are quite valid.

We can write RAA as inferring an and-sentence, a conjunct:

ρ,μ ⊢φ^~φ⊢ (ρ→~μ) ^ (μ→~ρ)

(ρ^μ) →φ^~φ⊢ (ρ→~μ) ^ (μ→~ρ)
(fixed error)

...and see that the choice is not in the reductio but in choosing between the conjuncts.

Leo is quite wrong to assert that Reductio Ad Absurdum is invalid.


_________________
For the folks following along at home, the greek letters allow us to write about the sentences of classical propositional logic. We can substitute for any greek letter, consistently, a well formed formula from that logic. "⊢" is read as "infer". or "we can write" So we can set out modus ponens as

ρ,ρ→μ ⊢μ

Read this as "given rho and rho implies mu, infer mu". Substitute any WFF from classical logic into this form, consistently, and you will have a valid inference.

More often folk will use capital letters instead of greek, but here I thought it useful to seperate these out from the use of capital letters in the OP

All of your premises are wrong except for number 1. — Lionino

And even if they were right, the conclusion does not obviously follow - indeed, it is very unclear what the structure of the argument is.

SO I supose one question is, can such an argument be constructed?

It depends upon the values given to the variables. — creativesoul

Hello, creative. How are the fish hooks?

It exactly does not depend on the values given to the variables. That's kinda the point of using variables - you get to put different things in and get the same result.

So a+b = b+a regardless of what number you stick in to the formula, and a^(a→b)⊢b regardless of what statement you put in, too. Or so it is supposed to go.