This isn't an answer to the question though. What do you think is being meant by "correct logic" in these articles? — Count Timothy von Icarus

The idea of a correct logic is endemic to logical monism. I'm not sympathetic to monism, and so I'm not the one to ask this question of.

But presumably correct logic for a monist would be only those logics that make use of the general laws of logic, whatever they might be.

Does that help?

Well, there are consistent and useful systems of logic.

Which is why I ask, what exactly do you think the monist is claiming? — Count Timothy von Icarus

Well, I've been trying to work out what you are claiming, on the presumption that you are advocating monism.

So again, a monist holds that there are logical laws that are common to every system of logic.

No, not that "every logical system people have created has the same entailment relation".

And so it is up to monists to show what it is that all logical systems have in common. I don't see that it can be done.

(edited)

Do some logics lack "a use?" — Count Timothy von Icarus

Perhaps. Although a logician's presenting a logic would be their making use of it.

What does it mean to hold in generality? — Count Timothy von Icarus

In all logical systems, presumably. But I would be happy to consider any other options you might offer.

why would monism remain the dominant position? — Count Timothy von Icarus

Appeal to popularity? So you are seeing the traction in the arguments here.

I've not seen any evidence one way or the other, although I suspect most logicians accept that there are a range of logics - that's pretty undeniable.

In virtue of what is a logic "applicable"? — Count Timothy von Icarus

Come on. When it has a use.

why don't you explain to me why you think pluralism and nihilism are even different positions? — Count Timothy von Icarus

From the core article:
1) To be a law of logic, a principle must hold in complete generality.
2) No principles hold in complete generality.
3) There are no laws of logic.

Monists hold that (2) is false. Pluralists hold that (1) is false. Nihilists hold that the argument is sound. On this account pluralism is different from nihilism.

If the question is "have people created systems with different logical consequence relationships?" the answer is obviously yes. — Count Timothy von Icarus

So we are back to puzzling over whether there are principles that hold in complete generality.

Russell, to be sure, is in that article giving an account of how pluralism can be maintained in the face of nihilism. She is not a nihilist, so far as I can make out.

Well, I imagine that can't use observation to decide between logics unless there are multiple logics.

Deflation is simply the observation that asserting something and saying it is true are truth-functionally equivalent. The cat is on the mat if and only if "The cat is on the mat" is true.

How you decide that the cat is on the mat - by observation, deduction or consulting a clairvoyant, is beside the point.

When people writing on this topic discuss "correct logics," what exactly is it you think they are referring to? — Count Timothy von Icarus

To be sure, it's not a term I would use. Logics are useful, applicable, valid, consistent, incomplete and so on, but not so much "correct".

If all logics are correct logics then nihilism is obvious. — Count Timothy von Icarus

Why? If

Truth just is truth as defined by some system. — Count Timothy von Icarus

what follows is that there are logical laws that apply within each system. What does not follow is that there are no logical laws.

Is the correctness of logic to be decided empirically?

Yes, — Count Timothy von Icarus

So there are multiple logics?

It seems it is worth showing that paraconsistent logic is useful. Have a look at Applications from the IEP article. A google search will reveal uses in engineering and computing.

The IEP article ends with

Affirming coherence and denying absurdity is an act, a job for human beings.

First, the argument is clearly valid.

So if the conclusion is false, one of the premises is false.

I do not pray, so the second premise is true.

Hence the first premise must be false. The first premise is "If God does not exist, then it is false that if I pray, then my prayers will be answered". ~G→~(P→A). Have a closer look at ~(P→A). Here's the truth table:

Notice that if "P" is false, ~(P→A) will also be false. ~P contradicts ~(P→A). But we know that ~P is true from the second premise. And if the consequent is false on a true implication, then the antecedent must also be false. That's how the logic works, and it's quite valid.

But that I don't pray can't imply that God exists. So something is amiss. Just not the logic.

If there is a god, then if you pray your prayers will be answered. This much seems true. So what can we conclude from this, if there is no god? We want to say that if there is no god, my prayers will not be answered. But this can be rendered in two ways.

Consider the difference between ""If God does not exist, then it is false that if I pray, then my prayers will be answered" and "If God does not exist, then if I pray, then it is false that my prayers will be answered". Between ~G→~(P→A) and ~G→(P→~A). These are not the same.

The simple answer is that, using material implication, it is not true that: if god does not exist then it is not true that if I pray then my prayers will be answered; but it is true that: if god does not exist then if I pray my prayers will not be answered.

But in ordinary English, we can say that it is not true that: if god does not exist then it is not true that if I pray then my prayers will be answered,

Only because, unlike the material conditional, the everyday sense allows that a conditional may be false even when its antecedent is false. — TonesInDeepFreeze

made much the same point.

The puzzle has nothing to do with the Inversion Fallacy, or the definition of God, or Denying the Antecedent fallacy, or the ambiguity of "If God does not exist..."; it's an ambiguity in the English use of "If...then" that, when done properly, formal logic sorts out.

As I've said repeatedly, STT need not be deflationary. It is often taking as a means of modeling correspondence truth and this leaves the door open for judging "correct logics" in terms of their ability to preserve correspondence truth not simply truth relative to some formal context. — Count Timothy von Icarus

Well at least we have agreement that the Semantic Theory is noncommittal as to deflation or correspondence. I'm at a bit of a loss as to what happens next. You say that the correct logic is the one that "preserves correspondence truth". Does that mean that correspondence gets to decide between logics? How could that work? Is the correctness of logic to be decided empirically?

And I'm now not sure if you are claiming that there is only one logic, and hence monism, or if you are saying that there are indeed multiple logics, only one of which "preserves correspondence truth".

And it remains unclear to me why you introduced deflation into the conversation.

I'm sorry, I just have not been able to follow what you are claiming.

One of the issues in this thread is indeed the nature of logical pluralism. Deal with it as you will, but repeatedly attacking me is petty.

Is that why I like bagels?


(Also, I much prefer the traditional way of making blastocysts. Much more enjoyable.)

Do us a favour, and read the first few paragraphs here.

Notice the bit that says

Given that, together with the fact that he took the instances of (T) to be contingent, his theory does not qualify as deflationary.

Now what do you make of this? I've understood you as saying Tarski is unavoidably deflationary, and that this is a bad thing.

For my part, talking off the top of my head, I agree with it, and add that deflation is pretty much the only description of truth generally, inflationary accounts only be of use in somewhat special cases.

THis by way of looking for common ground.

Antigone was Jewish? You learn something every day.

This is quite odd. As if we are talking about different things. That's why the detail is so important. I'll have a think and a re-read and see if i can make some sense of it.

Banno, do you really believe that it is equally as obvious that a woman should have a right to abortion as the fact that your hand exists? C'mon man. — Bob Ross

Yep. Although I'd characterise it as that a woman has standing not had by a cyst. I'm sorry you can't see that.

it is a complex issue, and is clearly not resolved in the philosophical literature on abortion. — Bob Ross

Well, yes. But you would have me add to that literature.

I'm not sure I understand the difference between Tarski and Kripke, though. By your sentences they look the same to me, so I'm missing something. — Moliere

Try this:

Tarski's ideas lead to a hierarchy of languages that, like Russian Dolls, each give the truth of the language that they enclose.

Can a language contain its own truth predicate? Various theories do manage this trick. The one I'd like to bowdlerise next derives from a paper by Kripke. The trick, as mentioned earlier, is avoiding the liar paradox: "This sentence is false".

Again, suppose we restrict the language to being about a group of people, Adam, Bob and Carol... and their respective nationalities, English, French... We can construct any number of sentences from these: Adam is English", "Bob is English", "Adam and Bob are french"...

We start by adopting three truth values instead of two. So as well as assigning "true" and "false" to the statements of our language, we add a third value, pictured as sitting in between - not true and not false. (a Kleen evaluation)

Let's call this third value "meh"

We assign "meh" to all the statements of our language.

Then we can give an interpretation to the language, and assign "true" or "false" to these as appropriate; so "Adam is English" is true, and "Adam is French" is false, and so on.

Notice that so far any sentence that contains the term "true" will still have the truth value "meh". So "'Adam is English' is true" is neither truth nor false.

We then start to permit sentences that contain "true" or "false" to be assigned values other than "meh", but under strict conditions. So:

If "Adam is English" is true, then we allow that "'Adam is English' is true" is also true.
If "Adam is French" is false, then we allow that "'Adam is French"' is false" is true.
And so on. Generally, if p is true, then "p is true" is true, and '"p is true" is true' is true, and so on; if p is false, then "p is false" is true, and '"p is false" is true' is true, and so on.

But notice that in this construction, we never get to assigning a truth value to the sentence "this sentence is false". So it remains with the truth value "meh" - neither true nor false. — Banno

So you are quite right that they both use the notion that if "Adam is English" is true, then so is '"Adam is English" is true'. But whereas Tarski uses layered languages, Kripke gives a methodical way to assign truths and avoid liars in the same language.

Abortion is a super controversial topic, and there absolutely no consensus — Bob Ross

That's not quite right. If there were a vote in 'merca, it would be legal. And elsewhere - in roughly comparable nations - it is a non-issue. Those nations in which it remains problematic are authoritarian, so whatever consensus there is remains hidden behind ideology.

What kind of intellectually lazy, disingenuous response is that?!? — Bob Ross

Not mine. I'm asking instead what folk think about the right of Mrs Smith and the rights of a cyst. If they think the cyst is the equal of Mrs Smith, that is not a fact about cysts and Mrs Smith, but a fact about them. They stand judged by their judgement.

Otherwise, there's nothing for me to engage with you about. — Bob Ross

I don't think there is anything here with which to engage. If I were to hold up a hand and say "here is a hand" and you asked for proof, there would similarly be little more to say.

As a side note, how do you expect to convince a pro-life person that your position is correct if you just blanketly assert and say it is obviously true as justification? — Bob Ross

That's not really my concern. First, I would not expect to change your mind, since your view is doubtless close to what has been called your "form of life" and not really open to discussion. Second, I'm not doing politics here, but ethics. I have shown a method that can be applied to ethical issues in order to cut through the bullshit. We differ as to what we think folk should do.

Actually that's another example that I'm wondering about with respect to pluralism -- do logics with more than 2 values count as plural logics, or no? — Moliere

Pretty much. Even including infinite-valued logics.

The liar is clear, in the way you have argued. Rejecting it as a "nonsense" is a failing of nerve, rather than an act of rationality. There are three ways of dealing with it that I think worth considering. Tarski would say that it is a mistake to assign truth values to sentences within the same language, but permissible between languages, so the problem with the liar is that it tries to say something about the falsity of a sentence within it's own language. Kripke would say that we can assign truth values within one language, but that we shouldn't assign them to every sentence, the liar being an example of a sentence to which we cannot assign a truth value. Revision theories would have us say "this sentence is true" is true on the first iteration, false and the second, true on the third... and so on.

Here we have three examples of how accepting and facing the liar enables the development of new and interesting approaches, of creativity. Whereas simply rejecting it as a nonsense closes of such play.

Perhaps that's a nice example of the methodological difference between pluralism and monism. I don't actually think this is quite right, but at the least it shows a difference in approach.

That's a brilliant, thoughtful and charitable post. Well done.

1. Truth is defined relative to different formalisms.
2. Different formalisms each delete some supposed "laws of logic," such that there are no laws that hold across all formalisms.
3. The aforementioned formalisms each have their own definition of truth and their systems preserve their version of truth.
C: There are no laws vis-á-vis inference from true premises to true conclusions. — Count Timothy von Icarus

Is that conclusion supposed to follow? That there are no universal laws does not deny that there are laws specific to each logic.

It is maybe worth pointing out that if someone proposes a new logic, they are obliged to set it out for us to see it, and we can judge it's consistency within itself, as well as its applicability to various situations in comparison to other logics.

This is simply using unclear terms. It's "P is true in L iff P is true in L." Whereas "P is true it and only if P," would simply be meaningless or ambiguous. — Count Timothy von Icarus

I don't follow this, and I don't think it is only becasue you appear to have left out a few quote marks. So let's make it clearer.

"P is true in L iff P is true in L" is a simple tautology, and nothing like the sort fo thing Tarski used. The sort of thing he would have said is more like "'P' is true in L iff S" where S is a sentence in a language other than L, carefully defined so that the S is satisfied only when P is satisfied. That's what that long bit in Tarski's paper that no one reads does - it matches the names in the object language with new names in the meta language.

Quoting oneself is becoming de rigueur...

Designation and Satisfaction
So we have, as a general form for any theory of truth, what Tarski called "Material adequacy",

For any sentence p, p is true if and only if ϕ

And we want to understand what ϕ is.

And we have that in order to avoid the Liar Paradox, we avoid having a language that can talk about itself. Instead, we employ a second language, and use it to talk about the truth of our sentences. We call this the metalanguage, and it talks about the object language. Our sentence "For any sentence p, p is true if and only if ϕ" is a part of the metalanguage, referring to any sentence p of the object language and ϕ is a sentence in the metalanguage

So what is ϕ?

The obvious solution is that ϕ and p are the same. ϕ=p.

But the problem here is that ϕ and p are in different languages. In the metalanguage, p is effectively a name for a sentence in the object language.

Tarski worked around this by introducing terms in his metalanguage that refer to the same thing as terms in the object language; the notion of designation; and then using this to define truth in terms of satisfaction.

Suppose we restrict the object language to being about a group of people, Adam, Bob and Carol...

And in the metalanguage we can have a definition of "designates":

A name n designates an object o if and only if (( n = "Adam" and o = Adam) or ( n = "Bob" and o = Bob) or( n = "Carol" and o = Carol)...

Doubtless this looks cumbersome, despite my having skipped several steps, but it gives us
a metalanguage and and object language both talking about the same objects, Adam, Bob and Carol..., and a way to use the same name in both languages.

We want to add predication. To do this, Tarski developed satisfaction. Suppose we have two nationalities in our object language, English and French. We need a way of talking aobut those nationalities in the metalanguage. We can define "satisfaction":

An object o satisfies a predicate f if and only if ((f="is english" and o is English) or (f="is french" and o is french)

And so, in a cumbersome way, we have the object language and the metalanguage talking about the same predicates and objects.

Here I've used finite lists, but it is possible to construct similar definitions for designation and satisfaction for infinite objects and predicates, and for n-tuple predicates. I'm just not going to do it here. — Banno

A name n designates an object o if and only if (( n = "Adam" and o = Adam) or ( n = "Bob" and o = Bob) or( n = "Carol" and o = Carol)...

There's no "unclear terms" here - indeed, it is clear to the point of being pernickety. Hence the improt of the paper.

I believe that Tarski did not say that truth was nonsense in natural languages, but that it was indefinable. That would be a natural consequence of his theorem that a language cannot contain it's own definition of truth.

Kripke subsequently showed that a language can contain it's own definition of truth, provided one makes use of paraconsistent logic.

So with Tarski we have truth in layers of language, each one talking about the one below it. This is, speaking roughly, what is used in the iterative conception of set theory.

Speaking generally, on the one hand we have clean and clear definitions of truth within formal systems and in terms of satisfaction, and on the other hand we have a broad, ill-defined notion of truth that is supposed to be useful in adjudicating between differing logics as well as in natural languages.

I was intrigued by this:

Deletion is shorthand for considering different sets - or using the set division operation. The sets I'm referring to were $\mathbb{R}$ and $\mathbb{R}^2/\{0\}$. — fdrake

And also weren't comfortable playing around with weird subsets of the plane. Those latter examples were attempts to make similar flavour counterexamples without the... nuclear levels of maths... that help you distinguish the surface of a sphere from flat space. — fdrake

is denying mathematician the right to write $\mathbb{R}^2/\{0\}$, and hence deny them the right to think about $\mathbb{R}^2/\{0\}$. I think this an interesting case study in what we have been discussing. Monism would have it that "you can't think that".

In terms of a puzzle analogy, this seems more like claiming the pieces don't fit together, in which case it doesn't even seem like a puzzle any more. — Count Timothy von Icarus

What if there were several puzzles mixed up? Then sometimes, some pieces would not fit together, being from different puzzles. But that does nto make the puzzles unsolvable. (Nice analogy,

You say the point at the center of a circle can be "deleted" and I say it can't, but you presuppose that there is no way of adjudicating this question. — Leontiskos

Of course there is no way of adjudicating this question. Removing the centre point is a stipulation, of the sort that mathematicians and logicians do as a matter of course. "What happens if we consider $\mathbb{R}^2/\{0\}$? Well, then we have a whole, cool new puzzled to play with..."

I am asking you why you believe that a zygote does not have the same fundamental right to not be killed when innocent like a woman does; and you refuse to engage. — Bob Ross

If you can't see that Mrs Smith has rights not had by a cyst, no theory that I could offer would help you.

Indeed, it's clear that moral theory can be a post hoc attempt to justify doing wrong.

If a theory in physics does not match how things are, we reject it. Again, if a theory of morals does not match how things ought be, then we should reject it.

A cyst ought not bump the rights of Mrs Smith. Thinking otherwise requires ideology.

May as well let him be. You know I enjoy the attention.

, I was responding honestly to questions asked.

So now the thread is about me? Nice.

There's only one correct way to think about it and no one seems to know what that is exactly. — Cheshire

Good summation.

~~

what exactly makes STT a better theory of truth than any other? — Count Timothy von Icarus

Well, it's right. "P" is true iff P is about as direct as you can get.

Return to the basic principle things ought to make sense. How that is accomplished may vary. — Cheshire

Yep. And if there are more than one set of basic principles, then we have one form of pluralism.

And if a set of basic principles is found, then the challenge is set to see what happens if we change them, try different basic principles, or diagonalise in some way... to look at logic differently and undermine it to see what happens.

Put another way, how could we ever be sure that some set of basic principles is sufficient for all of logic?

The story at least since Russell's paradox and Gödel seems to indicate that this is not what happens.

:rofl:
So I'm to blame for and @Tom Storm's questions. Fine.

From the SEP article...

One option available to the monist is to interpret the claim that there is one and only one correct logic noncognitively. Clarke-Doane, after finding no satisfying factualist construal of monism, interprets the claim as expressing an attitude. Perhaps this strategy could be extended to the debate between monists and pluralists more broadly.

That's were I came across the Clarke-Doane article and the discussion of approaching the issue as one of attitude.

But you are right, that things would be a lot simpler if we were just to go back to Aristotle.

I prefer "Keep your mind too open and it will fill up with garbage".

~~

On deflationary accounts, “all that can be significantly said about truth is exhausted by an account of the role of the expression ‘true’... in our [speech] or thought,” and we might add formal systems here. Thus, notions of truth are neither “metaphysically substantive nor explanatory.” — Count Timothy von Icarus

So what's the problem? It's not as if deflationary accounts say that there are not truths.

In Model theory truth isn't eliminated, but given a firm grounding in satisfaction.

Issues of "being" are not ignored by formal logic, either, but explicated by quantification, predication and equivalence.

If I am candid, it seems to me that your fears are ill conceived and unfounded.

Which means it's methodological - it's about attitude. Closed or open.

This goes back to the discussion with Tom:

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

Monism, and authoritarianism, offer certainty.

No, I'm not. I've simply cut to the core issue. Perhaps you can see that a cyst is not morally on a par with Mrs Smith, and so are nonplussed. I won't to engage in a clever debate over the meaning of "person" and "human being" and so on, in order to defend your ideology. It's you who must demonstrate that the moral worth of a cyst is the same as that of Mrs Smith, but I doubt it can be done without resorting to mysticism.

Yep. Kleene logic is explosive.

I've read that post twice and I'm still not sure what your criticism is.

I've seen that paper before. I give it credit for at least addressing the issue of metaphysical truth, but it is a prime example of implicit question begging re the deflation of truth. Truth just is something to do with formalism, and how can you pick between formalisms? According to which one is true? Well, you have to use a formalism to discuss truth, and different formalisms say different things. — Count Timothy von Icarus

Am I to read this as you saying truth is something to do with formalism, or as you saying that the flaw in the paper is that it considers truth only to be something to do with formalism?

Or do I just need more coffee?

I guess the obvious question is, if you know what truth is, apart from formal systems, then tell us. Otherwise, it seems to me that we could do far worse than Tarski's account of truth in terms of satisfaction.

And I am still not too sure what you mean by "deflation". Do you think Tarski's account is necessarily deflationary?

Thought you would enjoy it.

The Open Logic Project is a Wiki of sorts, designed to provide a free textbook on logic. It works thorough Naive set theory, propositional an predicate logic, model theory, computability, second-order logic, Lambda Calculus, many-valued logics, modal logic, intuitionistic logic and set theory.

At the end of the section on first-order logics is a short chapter named "Beyond First-order Logic". It ends with this admonition to creativity:

As you may have gathered by now, it is not hard to design a new logic. You
too can create your own a syntax, make up a deductive system, and fashion
a semantics to go with it. You might have to be a bit clever if you want the
derivation system to be complete for the semantics, and it might take some
effort to convince the world at large that your logic is truly interesting. But, in
return, you can enjoy hours of good, clean fun, exploring your logic’s mathe-
matical and computational properties.
Recent decades have witnessed a veritable explosion of formal logics. Fuzzy
logic is designed to model reasoning about vague properties. Probabilistic
logic is designed to model reasoning about uncertainty. Default logics and
nonmonotonic logics are designed to model defeasible forms of reasoning,
which is to say, “reasonable” inferences that can later be overturned in the face
of new information. There are epistemic logics, designed to model reasoning
about knowledge; causal logics, designed to model reasoning about causal re-
lationships; and even “deontic” logics, which are designed to model reason-
ing about moral and ethical obligations. Depending on whether the primary
motivation for introducing these systems is philosophical, mathematical, or
computational, you may find such creatures studies under the rubric of math-
ematical logic, philosophical logic, artificial intelligence, cognitive science, or
elsewhere.
The list goes on and on, and the possibilities seem endless. We may never
attain Leibniz’ dream of reducing all of human reason to calculation—but that
can’t stop us from trying.

The commendation to the student is to be creative. This is a methodological pluralism.

The whole point of having a discussion about abortion is to test and discuss our ethical theories. — Bob Ross

Well, no - the whole point is to decide whether we ought allow abortions or not.

We are to judge ethical theories by what they say we ought do. If someone presents an ethical theory that implies an unethical act, we ought reject that ethical theory.

Now treating a cyst as of equal moral standing to Mrs Smith is unethical.

Hence we ought reject any theory that implies this.

@fdrake, Have a quick look at What is Logical Monism? I suspect you would enjoy it, since it draws on the parallels with mathematics that you are using here.

To put it in super blunt terms, Euclid's theory would have as a consequence that the great circle on a ball is not a circle. The equidistant coplanar criterion would prove that the great circle on a ball is a circle. Those are two different theories - consequence sets - of meaningful statements. A pluralist would get to go "wow, cool!" and choose whatever suits their purposes, a monist would not. — fdrake

Nice. Now we are getting to an interesting bit, that the difference is not about the nature of logic but about logical method.

Have a quick look at What is Logical Monism?. I suspect you would enjoy it, since it draws on the parallels with mathematics that you are using here.

A crucial component of any account of logical consequence is therefore formalization: the process by which we move between meaningful and formal (meaningless) sentences and arguments. We define a logic as a true logic, roughly, when formalizations into it capture all and only consequences that obtain among meaningful sentences.

Interesting. Thanks for this. I'm a bit surprised by you referring to this, since I had taken it that you had a dislike for formalism.

But taking it at face value, how can we be sure that only one logic will "capture all and only consequences that obtain among meaningful sentences." If one logic has "Γ ⊨ φ" and another has Γ' ⊭ φ, what is our basis for choosing which is the One, True? Not either Γ or Γ', without circularity. Some third logic? And again, Which? Does the monograph address this? Are we faced with an explosion of logics?