I think your basic intuition is correct. It resists the crucial methodological error of "trusting the logic machine to the extent that we have no way of knowing when it is working and when it is not" (↪Leontiskos). We need to be able and willing to question the logic tools that we have built. If the tools do not fit reality, that's a problem with the tools, not with reality (↪Janus). — Leontiskos

I agree, and if formal logic contradicts the logic inherent in our ordinary ways of speaking and making claims about things, I can't see the fault laying with ordinary parlance.

However, reading (A implies notB) as "something other than B (caveat: also) follows from A". would be consistent with "B follows from A", because it would not deny that B also follows from A.
— Janus

Yeah that's a good explanation for why it intuitively makes sense that they're a contradiction. — flannel jesus

Actually I had thought that it was an explanation for why, on that interpretation, it makes sense that they are not a contradiction, while maintaining that on the other reading it seems to makes no sense to claim that they are not a contradiction.

Consider this as an intuitive explanation for why they aren't a contradiction:

A implies B can be rephrased as (not A or B)
A implies not B can be rephrased as (not A or not B)

Do you think (not A or B) and (not A or not B) contradict?

I read 'A implies B' as (if A then B) or (not (A and notB)). It's a fair while since I studied predicate logic, though.

Only if (A entails B) and (A entails notB) occur in the exact same respect (and, obviously, at the same time), which I find is most often the case. — javra

Is it not a given that we should understand A and B to refer to the same things in both?

I was referring to real physical systems which are not conceptual, I was not referring to mathematical systems, which are conceptual. It makes no sense to say that the Universe, a real physical system, is incomplete, but of course our understanding of the universe is incomplete, and always will be. So, the future is not comprehensively predictable, but it does not follow that it is incomplete or in possession of free will.

If a deterministic system is incomplete, its future is not predetermined. — Tarskian

It's not systems that are "incomplete": the idea makes no sense at all, but our understanding of systems.

Cheers. I have posted what I think will be my final contribution to that thread.

Some interesting points from both of you, so for me not "six pages too many".

Do (A implies B) and (A implies notB) contradict each other? — flannel jesus

I woke in the middle of the night and realized there is an alternative interpretation of the above in natural language. I remain convinced that reading the two propositions as "B follows from A" and "B does not follow from A" means that they contradict one another.

However, reading (A implies notB) as "something other than B (caveat: also) follows from A". would be consistent with "B follows from A", because it would not deny that B also follows from A.

That's my kindergarten contribution for what it's worth.

Thanks, you have shown yourself to be of honest and generous spirit, and in my book that is what is most important.

Because even informally, the statements don't entail a both statement and its negation. — TonesInDeepFreeze

I'm not sure what you mean: I was considering the two statements separately and it still seems to me, that regardless of the soundness or relevance of their content, that, taken informally as statements, they contradict one another.

"if lizards are purple, then they would be smarter" and "if lizards are purple, then they would not be smarter" is not a contradiction. — TonesInDeepFreeze

I see those two statements as saying contradictory things about what lizards being purple would entail.

"if lizards are purple, then they would be smarter" and "if lizards are purple, then they would not be smarter" and "lizards are purple" does imply a contradiction. — TonesInDeepFreeze

I see two of those statements, as above, as being contradictory and the third as being unsound. And I see the two contradictory statements as saying nothing about whether lizards are purple. I mean, I think it's fair to say that both of the conditional statements are untrue, because being or not being smarter has no logical connection with being purple. Or I could say that the two statements are nonsensical because the antecedent has no relevance to the consequent. However, I cannot but see them as contradictory.

What about these two statements: 'if I was more educated in logic, I would be able to see that those two statements are contradictory" and "if I was more educated in logic I would not be able to see that those two statements are contradictory"—do those two statements contradict one another?

Or what about 'if I was more educated in logic, I would be able to see that those two statements are contradictory" and "if I was more educated in logic I would be able to see that those two statements are not contradictory"?

I'm not sure, but maybe you want to check whether you are conflating "not intuitive" with "contradictory". — TonesInDeepFreeze

I don't believe I am conflating "not intuitive" with "contradictory", but of course I admit I could be wrong. Do I understand what 'contradictory' means? I think so.

What about "the present king of France is bald" and "the present king of France is not bald" do they contradict one another?

That's incorrect, formally or informally. I explained why it's not correct. — TonesInDeepFreeze

Why is it incorrect informally?

I sense that it is not logical connection you have in mind, but rather, what is called in logic, 'relevance'. — TonesInDeepFreeze

Yes, relevance is another way of saying logical connection in the context.

How are they nonsensical? — TonesInDeepFreeze

I asked you if any were nonsensical, I didn't say they were. In informal language if the antecendent has no relevance to the consequent then I would say that counts as nonsensicality.

The way you would usually use it in any sort natural language statement would be to say: "Look, A implies both B and not-B, so clearly A cannot be true." You don't have a contradiction if you reject A, only if you affirm it. — Count Timothy von Icarus

It seems to me that saying you don't have a contradiction is one way of interpreting it; that is, I don't think there is any fact of the matter. Consider "If lizards were all purple then they'd be a hell of a lot smarter" and "if lizards were all purple, they would not be a hell of a lot smarter": you don't see those two sentences as contradicting one another despite the fact that lizards are not all purple?

The original question regarded '->', which ordinarily is taken as the material conditional. — TonesInDeepFreeze

Thanks, you obviously know much more about formal logic than I do. However I was not thinking in terms of formal logic, since the original question contains no symbols from formal logic

Do (A implies B) and (A implies notB) contradict each other? — flannel jesus

My point was that if you have two sentences 'if A then B' and 'if A then notB' they simply contradict one another regardless of whether A obtains. Of course we don't know what A is. If the two sentences were 'if monkeys had wings, then they could fly to the moon' and 'if monkeys had wings, they could not fly to the moon' the two sentences contradict one another regardless of whether it is true that monkeys have wings or whether it is true that if they had wings they either could or could not fly to the moon.

Notice that "If snow is green then Emmanuel Macron is an American" and "If snow is green then Emmanuel Macron is not an American" is not of that form and together they don't imply the contradiction "Emmanuel Macron is an American" and "Emmanuel Macron is not an American". They only imply that contraction along with the statement "Snow is green". — TonesInDeepFreeze

I think that is one way of interpreting it, separating the obviously false, or disconnected conditional "if snow if green" from the two contradicting statements about Macron, but assuming that there would be some logical connection between the conditional and the implications (and why would we even bother thinking about statements where there is no such logical connection) then the two statements do contradict one another.

For example, the computer you're using now is based on logic paths in which "if then" is the material conditional. — TonesInDeepFreeze

Right, I do have some familiarity with logic gates. Are any of those useful logic paths nonsensical? Genuine question...

I can't think of any examples in natural language where "if A then B" and "if A then not B" do not contradict one another.If "proofs" do not accord with this fact, then so much the worse for the "proofs", given that formal logic is designed to illuminate natural language, not replace it.

But they aren't perfect translations because all sorts of shit that sounds very dumb in natural language flies in symbolic logic. E.g. "if Trump won the 2020 election then we would have colonized Mars by now."

Anything follows from a false antecedent, so anything would be "true" following the claim that Trump won the 2020 election, since he didn't. — Count Timothy von Icarus

I agree, I came across such things when studying logic as an undergraduate. I will just say that "if Trump won the 2020 election, then we would have colonized Mars by now" is neither true nor false (or at least cannot be determined to be true or false).

So I don't think it is true that "anything would be true following the claim that Trump won the 2020 election, since he didn't", because it could equally be said that "anything would be false following the claim that Trump won the 2020 election, since he didn't".

Does (A implies B) mean that 'if A then B'? Does (A implies notB) mean that 'if A then not B'? If the answer is 'yes' to both, then they contradict one another.

I grasp the basic distinction between "sins of commission" and "sins of omission". "Negligence" in the context of ethics and moral philosophy is a multi-faceted issue. If you want to claim I don't understand the notion of negligence, then you should be able to say what it is I don't understand about it, or just how what I've said displays my purported lack of understanding.

If you don't see that it was you who starting with the personal attacks via insinuation, deflecting by attempting to paint my understanding in a poor light, instead of actually addressing the points I made, then I can only hope that for your own sake you wake up to yourself.

The impression I am forming of you is that of a self-deluded, condescending fool who cannot bear losing an argument. I'll be happy to ignore you in the future. May you gain some much-needed self-knowledge...

Right, and it seems arguable that becoming preoccupied with the propositional aspects of philosophy in general, as though it could be an empirically determined subject that can deliver testable truths, would be a move away from the examined life

You seem like someone who just hasn't thought or read about this topics much at all, to the extent that in order to discuss them on a philosophy forum you would need to do some homework first. I'm happy to talk after you do some homework. If you don't want to, that's your call. — Leontiskos

:roll: Cut the bullshit—trying to dismiss others by insinuation is not a substitute for cogent argument. You have no idea how much or how little I've thought or read about this. If you are incapable of sustaining an argument in your own words, be man enough to admit it.

Consider people who get involved in cults? — wonderer1

Could they not learn from that experience? Perhaps in some cases to go down for a while is the only way to continue on the way up.

Seems to me that one's disposition is important here. I've never been drawn to philosophy (by this I mean deep reading/studying) But I am interested enough to want an overview of key themes and directions. And I certainly understand that we are all the product of philosophical presuppositions, but so what? — Tom Storm

I think studying philosophers excessively is a scholarly, and not so much a philosophical exercise. I mean I want to get an understanding of the whole tradition, and that task is enough to occupy considerable time, so I don't see much value in going down the Kantian or Hegelian rabbit-holes. With Plato and Aristotle, I think it is a bit different since they are doing "first philosophy" not elaborate system-building.

Anyway, the import of philosophy is only insofar as thinking about philosophical issues and the self0critiuqe that might enable, helps you to live better. Otherwise, it would just be a nerdy interest to pass your time with.

In interacting on here I am most interested in those who present their own ideas in their own words and not so much those who post lengthy excerpts from their favorite philosophers or who direct you to read some philosophical work or other.

I am not trying to solve any mysteries of existence or engaged in a poetic quest for self-knowledge. — Tom Storm

You strike me as someone who is vitally interested in self-knowledge or self-understanding, as well as knowledge and understanding of others. I count that as doing philosophy, whether it be poetic, scholarly or not.

I don't think it is a one-way street though. — Fooloso4

Do you mean our knowledge and understanding could just as well degenerate as improve?

No, but I understand that "The Good" is nonbeing. — 180 Proof

Do you mean that the good is "extinction" in the early Buddhist sense of nirvana? Or do you mean that the Good is not a being, and is also not being itself? Or something else?

I understand the Good to be being in the sense of flourishing, actualizing potential, and also care for others. When I say I don't know what the Good is I mean I don't know what its universal definition could be—what is good, what constitutes flourishing, for me may not be so for another. But then there would presumably be some common elements in what is good for everyone, insofar as we are all human and thus social beings.

I know that if she's a mortal, then she cannot "know" ... — 180 Proof

:up: It's a tricky word indeed that "know"! But I think you point to something salient when you make the distinction between understanding and knowing—we all have our own understandings of what is good.

So you think negligence pertains to the legal order but not to the moral order? — Leontiskos

Depends on what is meant by 'negligence'. Failing to feed and look after those who depend on you, your children or animals, for example, I would not consider to be morally acceptable.

I don't think in terms of "moral order", but rather in terms of "moral compass". The morally important things are cared about, due to normal human feeling, by all who are not sociopathic, in my view. Morality is not "given from above" but issues from out of the depths of healthy human feeling and rationality.

:up:

Yes, "irrelevant" because we just can't answer the question regarding determinsim vs free will.

But Janus, morality may have no rational justification whether determinism is true or not. — NotAristotle

If determinism is not true and we are somehow radically free to choose then on that assumption morality would be rationally justified.

Regardless, as @Banno says

It remains that you must choose. — Banno

And so, the need to examine what we ought do, remains. — Banno

:100:

All you've shown is that if determinism is the case, if no one could ever have done otherwise than what they have done, because all events without exception are completely pre-determined by antecedent events, then there is no rational justification for morality. However, if humans are determined to have morality, then they will have morality, rational justification be damned.

But is determinism the case? How would we know? If humans are truly free, there is no guarantee that that freedom is analyzable. If freedom were analyzable in causal terms it would not be freedom.

Yes, all design is artifice. It doesn't follow that all purpose is artifice—I'm not claiming that design and purpose are one and the same, but of course they are closely connected.

You are conflating the legal with the moral. If someone drinks and drives they are being negligent. If their ability to focus on the task of driving safely and/ or being physically coordinated enough to do it, is sufficiently impaired by the alcohol and they are unlucky enough to kill someone, they will not be excused and will be prosecuted and punished to a far greater extent than if they had not killed someone.

From the point of view of the law concerning negligence, they have committed a greater crime than if they had merely driven without incident, but this doesn't seem right from a moral standpoint. Call this moral luck (or unluck).

Another example is that someone might have a sudden and uncontrollable sneezing fit when driving and fail to see the pedestrian on the crossing and run them over and kill them. They will still be punished even though it was not their fault in any moral sense.

Doesn’t address my question. — Wayfarer

I think it does: you seem to presume that under the assumption of naturalism we could never have become the kinds of self-reflective agents who can deliberately plan and design things for a purpose. If that is your objection, then what is your argument against that being impossible under the assumption of naturalism? If that is not your objection, then what is?

How do we reconcile this distinction with a naturalistic view that sees humans and their capabilities as entirely natural phenomena, while at the same time denying that nature herself displays or generates designs as such? — Wayfarer

It's easy: we understand ourselves self-reflectively to be capable of planning and deliberately designing things, and under the normal usage for there to be design implies an agent, such as ourselves, capable of planning and deliberately designing.

But I notice that nothing in your reply evidences the logical impossibility you so far assert – and logical impossibility is not a matter of mere opinion last I checked. At least not in realms of philosophy. — javra

Explain to me how the notion, not to mention the imputation, of purpose makes sense in the absence of an agent that purposes. The issue here is coherence not possibility. In other words, you need to be able to say what you mean by ascribing purpose to the cosmos as a whole before worrying about whether or not you can find an argument or evidence to support your ascription.

A better question is: have you been able to shape your world so that it's a paradise you roam in? Or is it a hell you constantly fight against? — frank

Can it ever be exclusively and continuously one or the other?

This is what is at issue in the trial of Socrates. Some think that the tension between philosophy and the city remains with us but others think the tension has or can be resolved and that reason and revelation reconciled or that the solution is political tolerance, the separation of church and state. I think tradition is important but that we are not slaves to it as long as we question its authority. Questioning its authority has become part of our tradition. — Fooloso4

I agree, but I think it depends on what is meant by "tradition". There is the philosophical tradition, then there are the changing, mostly unexamined (until they are) socio-cultural traditions that amount to dogma.

It has long been a central part of philosophy to question dogma, but how often do the arrived at alternatives to dogma themselves crystallize into dogma? I conclude that the dialectic is radically open-ended, that there is no final endpoint of knowledge or understanding. That doesn't mean that our knowledge and understanding cannot improve as we go along.

Must we be equally skeptical of all claims about what is good? — Count Timothy von Icarus

Do you know what is the Good? If someone claims to know what is the Good, do you know, can you know, that she knows what is the Good?

There seem to be many things that all (or at least most) people take to be good. Does that consensus amount to knowing what is the Good, or what goodness universally consists in, its essence?

All I can say is lets hope you aren't quite this fragile in the real world. As with Tobias, I don't care, and nor should you. — AmadeusD

Fragile? :rofl: What an idiotic inference; what makes you think I care about some random ad hominem projections beyond making the effort to call them out for what they are? I'm not interested in participating in your silly game of one-upmanship.

Yes, as in freethought: thinking (inquiry) free of "tradition" in such a way that we are free for recreating (reasonably extending, or modernizing) tradition. — 180 Proof

:up: :up: Yes, that is the only conceivably good way forward...

That is what is at stake in pretty much every election on the continent. It is not about to biosphere but about immigration. They do not want to make children but they also do not want to get replaced by people who do. — Tarskian

That may be a general trend, but I think you should be wary of too much generalization. The biosphere is the pressing concern, regardless of whether it is uppermost in most people's minds. If it had been and was now the most urgent issue in most people's minds, then we would arguably be in better position than we currently are.

Tradition reflects survivorship bias over centuries or even millennia. People who did not keep them, did not have any progeny, and disappeared in the course of history. — Tarskian

I allowed that traditions and organized religions may be necessary for many. Nonetheless, they are hindrances to others. It is false to claim that those who reject tradition do not have progeny. Everyone "disappears in the course of history", so that is hardly a salient point.

Of course, social values matter, and you might refer to those as "tradition". But they change and become new (and hopefully improved) traditions over time. So, I will not disagree that societies without social values cannot survive for long. However, I doubt there actually are any such societies to begin with.

The danger of collapse we face today is on account of overuse of resources and neglect of the biosphere, and it is arguable that traditional tropes, such as the Biblical vision of God creating the world for the use of humanity have contributed to this looming crisis.

Our economic system is unsustainable, being predicated on endless growth, with collapse being the only alternative. Nothing to do with tradition, unless you count the tradition amongst economists of discounting ecological costs as a part of the economy. That greater disrupter of tradition, science, has been telling us how wrongheaded this economic thinking in terms of "externalities" is for at least more than half a century.

An excellent OP! I think we all seek the good. We either adopt what is socio-culturally set before us, or we embark on a dialectical search for what is good. It concerns us all since we are all, to at least some extent, or at least potentially, self-reflective beings, and to the degree that we take our lives seriously, we wish to live the best way we can.

There can be no empirical evidence for the "truths" of philosophy. Philosophical truths are accepted on faith, and our faiths are determined by what seems most plausible to each of us. The only alternative to that would be to remain or become slaves to tradition and authority—and I think philosophy, with its open-ended questioning and uncertainty can be an antidote, along with science, the arts and literature, to that curtailing of human potential.

For that reason, I reject (for myself) organized religion in any form, although I acknowledge that it may be needed by those who cannot free themselves from the bonds of tradition and authority, bonds which Hegel refers to as "the aegis of tutelage".

This kind of response leaves me only with the hope that you might grow up. Your argumentation, and what seems to motivate it, is of such a low quality that I am amazed that you haven't been banned.

:roll: Weasel words!

But then, it was also constantly informed by the presence of actual teachers and exemplars of the faith, who provided a living dimension to the tradition which is generally absent in modern academic philosophy. — Wayfarer

I think it is still possible to have teachers in a secular context, because what they would be teaching are psychological and physical techniques for gaining self-knowledge and altering consciousness. That said I also believe that not everyone needs a teacher, a tradition or a "sangha".