Hence @fdrake's pointing out the inadequacy of @Leontiskos' definition.

A great circle is the longest possible straight line on a sphere. No midpoint and diameter in that definition.

I'd say the main point of the OP was snark, — Hanover

"Just the place for a Snark!" the Bellman cried,
As he landed his crew with care;
Supporting each man on the top of the tide
By a finger entwined in his hair.

Super cool stuff. — Moliere

Yeah, I agree. Links form here to a whole lot of other stuff.

Banno, my position is that a blastocyst is a human being, not that it is a person. Can you please critique that instead of a straw man? I want to hear why you don't think that the blastocyst is alive, a separate alive entity than the mother, and is a member of the human species. It is really weird, to me, to say that it is not a new member of the human species. — Bob Ross

Ok, then: A blastocyst is not a human being. The blastocyst is alive. It can be considered as a seperate entity - it might be moved to another host, for example. It has human DNA and so on, but it is no more a "member of the human species" than is your finger.

All this is insubstantial in the argument I presented to you. We have on the one hand a woman, perhaps a nurse, perhaps a CEO, perhaps a sister, mother, daughter, perhaps a care giver or volunteer. Someone who can express their needs, who makes plans and seeks to fulfil them and who has a place in our world.

We have on the other hand, a group of cells.

That you value those cells over the person who must carry them is heinous.

Yes, indeed.

If god does not exists, our prayers would be answered by Un, and hence it is false that if there is no god your prayers will not be answered.

If Un is not distracted by Hanover's screams, of course.

There's the nub. It looks circular...

I have a predilection for Feyerabend over Lakatos, but Feyerabend's view is difficult to maintain.

You artificially inserted an extraneous conversation into your own thread and then invited me here, remember? — Leontiskos

No.

―― I don't know why I'm participating in this. — Srap Tasmaner

I'm glad you dropped in, at Leon's invitation, I think?

It wasn't I who engaged in necromancy - that was @frank. And you do not have to be here, if you find it too arduous.

I'm gonna bugger off now too. — fdrake

Cheers. I'm glad someone looked at the Russell article.

If it makes you uncomfortable, stop tromping on my bridge.

It is a lot like something from Proofs and Refutations. — fdrake

I had thought the example, Euler’s formula, a bit obtuse. But perhaps Lakatos chose it so as to minimise the number of auxiliary hypotheses that his students could produce.

I'm enjoying this discussion. I'd like to pause in order to draw attention to the similarities between the insistence here on euclidean space and Leon's previous insistence on Aristotelian logic, or Count Timothy von Icarus' insistence on "material logic'.

There's a pattern...

@Leontiskos as student Delta:

But why accept the counterexample? We proved our conjecture— now it is a theorem. I admit that it clashes with this so-called ‘counterexample’. One of them has to give way. But why should the theorem give way, when it has been proved? It is the ‘criticism’ that should retreat. It is fake criticism. This pair of nested cubes is not a polyhedron at all. It is a monster, a pathological case, not a counterexample. — Lakatos, as quoted in Russell

What about the summary here is unclear? — Count Timothy von Icarus

So it's bits of applied logic and ontology and model theory and metalogic. Fine.

I agreed with

Trick question. As long as you are talking about tiny triangles the sides add up to more than the diagonal. No matter how small they get. So the only question is what do the sides add up to in one tiny triangle. Then multiply by the number of triangles to get 2. A triangle is not a diagonal! — EnPassant

But that's cheating, of course. "Monster barring" in Russell's terms.

Nice post.

...you could insist that we're not talking about a circle when we're talking about sets equidistant from a point in the taxicab metric. — fdrake

Importantly, doing this would not be wrong, as such. It's just one approach amongst many. The error here, if there is on, would be to presume that this was the only, or the correct, approach - that it's what we ought do.

Cognitive biases are odd things.

And I, for one, take up the liar's paradox as a good example of an undeniable dialetheia: A true contradiction. — Moliere

A good example of how re-thinking how we phrase the apparent paradox can provide new insight. We have "This sentence is false". It seems we must assign either "true" or "false" to the Liar – with all sorts of amusing consequences.

Here is a branch on this tree. We might decide that instead of only "true" or "false" we could assign some third value to the Liar - "neither true nor false" or "buggered if I know" or some such. And we can develop paraconsitent logic.

Here's another branch. We might recognise that the Liar is about itself, and notice that this is also true of similar paradoxes - Russell's, in particular. We can avoid these sentences by introducing ways of avoiding having sentences talk about themselves. This leads to set theory, for Russell's paradox, and to Kripke's theory of truth, for the Liar.

Again, we change the way we talk about the paradox, and the results are interesting.

And again, rejecting an apparent rule leads to innovation.

Knowing something about logic and the context helps to understand why the liar paradox is of interest. — TonesInDeepFreeze

I'm finding this hard to follow - is your claim that the argument is invalid? It isn't. Seems Leon addressed this.

"come on dude, no way you think that thing is a person" — Hanover

I see your point now. Unfortunately perhaps the only answer is reliance on good judgement.

"Pure logic" as you describe it could never get off the ground because it would be the study of an infinite multitude of systems with absolutely no grounds for organizing said study. — Count Timothy von Icarus

A quick look at the Open Logic Project will show you how logic grows, tree-like, each system depending on, but slightly different from, the others. It's already "off the ground".

Therefore it's ok to do pointless investigations. — frank

More than OK.

When we do come across a "paradox in nature", so to speak, what we do is change the way we talk about what we see. Perhaps the commonest example now is the supposed paradox of the dual nature of particles and waves. Instead of talking about particles and waves we use Schrödinger's equations and things work nicely. Similar tales can be told about heliocentrism and the speed of light in a vacuum and many other adjustments to our understanding. We don't come across "paradoxes in nature", not because the world is made so as to avoid paradoxes, but becasue we change the way we describe things in order to accomodate what was previously spoken of paradoxically.

That is, we adapt our logic to match what we see.

I'll take your word for that. The difference here is the rigour introduced by formality. In particular, the argument is not subjective, nor deriving from perception. But yes, there are similarities to less "analytic" philosophies.

The chart shows that the expression you are using is not a commonplace. That's all.

Seems to me that it remains unclear what "material logic" is. But that is not true of formal logic.

A tale. One of the pre- socratics - I forget which - "proved" that air becomes colder under pressure by blowing on his figure. The breath feels cold. And we all know that a wind is cold. Hence, he disproved that gases under pressure increases in temperature. Do we take this as a refutation of thermodynamics?

Seems to me that you are truing to do something similar with formal logic. It just doesn't work. So:

Basically I see the appeal of Aristotle and common sense as a mistaken appeal — Moliere

Put bluntly, I do not see that you have differentiated formal and material logic in a way that can be maintained beyond "material logic is an over-simplification of formal logic".

And in any case, this does not address Russell's case.

Here's a Proofs and Refutations - the source of Lakatos' concept of lemma incorporation - inspired investigation into square circles. — fdrake

Nice. That's the sort of playfulness we get by adopting these considerations. I can't help you with re-defining smoothness for Taxicab space, but since every point is on a corner I don't see how the path can be differentiable, and hence smooth.

This Interactive Mathematics page shows the problem, under "An interesting question arrises". There are two values for the limit - 2 and √2. So the space is not smooth, unless we re-define "smooth".

...logical impossibility isn't all it's cracked up to be... — fdrake

That's the take-away. It's related to what I was trying to show with Banno's game - in which any rule can be undermined; but also, and yet again, to the analysis of language in A nice derangement of epitaphs.

Thanks.

Consider:

Yep.

:roll:

Yep.

Understood. — javi2541997

It isn't anything to do with probability.

Banno brought charts to a word fight. — Cheshire

:wink: Yep. Unfair advantage.

Think on i. $\sqrt -1$ isn't a thing except it is. What would we get if we just assumed a perfectly round square circle with four corners? What would be the implications? Could we construct a geometry that was interesting, if somewhat divergent? When we assumed the three angles of a triangle add to more than 180 degrees we were able to develop a geometry to navigate the globe.

Still makes no sense. What's an "inversion fallacy" in this context? Do you think that the argument is denying the antecedent? It isn't.

Why would our language/logic correspond to the world? — schopenhauer1

Isn't that oddly passive? A bit like puzzling over how the Philips Head driver just happens to fit a Philips head screw. We use language so that we can talk about the world. If it didn't work, we would use a different language.

I should have put this here:


If God does not exist, then it is false that if I pray, then my prayers will be answered. So I do not pray. Therefore God exists.

"Material logic," is not an esoteric term — Count Timothy von Icarus

Well, the little evidence I could find says otherwise. Here's an Ngram of interest.



The point is moot, since it is so off-topic.

And yes, the topic here is logic. Not Aristotle.

Logical nihilism and a deflationism vis-á-vis truth and a denial of causes certainly seem to go together as a package deal much of the time. — Count Timothy von Icarus

And not deflationary theories of truth nor a denial of causation, neither of which have any relevance to the arguments offered here. And nothing about square circles, either.

...material logic... — Count Timothy von Icarus

A new term to me - no mentions in SEP or in IEP. Not just no article, but no use of the phrase. so I googled it. A couple of blogs, none of them very clear, and with a few obvious errors. Merriam-Webster gives "logic that is valid within a certain universe of discourse or field of application because of certain peculiar properties of that universe or field —contrasted with formal logic". I gather it means informal logic or possibly applied logic.

So I could find no justification for your claim that "many people who oppose logical nihilism (and many, but not all forms of pluralism), would rather say that material logic has priority over formal logic in some important respects.". Many people do not talk of "material logic".

Logical nihilism is not the view that things have no causes. It is the view that there are no laws of logic. But also, despite the title, it is not the conclusion being argued for in the Russell article. The article that this thread concerns, and which neither you nor Leon have so far addressed. It is also not concerned with any form of pragmatism.

Logic has moved on a bit since Aristotle.

I never am wrong, — unenlightened

's true, that.

Hmm. Pragmatism over all.

:razz:

But what Russell is doing is a bit beyond all this - the next generation, if you will. She is considering:

• To be a law of logic, a principle must hold in complete generality.
• No principles hold in complete generality.
• There are no laws of logic.

And the approach is the antagonistic one of "You give me a law you think holds in complete generality, and I'll give you a counter-instance". The playfulness and creativity are appealing. Compare it to A nice derangement of epitaphs. The bit about undermining the law certainly will stick in some folk's craw.

She does not wish to conclude that there are no laws of logic, and so argues that a principle need not hold in complete generality. Instead, they hold in given logics.

(sorry - lots of edits.)

Oh, and there are paraconsistent logics that are being used in non-woo quantum mechanics.

It is a thing.

A lot to think about here. — Tom Storm

Yep, interesting stuff. In classical logic, A,~A ⊨ B (From A and not A you can derive whatever you want). This would cause all sorts of problems. Paraconsistent logics remove this problem, usually while maintaining the Law of Noncontradiction. One can get a handle on the idea by looking at many-valued logics.

Supose we allow three truth values - "true", "false" and "buggered if I know" - abbreviated to T, F, B. Then we set up truth tables with three values instead of two. With a bit of fiddling we can make it so that A ^ ~A (A and not-A) gives the truth value "buggered if I know". I'm cheating here, but the idea heads roughly in the right direction. A contradiction does not lead to just everything being true. If you want more, see here or Chapter Ten of Open Logic.

Point is, there are formally developed logics that are coherent, if inconsistent. So fears of Woo are dissipated...

Well, for some. Perhaps those feeling less conservative?

Yep - although the rigour is predominantly provided by mathematics rather than syllogism. And I sympathise with the conceit that science is essentially liberal.

I suppose I was thinking of conservatism as something more along the lines of 'there is one truth and it can be discovered by philosophy'. — Tom Storm

Ok - I'd be more comfortable calling that authoritarian, a word I nearly used in the place of "conservative" in what you quoted. The normatively of telling someone "This is how you ought think..." differs from the normatively of "If you think in that way, then this will be your conclusion..." That is, the logics here are systematic, not arbitrary - what "full-blown logical pluralism" might be remains unclear until Leon addresses the issue instead of my failings. If Aristotle showed long ago why attacks on PNC cannot work it should be a small thing to show why paraconsistent logic is flawed; yet instead it is an area of growth.

Ohh, thank god! The horror! I was having such visions...

Goodness, that goes back a bit. I'd quite forgotten that thread. And a whole section was missing from the OP - I fixed it.

Thanks.

I'm not sure what in Hack you are pointing to, but Feyerabend was an anti-science hero of the left, so there are probably some crossovers with Hack. And some distance.

"Anything goes" is a recipe for conservatism, since if anything goes then the way things are is as viable as the way they might be, and there is no sound reason for change. Think of the new-found love for free speech amongst those advocating for autocracy in recent politics. The confusion of voices shouts out rational discourse.

I supose a blanket rejection of even considering the possibility of alternate logics might be considered conservative. There might be a closer relation to views on normativety.

:lol:

Welcome back. The thread became denecrotised as a result of a discussion elsewhere.

This?

So Logical Nihilism has me returning to what I had taken as pretty much settled; that scientific progress does not result from a more or less algorithmic method - induction, falsification and so one - but is instead the result of certain sorts of liberal social interaction - of moral and aesthetic choice. — Banno

Yeah, and I think Wittgenstein would agree with you that it was a mistake. But for elsewhere.

And yeah, there is something of modality in the Tractatus "logical space".