I doubt that the SEP article – co-authored by Russell – is much easier. I find the extensive use of acronyms unsettling.

I'm not sure why the liar is your focus. As the article suggests, a para-consistent logic might assign it "both true and false" and move on.

Fixing the typo: 'The One True Logic, then, is the one that describes the relation of truth-preservation over all cases—where “all” is construed as broadly as possible'. That section then goes on to set out that construing "all" as broadly as possible may well lead to there being no valid arguments left. Logical monism would lead to logical nihilism.

The interesting issue here is, if there is One True Logic, which logic is it?

Just to give a taste of what is being discussed, here are some of the articles on "alternate" logics in SEP:
Classical Logic
Connexive Logic
Dialetheism
Free Logic
Infinitary Logic
Intuitionistic Logic
Modal Logic
Paraconsistent Logic
Relevance Logic
Second-order and Higher-order Logic
Substructural Logics

Not a complete list, but you might get the idea. Each of these is useful in some circumstance, and each is studied in its own right. Logical monism must in some way make sense of the many and varied treatments of validity, domain and truth in these logics, and either rejecting or incorporating them.

That there are multiple logics is a fact. The meta issue is how to understand the relation between them. Monism rules some in and some out - but which? Nihilism rules them all out - so no logic. Pluralism suggests we might use each as appropriate.

Now it seems to me that Pluralism is the better of these options, but the devil is in the detail, and the discussion is on-going.

What is relevant for the discussion at A challenge to Frege on assertion is that one can no longer simply presume that there is One True Logic, which is what @Leontiskos appears to do.

That section then goes on to set out that construing "all" as broadly as possible may well lead to there being no valid arguments left — Banno

Would you want to flesh that out?

Really interesting.

Now it seems to me that Pluralism is the better of these options, but the devil is in the detail, and the discussion is on-going. — Banno

Sounds fair. Is there a risk with pluralism that one might simply select the logic one wants to suit ourselves? How do we determine which logic is appropriate for a given situation/problem? Sorry if this is a banal quesion.

If we were to take an investigation into the logical soundness of theism, for instance, which alternate logic would we use? Classical logic seem traditional.

It's just the continuation in the next paragraph...

Perhaps if we construe “every case” broadly enough, we will find that there are no valid arguments left, and hence the result will not be logical monism, but a form of logical nihilism, or something close to it.

But why? That's what I was asking.

Why what? If there are no valid arguments left, then there is no One True Logic, and monism is defeated.

Is there a risk with pluralism that one might simply select the logic one wants to suit ourselves? How do we determine which logic is appropriate for a given situation/problem? Sorry if this is a banal quesion. — Tom Storm

Well, theism is interesting. So take the sorts of arguments that treat existence as a first-order predicate - ∃!. Free logic takes this seriously, but goes on to show that one cannot deduce the existence of some individual in a valid free logic without question-begging. It seems existence is presumed, not proven. That is, taking the theistic supposition seriously does not lead to the desired conclusion. What it does do is clarify what is going on when one claims that something exists. (See Inexpressibility of Existence Conditions)

But how we might deal with a case where, say, two logics over the same domain reach opposite conclusions remains an interesting question.

And one ring to rule them all...

Actually I still don't know what logical pluralism is supposed to mean. I'll continue trudging through the article.

Further on your point...

That's part of what the Russell article in this thread is addressing - the idea being, roughly, that if we reached the sort of impasse you describe, we might do well to develop a logic that frames the problem by adding more bits - "lemma incorporation" in the article. A logic to decide between competing logics.

The discussion would then be ongoing, keeping Logicians in paid work...

The discussion would then be ongoing, keeping Logicians in paid work... — Banno

Given the benefits of the various logics I see no downsides.

A logic to decide between competing logics. — Banno

Goodness. I'll leave this to the pros.

But how we might deal with a case where, say, two logics over the same domain reach opposite conclusions remains an interesting question. — Banno

That's fascinating. As above.

Thank you.

Sounds fair. Is there a risk with pluralism that one might simply select the logic one wants to suit ourselves? How do we determine which logic is appropriate for a given situation/problem? Sorry if this is a banal quesion. — Tom Storm

Banno looks like the cat who has climbed and climbed and now cannot get down, and does not know where he is. What is logic? Banno thinks it is something like the arbitrary manipulation of symbols - and of course there are many ways to arbitrarily manipulate symbols. But that's not what logic is.

Historically logic is the thing by which (discursive) knowledge is produced. When I combine two or more pieces of knowledge to arrive at new knowledge I am by definition utilizing logic. If logical pluralism were true then you could know X and I could know ~X, and we would both have true knowledge, which is absurd. When, "two logics over the same domain reach opposite conclusions," we do not arrive at an "interesting question." We arrive at contradictory conclusions and conflicting arguments, one of which must be wrong.

Meh. it ain't just me up this tree.

- Not just you, but there are also fewer up there than you suppose. Most people recognize that contradictory conclusions cannot both be the result of sound arguments—even and especially laymen.

It's called dialetheism. I thought about doing a thread on it. Probably not.

Cheers. Leon. Sometime, take a read of the Russell article and maybe address it.

Historically logic is the thing by which (discursive) knowledge is produced. When I combine two or more pieces of knowledge to arrive at new knowledge I am by definition utilizing logic. If logical pluralism were true then you could know X and I could know ~X, and we would both have true knowledge, which is absurd. When, "two logics over the same domain reach opposite conclusions," we do not arrive at an "interesting question." We arrive at contradictory conclusions and conflicting arguments, one of which must be wrong. — Leontiskos

Logical pluralists seem to argue that different contexts require different logics and this seems to be determined by the kinds of reasoning or the goals of inquiry involved. So, for the most part, I'm not sure if the result is different conclusions for the same matter, more like different logics used for different situations. But I am just a curious amateur, so for me it's all about the questions.

But how we might deal with a case where, say, two logics over the same domain reach opposite conclusions remains an interesting question. — Banno

How common would this be and how do we determine which logic to employ?

A logic to decide between competing logics. — Banno

This is a slightly scary idea. Could we end up with an infinite regress?

Logical pluralists seem to argue that different contexts require different logics and this seems to be determined by the kinds of reasoning or the goals of inquiry involved. — Tom Storm

No, that's really not it. See:

Logical pluralism takes many forms, but the most philosophically interesting and controversial versions hold that more than one logic can be correct, that is: logics L1 and L2 can disagree about which arguments are valid, and both can be getting things right. — SEP | Logical Pluralism

For example, someone who believes in deductive, inductive, and abductive reasoning is not a logical pluralist. It is in no way controversial that there are different ways of reasoning.* Even SEP's phrase, "getting things right," is weasel language. The controversy and uniqueness of logical pluralism arise with the idea that there are conflicting logics that are all correct.

Each time I look into these theories they turn out to be smoke and mirrors. It looks a lot like the pseudoscience of the logical world. But even on TPF this is largely acknowledged, so there seems little reason to argue.


* Similarly, someone who utilizes different logical languages or formalisms for different arguments is also not a logical pluralist.

How common would this be and how do we determine which logic to employ? — Tom Storm

Could we end up with an infinite regress? — Tom Storm

Both interesting questions. I don't have an answer - this is a developing area of enquiry.

Russell borrows lemma incorporation from Lakatos, who was student of Popper and involved in a notary altercation with Feyerabend. In the process she is inviting comparisons between the logic of scientific discovery and meta-logic, and perhaps anticipating a response along the lines of Feyerabend's "Anything goes".

Where that leads, well...

...dialetheism... — frank

From the SEP article:

Since Aristotle, the assumption that consistency is a requirement for truth, validity, meaning, and rationality, has gone largely unchallenged. Modern investigations into dialetheism, in pressing the possibility of inconsistent theories that are nevertheless meaningful, valid, rational, and true, call that assumption into question.

And that is where we stand. Presuming that there is one true logic is no longer viable.

I don't consider this at all unique. I take it that logical pluralism (and nihilism) is just the logical extension of what has occurred in all other areas of discourse, i.e. pluralism and/or nihilism. Historically speaking, such developments look to be inevitable given our overarching ideation. This all perhaps began when religious pluralism was baptized with modern liberalism. The hold-outs seem to be things like scientific and physical pluralism, but maybe that will eventually come too.

And that is where we stand. Presuming that there is one true logic is no longer viable. — Banno

Lol. I suppose that's where things stand if you just ignore the rest of the article and/or appeal to SEP as some sort of normative source, setting out what is allowed and what is not, even though it doesn't present itself that way. (Michael has that difficulty as well). In your case it is less excusable given what I have already pointed out to you. Dialetheism qua dialetheism is the flat-earthism of the logical world. Yet the inquiries of dialetheists can and have been interesting, even if they don't ultimately achieve their purported aim.

Drop in after a couple years to concede your point on knowledge and find you discussing Popper and Russell. Anyways, you're probably right. Whatever that means.

: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

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 — Banno

along the lines of Feyerabend's "Anything goes". — Banno

Yes, I can see this to some extent.

Doesn't Susan Haack argue a somewhat tamer version of this?

https://core.ac.uk/download/pdf/131210177.pdf

pp.13-15

To what extent does your disagreement on this involve, perhaps, one being a conservative and the other liberal?

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.

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

I think we have to differentiate "doing science" and presenting scientific evidence. Inspirational moments and the willingness to try anything isn't the same thing as establishing support for a conclusion. Popper is pretty clear on this point. He encourages people - sometimes - often times the wrong people to question scientific fact and make bold guesses. And insists they try to prove themselves wrong with tests. So, perhaps the thought process is as it's quoted by you but the rigor might be closer to algorithmic.

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'.

In relation to Haack, she seems to be saying that the scientific method is more like 'methods' - a diversity of approaches including creativity, but it is not quite 'anything goes'.

"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. — Banno

Yes, Chomsky says this is the effect of postmodernism (as you say a 'recipe') - radical skepticism about truth and objectivity has insulated the intelligentsia from popular movements and activism. But isn't the conservative approach per-say one where orthodoxy rules, where there is a right way and a wrong way to do pretty much everything? In the case of our question about logic, I'd imagine a conservative might balk against the possibility of logical pluralism. Just a thought.

↪Leontiskos ↪Banno To what extent does your disagreement on this involve, perhaps, one being a conservative and the other liberal? — Tom Storm

It's an understandable trope, but in this case I think it is just that Banno is concerned with what I call metalogic/metamathematics and I am concerned with what I call logic. He was trained in that emphasis and so he thinks of it as logic. Would Banno actually bite the bullet and accept full-blown logical pluralism? I doubt it. I think he is just flirting with it as a contrarian who discovered an exotic idea. And I don't see enough support for that position on TPF or elsewhere to expend much effort critiquing it. Srap's logical pragmatism is an example of an approach which is much better represented.

But the substantive question relates to knowledge, which is why my first post in this thread concentrated on that topic.

(At the end of the day the principle of non-contradiction is the issue, and Aristotle showed long ago why attacks on the PNC can never succeed.)

How do we determine which logic is appropriate for a given situation/problem? Sorry if this is a banal quesion. — Tom Storm

This is a fine question, but I want to say that the better question along these same lines is this: How do we differentiate an argument which is invalid from an argument which is merely pluralistically different? There is no differentiation between the two at the level of the object language, and this inevitably pushes the formalists into a metalanguage.

Stated more simply, if different approaches to logic are just different tools, are there nevertheless tools that won't work? Are there any bad arguments at all? And can someone who says that there are no bad (or good) arguments really call themselves a logician?

Thank you.

But the substantive question relates to knowledge, which is why my first post in this thread concentrated on that topic. — Leontiskos

Well, yes, in the end that's what all this leads to. Fair point.