Leon seems guilty of making a strong assertion in favor of the PNC being conclusive. There's a bit of tentative weight inherent in the PNC that it could be both sub-dominate and remain legitimately problematic.

To your point though I think the detail is in the nature or a better word for how our reality is both seemingly real in a naive sense and yet participatory. I can acknowledge a logical argument, note the premises are correct and concede the conclusion while believing it's wrong. Logic is contractual discourse.

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.

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. — Banno

I just go around assuming I'm wrong a lot. It's gotten less efficient with age and education but I'm always the one pleasantly surprised at the end. So, we have systems that allow for the occasional violation of the PNC or has a suitable alternative been found?

I have come across the paper before and Russell's other stuff. I'm not sure exactly how what you've quoted is supposed to address the question.

support

So replace it with "affirm." I assume you understand what I meant.

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

I don't see it. It doesn't say "pluralism implies a contradiction, thus not-pluralism" but rather "if pluralism then not-PNC.*" How does this give priority to PNC? One might affirm pluralism here and just deny PNC.

And then "if PNC, then not-pluralism." (But this seems irrelevant, and would seem to depend on how pluralism is defined.)

* Whether this premise is true is another question.

No, Leon. If you are going to use the claim to reject there being contradictory logics — Banno

But I never did that, so that makes you wrong four times in a row now. Shoot. I can't have begged the question with a claim I never made.

( - Yep)

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

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.

I don't see it. It doesn't say "pluralism implies a contradiction, thus not-pluralism" but rather "if pluralism then not-PNC.*" How does this give priority to PNC? One might affirm pluralism here and just deny PNC. — Count Timothy von Icarus

I was reading this part as making the PNC conclusive. "Destroyed"? Things will remain contradictory even if there exists more than one way to arrive at a conclusion following a self-consistent process. In any other thread I would agree, but if the matter is logic itself then it cost a bit of the contextual adherence to the assumption that the PNC is a boundary that can't be crossed. Granted it's a nuanced question begging, but I'm curious about the follow through.

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

Pick your poison. Your thesis is that there are true/correct logics with nothing in common, such that we cannot call their similarity logic in a singular sense, and we cannot apply a rational aspect under which they are the same. — Leontiskos

They aren't logical without total adherence seems strong, not incorrect or unintuitive.

They aren't logical without total adherence seems strong — Cheshire

Where do you find that claim, "They aren't logical without total adherence"?

I have asked Banno multiple times whether he agrees or disagrees with the argument, but he is being his usual coy self.

Can you answer the question? Do you agree with the argument? If you disagree then please explain which premise you oppose.

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

Have you stopped beating your wife yet?

To be a law of logic, a principle must hold in complete generality
No principle holds in complete generality
____________________
There are no laws of logic. — Gillian Russell

To be an argument, words as premises and words as conclusions must be related with [laws of] logic.
Gillian Russell made an argument.
______________________
There is [laws of] logic.

Have you stopped beating your wife yet? — Banno

You want to talk about logical pluralism without talking about the PNC? All that means is that you don't want to talk about logical pluralism. You are pretending.

it would turn this thread away form the mere bitch session it is becoming — Banno

Bitch session? It's just another rerun of, "Banno refuses to do philosophy." This is why I said I wanted a thread on Srap's logical pragmatism instead of Banno's logical nominalism. I've seen the episode too many times.

Where do you find that claim, "They aren't logical without total adherence?" — Leontiskos

Implied by stating it's violation is a destruction.

Can you answer the question? Do you agree with the argument? If you disagree then please explain which premise you oppose. — Leontiskos

I haven't encountered all the P logics, so it's inductive. Very persuasive, easy to corroborate, sound, etc.

If two proper logical systems arrive at a contradiction I think we just call it a singularity and move right along. I don't think the argument, no one would normally have to make, has been made. A counter-example of the PNC doesn't destroy it in the sense it hasn't been demonstrated.

I disagree with the first premise. They could have systematic disagree and remain consistent in their conclusions. Somehow, presumably. Or how they couldn't is the argument and this premise is the conclusion. Hence, light begging of the question.

- Remember back when you thought this was an "interesting question"? Now you refuse to look at it.

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

Implied by stating it's violation is a destruction. — Cheshire

Okay, so you think the PNC can be violated without being destroyed?

I disagree with the first premise. They could have systematic disagree and remain consistent in there conclusions. Somehow, presumably. — Cheshire

I'm not really following. Presumably you think the first premise presents a false dichotomy.

Again, I would suggest focusing on the argument I gave, not some argument you are afraid I will give at some point in the future.

Okay, so you think the PNC can be violated without being destroyed? — Leontiskos

I think we don't know that it can't. Things are certainly going to remain contradictory in many cases.

Again, I would suggest focusing on the argument I gave, not some argument you are afraid I will give at some point in the future. — Leontiskos

Not presupposing anything other than you don't get to assume the PNC is a LNC in an argument about whether logical systems can find themselves in opposition and remain true. Does it break a lot of rules about doing philosophy? Yes and no, ironically.

- Okay, well thanks for answering the question. Given that I have an outstanding reply to @Moliere in this thread and Baden elsewhere, I'm going to leave it there as far as our dialogue is concerned. I can't maintain too many conversations at the same time. Take care.

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...

And in virtue of what is a logic appropriate?

I'm not sure how the proposed interpretation of logical consequence is supposed to answer this question.

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.

Now, if there are multiple correct logics, and they contradict each other, what exactly are they both preserving? (Earlier you said pluralism has nothing to do with deflation. This question is precisely why I think the two are related. If one correct logic affirms PNC and is contradicted by another correct logic, then it seems that "truth" has to be deflated and relativized.)

Russell leads with intuitionists' and the denial of LEM for a reason, and presumably it is because there are good arguments, reasons in virtue of which, one might think it is true that some propositions might lack a truth value. But if truth is allowed to be defined entirely arbitrarily, it seems trivial to generate counter examples to modus ponens, disjunctive syllogism, LEM, you name it. We could have a "Protagoras logic," where every premise and conclusion always has the value true for instance; its truth tables would be very easy to develop.

This is what I mean by saying that refusing to allow any metaphysical notion of truth in logic (presumably something all about truth and its preservation) comes close to begging the question re nihilism, or at the very least it makes things very opaque. We wouldn't want to say it's a matter of democratization, but it seems easy for it to head in that direction (e.g. the removal of LEM is introduced by noting that "many philosophers" think it is plausible.)

When you choose to enguage with the articles cited, I'll be happy to join in. — Banno

Can't you do philosophy in your own words, and answer simple questions put to you?

• In an OP with three different articles, you post first, ignore the entire OP and its articles, post your own article, and derail the thread.
• In an OP on Kimhi and Frege, you post first, ignore the OP, and derail the thread with an anachronistic post on illocutionary force. Later on in the thread you were explicitly asked more than once to try to engage the arguments on their own terms.
• In this thread, you literally took a conversation between Srap and I, transplanted it into this thread while calling me out, and then went on to complain that I haven't addressed the OP of this thread.

This shit just happens over and over and over. The double standards are wild. I have a reminder from August 6, "Put Banno on ignore." I had some technological difficulties in the meanwhile, but it's probably time to honor that reminder and start focusing on people who are sincerely interested in philosophy. ...Interested in engaging ideas other than their own.

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.

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'.

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

You don't need to look at the counter example to see how she answers the question, in the opening paragraph she lays it out in that paper: "Logic is the study of validity and validity is a property of arguments... We say an argument is valid just in case it is truth-preserving."

So, again, if two "valid" logics contradict one another, what are they preserving? Can something be true and not true tout court? Or does the truth and validity depend on the system being used? If the latter, how is this position not the very definition of deflationism?

I fail to even see the relevance of the counterexample for the question I asked for this question.

That looks like a stripe of logical pluralism.

Of the sort that basically fails to allow for any substantial difference between pluralism and monism (a "weak" pluralism), sure. Same with the claim that the existence of multiple truth-preserving logics might be taken as evidence for pluralism. But this is obviously a far cry from a strong pluralism where:

-Gillian is in New York
-I am Gillian
-Therefore, I am in New York

Can be used to construct equally "truth-perserving" arguments that prove that the conclusion is true and false.

Or does the truth and validity depend on the system being used? — Count Timothy von Icarus

The validity of Russel's argument depends upon the interpretation mechanism you apply to the sentences in it, and their terms. The first formalisation of it is:

1) Gillian is in Banf,
2) Therefore, I am in Banf.

In standard predicate logic, there would be nothing saying that Gillian=I, because all you can do is assign symbols based on what's in the argument. "I" and "Gillian" are distinct referential symbols, therefore they must be parsed as different entities. In standard predicate logic, something being red does not imply that it is coloured.

If you're thinking "that's nuts", because the argument clearly is "valid" in some sense, you need to come up with a reason why. And you did just that, you mapped the argument as presented to another argument:

1) Gillian is in Banf
2) I am Gillian
3) Therefore, I am in Banf — Count Timothy von Icarus

Which is clearly valid in the original predicate logic. However the mapping between the arguments:

1) Gillian is in Banf.
2) Therefore, I am in Banf.

to

1) Gillian is in Banf
2) I am Gillian
3) Therefore, I am in Banf

is not an operation available to you in original predicate logic. It's an extra logical operation to map argument to argument like that, through the means of natural language comprehension. In effect you've supplemented the original predicate logic with an extra rule, in which you resolve coreference classes of each denoting term in the argument's sentences prior to evaluating whether the premises can be true and the conclusion nevertheless false.

You could then prove a meta-theorem that states that any argument of the first form is valid so long as it's valid in your new logic that resolves the coreference classes - any one where "I" and "Gillian" co-denote.

That is, you stipulate a set of equivalent denoting terms prior to evaluating it - in this case, you would stipulate that "I" would denote the same entity as "Gillian", which makes sense since Gillian was understood to be author.

In another interpretation of that same argument, the argument would be invalid, since when fdrake writes the argument, fdrake is the author, so we don't belong in the same coreference class.

There's a considerable ambiguity in natural language terms and concepts, which gives them a kind of cohesion through fuzzy boundaries, which can then be interpreted as a coherent unity, which seems to be @Leontiskos's method of argument in this thread, to my reckoning.

There's a considerable ambiguity in natural language terms and concepts, which gives them a kind of cohesion through fuzzy boundaries, which can then be interpreted as a coherent unity, — fdrake

Maybe there's a basic imperative to gather everything into a single framework.

If I'm doing something dumb, it's okay to just say that. — Srap Tasmaner

It's just a question of understanding the detail for me.

And you might then think of the center of the circle as a projection of the center of the sphere. And it is, but it's entirely optional. That projection comes after we already have the circle. It's the canonical projection alright, but you could also project that point to any point on the plane, because this projection is just a thing you're doing ― the circle doesn't need it, isn't waiting for this projection, you see? — Srap Tasmaner

1) So I pick a point A in 3 space A={0,0,10} as {x,y,z} coords.
2) I place a plane cutting the point {0,0,0} with unit normal vector {0,0,1} (that's the xy plane). The axel is parallel to the z-axis, it points in the direction of the unit normal.
4) I then pick a circle in the x-y plane, let's just say it's centred at the origin O={0,0,0} with radius r=sqrt(10), which I think is the appropriate distance to make your construction with the cone work.

The center circle O is equivalently determined by the distance sqrt(10), the point A and the choice of the x-y plane.

That connotes a more general construction.

1) I form the sphere of radius R around A.
2) I pick a projection P and a point A. I constrain the projection P that it projects onto a plane whose normal vector is parallel to the sphere radius and that norm(PA)<=R. Intuitively, you travel along a sphere radius and blow up a plane orthogonal to the radius from a point on the radius.
3) I apply P to A, producing PA.
4) I collect the points this plane intersects the sphere's surface together, this will be a circle of radius... sqrt(d(A,PA)^2 + d(PA,intersection point of plane with sphere surface)^2)
5) I have more than enough degrees of freedom in the distance expression in 4, when I can pick A and P and R, to define any circle centred at any point.

Was that the construction?

Thanks for the attempted clarification, but this seems to entirely miss the context of the quoted part of my post, which is not about Russell's thesis.

To clarify, for Russell (and I would suppose most) a "correct logic," is one that is truth-preserving, where true premises lead to a true conclusion.

If it is the case that different "correct (truth preserving) logics" contradict one another, what exactly are they preserving?

If it is assumed that truth is relative, with many unrelated types of truth, this seems to come close to begging the question re logical monism. There will not be a single set of valid, truth-preserving arguments, but many sets that vary according to what "truth is" or "which truth" we are using.

The problem here is that questions regarding logical monism are questions about what is true tout court, analyzed in a discipline that tries to avoid discussions about what exactly truth is. But ignoring this just seems to allow people to talk past each other or engage in less than obvious question begging.


I can't think of any other context where a conversation like this would be considered good philosophy:

Jack: My thesis is that the relationship between these two sets is empty.
Jill: Interesting, how are the two sets defined?
Jack: Hey, stop trying to do metaphysics!

Or alternatively:

Jack: I don't know. We know a member when we see one... except lots of people disagree about membership.

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.

I guess I wasn't sure what this meant. You don't think it is appropriate to judge logics based on whether or not they are truth preserving? If not, what is the measure of appropriateness? The rest of your post doesn't really help me figure out what this is supposed to be. A definition of logical consequence helps us determine the appropriateness of logic how? Just in case the relation isn't empty?

If it is the case that different "correct (truth preserving) logics" contradict one another, what exactly are they preserving? — Count Timothy von Icarus

Jack: I don't know. We know a member when we see one... except lots of people disagree about membership. — Count Timothy von Icarus

It breaks down ambiguities in a concept, attempts to clarify and resolve them, and if the resolutions contradict each other they are presented with their merits and drawbacks. That seems like standard flavour "conceptual analysis" to me. There's just no presupposition that there's one right way of doing things, even if there is a presupposition that people can come to understand the same things with sufficient thought and chatting.

And regarding truth, truth as a concept applies to both.

Gillian is in New York
Therefore, I am in New York.

will have true premises and conclusion when and only when "I" and "Gillian" refer to the same entity. It's thus not a valid argument in the standard sense, as it can be false (the author need not be understood to be Gillian).

vs

Gillian is in New York
I am Gillian.
Therefore, I am in New York.

will be valid, as you've plugged the hole in the previous argument.

If it is the case that different "correct (truth preserving) logics" contradict one another, what exactly are they preserving? — Count Timothy von Icarus

Referencing the above, what they preserve is truth of conclusion given true premises. That is just what truth preservation means. Stipulate what you like, see what follows from it.

Whether you have true premises is a different issue. When you stipulate axioms, you treat them as true. Are they true? Upon what basis can they be considered as such?

Whether you have a true axiomatic system is a different issue again, and I don't really know what it means. How would you compare Peano Arithmetic and Robinson Arithmetic, for example? Which one is true? Is one "more true" than another? What about propositional logic and predicate calculus? These aren't rhetorical questions btw.

I would posit that axioms can be considered to be correct when they entail the intended theorems about the object you've conceived. That is, when they reflect the imagination. For example with @Leontiskos using Euclid's characterisation of circles as a plane figure, it would entail that a great circle on a sphere surface is not a circle... whereas it seems to be "contained in the intended concept" (scarequotes) of a circle. Which might lead you to reject the axioms, or insist upon them... Hence the method adopted in the paper and my dialogue with Leontiskos.

And there is a formalistic definition of truth, a statement is true in a theory when that statement holds in every model of that theory. Like "swans are birds" is true because there are no swans which are not birds, but "swans are white" is false because there are swans which are not white. Every collection of swans is a model of the term "swan", and all you need is one collection with a black swan in it to show the latter is false. Similarly if you wrote down the axioms of a group, something would be true of groups when it is true of every model of the theory induced by group axioms - the sets the groups are made of, and the set operations the group mappings use.

You can think of the latter as related to my dialogue with Leon in the following way - the intuition of a circle makes you want to put the great circle into every theory of circles, everything which describes what circles are, so if you think it should be in the theory, you have to reject (or repair) Euclid's definition.

Edit: or, my preferred option, acknowledge that "circle" is an imprecise concept in natural language and also that there are lots of different useful ways of fleshing it out.