Cheers, Leon. Let me buy you a beer some time.

The idea that different formal logics can each yield sound arguments without contradicting one another is not in any way controversial, and I would not call it logical pluralism. — Leontiskos

Fair enough. Part of the issue here is whether pluralism can be set out clearly. As the SEP article sets out, the issue is as relevant to monism as for pluralism. The question is how the various logics relate. It remains that monism must give an account of which logic is correct. You've made it plain that you don't accept Dialetheism, and will give no reason, so the point is moot.

, "This sentence is false" is about that sentence. It says that it is false. It's like "This sentence has six words" in some ways, and "That sentence is false" in others. There is no obvious reason to think it meaningless.

Not all paraconsistent logics accept dialetheism, but dialethiests are pretty much obligated to accept paraconsistent logic.

There cannot simultaneously be knowledge both of X and ~X. — Leontiskos

And yet Dialetheism. You at least need to make a case, rather than an assertion.

Yep.

And again, there is the challenge set up by that very specification, to find a logic that does not meet it. Monism again restricts development.

, The problem for logical monism is that if there is only one logic, then which one?

(I did read somewhere that modal logic could be "reduced" to first order logic...)

Thinking of all systems as univocal would appear to be putting unnecessary restrictions on the development of logic.

(Quine's rejection of modal logic)

@fdrake, what is the confusion here, do you think? Is it to do with the commensurability of differing logical systems? If logical monism is the view that all logical systems are commensurable, then there is presumably some notion of translation that works between them all. I find that difficult to picture. Perhaps all logics might be found to be variations on Lambda Calculus or some other "foundational" logic, in which case there would be one true logic, begging for some wit to find a logic that is not based on that foundation.

No point. If you can't see that a cyst has less standing than Mrs Smith, you are not even in the same game.

Logical nihilism is not a claim about what is true in classical extensional logic. — Count Timothy von Icarus

Sure. I drew attention to that. But that's were it starts. We can move on to formal intensional logics, if you like, and their algorithmic interpretations. Probably should leave that until we have a bit more agreement, though. It's important to understand that this is an area of development, and not all questions have been answered. For intensional logics, use is made of Kripke's theory of truth, but I certainly don't have the details.

I don't understand why you are talking about truth being defined arbitrarily. Tarski's definition is far from arbitrary.

And yes, I have a rough idea of what deflation is with regard to truth. I'm just not sure what part you take it to play here. For extensional languages we can define truth in terms of satisfaction. I gather you understand that as deflationary? Fine. What's the problem? Is it that you object to such an approach setting up truth in terms of interpretation? But it works.

It looks as if you have not followed the argument. I guess you can't, not without losing too much. Yes, it is about degrees of moral standing. Your essentialism aims for an absolute moral law. But morals are decided, not found, oughts, not is's. That your proposal gives at least the same rights to a cyst as to a person is damning.

Cheers. I've got you off your topic - apologies - becasue what I was considering is what a circle might be defined intrinsically on the surface of a sphere. I might need to draw a diagram...

Anyway, the relevance was the difference between the maths of a sphere in $\mathbb {R}^3$ and intrinsic spherical geometry.

Thanks, . I might add the following, more or less by relating your comments to the article.

It perhaps comes down to what is meant by "truth-preserving". A sentence in a classical extensional logic is consistent if there is at least one interpretation in which it is satisfied. If there is no such interpretation, then it is contradictory. If it is satisfied under every interpretation, then it is valid. Here, "truth-preserving" is replaced by satisfaction.

A given sentence is neither true nor false until given an interpretation. "Γ ⊨ φ" is understood as "Γ satisfies φ". So since Tarski, truth and validity are defined in terms of satisfaction.

Logical nihilism, is the view that "there are no laws of logic, where a law of logic takes the form "Γ ⊨ φ"(p.4). That is, logical nihilism is the view that there are no cases in which Γ satisfies φ.

Russell lists three approaches, as follows:

The cases approach allows us to say more about what logical nihilism amounts to: it is the view that for any set of premises Γ and conclusion φ whatsoever, there is a case in which every member of Γ is true, but φ is not. — p.4

On the interpretations conception then, logical nihilism is the view that for every argument, Γ φ, there are interpretations of the non-logical expressions in Γ and φ which would make every member of Γ true, but φ not true. — p.5

On (the universalist) approach, logical nihilism would be the view that for any argument, there is an assignment which makes all the premises true without making the conclusion true. — p.5

She adopts the interpretations approach, but for simplicity. She gives the impression that her argument might be made using the other two approaches. She proceeds to show how P →Q,Q ⊨P is truth-preserving if the interpretation includes only T; but not if it includes both T and F. That is, it is a logical law under one interpretation, but not under another. She then shows how the law of excluded middle is a logical law in the interpretation (T,F), but not in (T,F,N).

Now what this shows is that truth-preservation is a function of the interpretation. So yes, in your rough terms, truth and validity do depend on the system being used, since that system includes the interpretation.

Now I am not at all sure what you mean by 'deflation". But I am confident that all of the above could, at least for extensional cases, be put in terms of satisfaction, without mention of truth-preservation. If that for you is deflation, than so be it.

I'm not sure where that leaves our chat.

We're just taking a section of the sphere, without any further reference to the point A, which has already done everything needed to guarantee that its coplanar subsets are circles. In particular, we did not need to project A onto the plane that sections the sphere. (We can project it onto that plane, using the obvious orthogonal projection, or anything we like.) — Srap Tasmaner

Nice. That cleared something that I was puzzling over. A Great Circle is defined by only two points on the surface. It can do this becasue it is a straight line. So as on a plane, a line can be defined by two points and a circle by three.

I guess the question then is, in what way are these the same argument?

Would that I were so wise as you. I could have avoided various unpleasantries today.

Ok, so you want a rational way to compare logical systems, an I think this is not the way to talk about the issue. I'll try again.

Anyhow, I would assume the default answer (the one Russell seems to assume as well) is that logics are correct if they are truth preserving, i e., true premises will lead to true conclusions. — Count Timothy von Icarus

Let's look at the example that Russell gives:

One may indeed, according to the view, ask of the following argument:

(32) Gillian Russell is in Banff.
_____________________________
I am in Banff.

as it is presented on the page, whether it is valid or not, and receive two different and equally correct answers. The first might say that the argument is valid, since its premise and conclusion are identical propositions and logical consequence is a reflexive relation, and the second might say (as we normally do) that the argument is not valid, since there are contexts of utterance with respect to which the sentence-character pair which is the premise is true, and the sentence-character pair which is the conclusion is false; a counter-example would be the context in which Kenny is the agent of the context. But this is not yet full-blown logical pluralism, since the only reason there were two answers to the
question was that it was unclear which argument the question was about. Once we disambiguated the question, there remained only the single answer — One true Logic?

But then

One can think about it differently. If one simply stipulates that arguments are made up of sentences, syntactically construed, then one might say that there is a single argument which is unambiguously picked out in the question above, but that that argument is valid, or invalid, relative to different interpretations, or even, less platitudinously, the question of its validity depends on the depth
of the interpretation intended. Assign mere characters to the sentences, and it is possible for the premises to be true and the conclusion false, so the argument is not valid. Assign propositions to them (relative to the context in which this paper was presented) and that is no longer possible, and so the argument is valid. That looks like a stripe of logical pluralism.

What Russell seems to be suggesting is that the difference in interpretation leads to our assigning "valid" and "invalid" to 'the very same' argument. It's not so much that one interpretation is correct, and the other not so. Instead, for Γ, Γ ⊨ φ is true iff in a given interpretation, every member of Γ is true, then so is φ; and for some other system, Γ', Γ' ⊨ φ' is true iff in a given interpretation, every member of Γ' is true, then so is φ'.

Again, you do not have to be here. You do not have to make this thread about me. You could even read the article that this thread is about, and address it.

Good. Notice that in the rest of that introduction she is rejecting this nihilist argument, by suggesting that laws of logic may not have to hold in complete generality.

Now you refuse to look at it. — Leontiskos

When you choose to enguage with the articles cited, I'll be happy to join in. In the mean time, consider:

Loaded question fallacies are particularly effective at derailing rational debates because of their inflammatory nature - the recipient of the loaded question is compelled to defend themselves and may appear flustered or on the back foot. — Your logical fallacy is...

I'm not sure exactly how what you've quoted is supposed to address the question. — Count Timothy von Icarus

Then perhaps I haven't followed your question.

...in virtue of what would true/correct logics be true/correct and false/incorrect ones not be? — Count Timothy von Icarus

Again, true/correct is not my choice of terminology. A logic might be appropriate rather than true. Hence it depends on the interpretation given it. So, as i quoted, "Γ ⊨ φ is true iff whatever.. interpretation is given to the non-logical expressions in Γ and φ, if every member of Γ is true, then so is φ." For extensional logics, satisfaction will suffice.

That's all I can offer, since there not being a general case is kinda the point.

Sure. See Dialetheism. For Aristotle it was “the most certain of all principles”, apparently. I wouldn't use it unless under duress...

Counterfeit money is real money when you buy things with it. It is only when someone is able to make the distinction (measured) and no longer accepts it does it become counterfeit — Harry Hindu

I disagree. Counterfeit money is counterfeit from the get go, having not been manufactured in a way that grants it legitimacy.

(if we are to apply the same line of thinking Wayfarer described about electrons) — Harry Hindu

There's your problem, right there.

Leon seems guilty of making a strong assertion in favor of the PNC being conclusive. — Cheshire

Seems so. Various systems offer alternatives.

Logic is contractual discourse — Cheshire

I could go along with your suggestion as a way-point, but not as a conclusion. If the argument is sound and the premises true, then if the conclusion is false something is amiss and must eventually be addressed.

Sure. So long as the vast gap between the moral worth of an adult human and that of a cyst is recognised.

No, Leon. If you are going to use the claim to reject there being contradictory logics, then you have given primacy to PNC.

You may be right, but True/correct is Leon's term. There's plenty in the detail, and looking to it would turn this thread away form the mere bitch session it is becoming.

The inference depends on accepting PNC. The article mentions goes into this in some detail, but doubtless you will not read that, either.

The only doge here is your refusal to engage with the content.

Can I suggest having a look at the discussion in the article that this thread concerns? Section 1.2, concerning the interpretation of logical laws.

On the interpretations view Γ ⊨ φ is true iff whatever (syntactically appropriate) interpretation is given to the non-logical expressions in Γ and φ, if every member of Γ is true, then so is φ.

"Support" is what one gives a football team. I find the ideas here very interesting, and they fit in with a bunch of other stuff. I reject logical nihilism, but there are also good reasons to reject logical monism. The article that this thread is concerned with tries to show a third path. Some have understood that.

Where have I given primacy to the PNC? — Leontiskos

Where you used it to adjudicate over logics:

If they do, then the PNC has been destroyed. — Leontiskos

Are you disagreeing with my argument or not? — Leontiskos

You are not here to addressing the topic of this thread, by your own account. You do not have to be here, and I am not under any obligation to address your posts.

So we end up with this:

The "true/correct logics" either contradict one another or they don't.
If they do, then the PNC has been destroyed.
If they don't, then we are no longer talking about logical pluralism — Leontiskos

Which is just to give primacy to PNC, and so to beg the question.

B1. There is no true/correct logic. — Leontiskos

That'd be logical nihilism. What is being suggested is logical pluralism.

You might try
1. If we have discursive knowledge, then there are true/correct logics
L1. We have discursive knowledge.
L2. Therefore, there are true/correct logics.

something is happening internally/cognitively that is going on prior to the formalization process of symbolic logic. — schopenhauer1

Language.

I'm not keen on evolutionary teleologies.

...your joke post in the Lounge... — schopenhauer1

...mostly shows how poorly folk hereabouts deal with logic.

Considering this is one of the more fraught moral dilemmas of our time, I am not sure if "it just is, and if you don't agree there is nothing to say," is a particularly good argument. — Count Timothy von Icarus

Indeed, it's not much better than "Here is a hand. If you hold my hand up before us both, and say "here is a hand", and I disagree, that would put an end to one way the conversation might go. At some stage it is reasonable for you to say that I am wrong to say this is not a hand.

If you like. "Natural logic" will collapse into "formal logic" as soon as you take it seriously. The "rationalisations we make" are the very subject of formal logic.

So my problem again here is the use of "foundational". — schopenhauer1

I'd only used "foundational" in response to posts here. Even in propositional logic, axiomatic systems are but one of many, and in those systems there are ma y variations as to which axioms are chosen. Modus Ponens is common, but not essential. Sequent Calculus does not rely on Modus Ponens, but derives it. Natural deduction usually has modus ponens as a propositional rule. Tableaux has a rule concerning what we can write after an implication, more or less in place of modus ponens.Lambda Calculus has nothing analogous to Modus Ponens.

And most certainly, not all logics are axiomatic.

All this by way of suggesting that proposing a foundation for all logics is to invite logicians to undermine that very foundation.

That's kinda the point of logical pluralism.

What exactly is the argument? — Count Timothy von Icarus

That "exactly" is again a pointer to essentialism. What gives someone moral worth need not be a single characteristic or even a given group of characteristics. The rope is a rope despite no one thread running through it's whole length. There need be no essential common feature but instead a series of overlapping similarities. But when we stand back and consider what is before us, it is one rope.

Stand back and consider the differences. We ought not give the blastocyst the same moral standing as the person who carries it. If you cannot see the difference then there isn't a lot more to be said.

It ought be the person carrying the blastocyst who has the main say in what to do with it.

Sure, all that. There is a version of the naturalistic fallacy sitting in this thread. Roughly, folk argue as if, if we could only set out explicitly what it is to be a person or a human or whatever, then we would know for sure if we are allowed to do abortions - we need the "is" to decide the "ought". I think that fundamentally flawed. We decide what is to count as human, and what isn't; we don't discover it.

@Bob Ross has dragged the discussion back to essentialism again. "It's human, so you mustn't kill it", ignoring capital punishment and war and euthanasia.

It's a bunch of cells. It does nto have the moral standing of the person carrying it.

What's the "foundation" mean here? — schopenhauer1

Those supposed foundations are addressed in the Russell article.

Few implementations of propositional logic start with modus ponens. It's most often just a theorem.

Just the shortest path between two points. So pick two points on a sphere, draw the shortest line, then extend that. The result is a great circle. The maths can be done intrinsically, without reference to some coordinate system in which the sphere sits.

Interpretive monism to go with logical monism - the One True Understanding of Lewis Carrol. I prefer Martin Gardiner's analysis.

Besides, I haven't said it three times yet.