Not "what", but "who", surely?What draws that line? — Mp202020
The experience of your companion doesn't matter, so long as they hand you the red pen. That's why we know about colour blindness - there is a difference that can be examined and explained.Any color, not matter the shade, how can we know it’s experience is as shared as the cause of its experience? — Mp202020
I can ask someone to recommend a funny movie, and they can deliver, but I don't think it makes much sense to treat being funny as some mind-independent property of movies. — Michael
Well, that's not right, either, it seems. The red of a sunset is very different to the red of a sports car, or the red of a sore eye.red must represent some state of external reality that when manifesting visually becomes “red.” — Mp202020
But if red refers to the experience, then when you say “red” it refers to your experience, but when I say it it refers to my experience. If we are going to be talking about the same thing then we need something that we both have access to. — Banno
Bang. What reason is there to think that red is more than a word we use for certain purposes?What is red but a word we’ve agreed to call something that looks red? — Mp202020
Even if this is so, "red" can't mean "Light with a frequency of around 430 terahertz"...From a materialistic perspective, red is a specific light wavelength. This is universal. — Mp202020
...you gaslit Gemini, given it said "You are right...". — Lionino
Yawn yawn — Lionino
A Challenge in Proving RAA
RAA stands for Reductio ad Absurdum, which is a proof method rather than a theorem itself. It's a rule of inference, a logical principle that allows us to deduce conclusions from premises.
As such, it cannot be proven within the same logical system in which it is a rule.
To prove RAA, we would need a meta-logical system, a system that talks about the logical system itself. This is a level of abstraction beyond what is typically considered in standard logic courses.
Analogy
Imagine trying to prove the rule of addition within arithmetic. It's inherently circular; addition is a fundamental operation used to establish other arithmetic truths, but it cannot itself be proven within the arithmetic system.
Alternative Approaches
While we can't prove RAA within the system, we can:
Justify its use: Explain why it's a valid inference rule based on intuition or other accepted logical principles.
Show its consistency: Demonstrate that using RAA doesn't lead to contradictions.
Explore its relationship to other logical principles: Analyze how RAA interacts with other inference rules.
Would you like to explore one of these approaches? Or perhaps you have a specific context in mind where you're questioning the validity of RAA?
Show drafts
A Challenge in Proving RAA within an Axiomatic System
You're absolutely right. Proving RAA (Reductio ad Absurdum) within the axiomatic framework of propositional logic is not possible.
Why?
RAA is a meta-logical principle: It's a rule about how we reason within the logic, rather than a theorem of the logic itself.
Axiomatic systems are object-level: They deal with propositions and their relationships, not the rules of inference governing those propositions.
Analogy
Think of an axiomatic system as a game. The rules of the game are fixed. You can't prove one of the rules by playing the game itself. You need to step outside the game to analyze its rules.
What Can We Do?
While we can't prove RAA within the system, we can:
Justify its use: Explain why it's a valid inference rule based on intuition or other accepted logical principles.
Show its consistency: Demonstrate that using RAA doesn't lead to contradictions.
Explore its relationship to other logical principles: Analyze how RAA interacts with other inference rules.
Would you like to explore one of these options?
Perhaps we could discuss how RAA is typically justified in logic textbooks or explore its role in proof systems like natural deduction.
Reductio ad absurdum (RAA), also known as proof by contradiction, is a fundamental technique in propositional logic. To prove RAA in an axiomatic system, we typically use a set of axioms and inference rules such as those found in Hilbert-style systems. Let's outline a proof of RAA within such a system.
Axioms and Inference Rules:
Axioms:
A1: α→(β→α)
A2: (α→(β→γ))→((α→β)→(α→γ))
(α→(β→γ))→((α→β)→(α→γ))
A3: (¬α→¬β)→(β→α)
Modus Ponens (MP):
From α and α→β, infer β.
Goal:
To prove RAA, we need to show that if α→¬α leads to a contradiction, then ¬α must be true.
Proof:
Assume α→¬α. (Assumption)
From α→¬α, derive ¬α→¬α using A1.
By Axiom A1: ¬α→(α→¬α)
Since α→¬α is assumed, we have: ¬α→(¬α)
To derive a contradiction, we need to introduce α.
By Modus Ponens on α and α→¬α:
¬α
Since ¬α is derived under the assumption that
α
α leads to ¬α, we can conclude ¬α.
Thus, we've shown that α→¬α leads to ¬α, which concludes the proof by contradiction (RAA).
This establishes that if assuming α leads to a contradiction, then ¬α must be true, thereby proving RAA within our axiomatic propositional logic system.
Does the color “red” exist outside of the subjective mind that conceptually designates the concept of “red?”
— Mp202020
If "red" is just in your mind, when you ask for a red pen, how is it that the person you are asking hands you what you want? — Banno
You missed the point of my post. Any definition will be contradicted by some philosophy.If this is a problem, then how can we exclude it from the definition? — Tarskian
"Know thyself"....find a statement that is philosophical but that does not satisfy the definition — Tarskian
No sooner would that be done than philosophy will then be about undermining that very definition.One goal of metaphilosophy is to finally discover a usable definition for philosophy. — Tarskian
A statement is philosophical, if it is a statement about another statement. — Tarskian
Yep. Good point.We know that the assumptions are inconsistent — TonesInDeepFreeze
...back to the original, from Anscombe, in Intentionality, and as used by Searle and many others. Cheers.I revised your quote — Fire Ologist
That's your problem, not mine. If you can't even address the simple concerns of an aged retiree, then all that is irrelevant. An appeal to your own authority is still invalid. And if you don't give a shit, don't reply.Your problem is that I win national awards for my writings on these issues. I publish books. I speak at conferences. — apokrisis
Presumptuous.But as I've pointed out, you haven't inquired deeply enough into how indigenous lives are actually structured, both as biology and sociology.
My own position here is based on a deep knowledge of all that. — apokrisis
Given a thesis and a synthesis, anything goes. The juxtaposition of cooperation and competition does not lead of necessity to either Model A or Model B; they are not inevitable.Reiterating, there are two bits of logic in my post, not unrelated but also not the same. The first is the classic Popperian argument that historicism is generally unfalsifiable, which we can to some extent extend to dialectic arguments generally. The second is the lack of fixity as to the third moment, the synthesis.
This latter is shown explicitly in classical logic by the explosion ρ^~ρ⊃ψ, that from a contradiction anything follows....
My suggestion is that in most cases the synthesis is fixed by other factors external to the dialectic, and the dialectic then used to justify that fixing. Which is an invalid move. — Banno
Perhaps he did. Hard to tell. I wouldn't presume to represent indigenous cultures.So I think he acknowledges this would have been the way to go, but now the best we can do is maintain since reversing is out of the question — schopenhauer1
Perhaps, but I wouldn't have thought so - his Mad Max Model B involves "bug-out survivalist with guns", and no home garden will feed a family. Indigenous ethics appear to depend on a level of cooperation absent from Model B. But the point I would contend is not just that the only options are Model A or Model B, but that a better response to your question of "what would be an ethical stance" is not various ethical theories so much as whole ways of living. This by way of bringing us back to ethics as about what we should do, not what is the case.Isn't this sort of apokrisis Model B steady state notion? — schopenhauer1
If what this says is that people have experiences, then we agree, and I don't think it's me doing the obfuscating.That humans and other sentient beings are subjects of experience is both obvious and central to any philosophy, but somehow you still manage to obfuscate it. — Wayfarer
One does not have to look far to find ethical stances quite divergent from those suggested in the OP. Indigenous ethics for example might involve circular time, self-control, self-reliance, courage, kinship and friendship, empathy, a holistic sense of oneness and interdependence, reverence for land and Country and a responsibility for others. The actions implicit in such a view are very different to those in either of options A or B in the OP. Yet such an approach might be quite conducive towards long-term stability....what would be an ethical stance and what would be its justification towards resource management? What should we do? — schopenhauer1
Yep...."is" and "ought" exists as a two-way feedback relationship that couples the organism to its environment in a... loop — apokrisis
Oh, go ahead and speculate. Just don't mistake speculation for fact....disparagement of "mere speculation"... — Gnomon
Yes. We have the capacity to make things other than they are. So we must ask how things ought be. That question is not answered by physics.I guess, this might be the question here. Not what is happening, but what ought to happen. — schopenhauer1
Do (A implies B) and (A implies notB) contradict each other? — flannel jesus
Surely that would be the object of your experience? — bert1
‘the mind’... (is) ‘the subject of experience’. — Wayfarer