Yep.

While I think it's defensible to say that "knowledge does not exist outside mathematics," I don't think I have to, to show the difficulty. — Srap Tasmaner

If an epistemological theory leads us to think we don't know anything, isn't that just evidence that the theory has gone astray?

You know you are reading this.

It's not as if you can do just anything with words - TONK is useless.

Ok, that's neat - formal languages as decidable.

Speaking roughly, truth-theoretical semantics has realism built in to it from the ground up, while proof-theoretical semantics has meaning as use built in to it from the ground up. So again I find this central issue, Davidson against Wittgenstein. I want a way to reconcile this odd dichotomy, to bring the two together.

Well, I never much liked the way the screen in the Tesla looks like an afterthought. No way I'd buy one now.

But I don't know what it means to say "all sets are in the real world". — TonesInDeepFreeze

Yeah, I baulked at that too.

From what I understand, if we allow TONK as a rule then any statement is provable. If we define logical consequence in terms of proof, and since any statement is provable by TONK, any statement is a logical consequence of any other. TONK shows that not just any rule will do for a proof-theoretical approach.

There are subsequent developments in Proof-Theoretic Semantics...

The specific relationship between introduction and elimination rules as formulated in an inversion principle excludes alleged inferential definitions such as that of the connective tonk, — Proof-Theoretic Semantics

But these seem ad hoc to me... I may be just misunderstanding them.

I'm not (or mustn't...) drawing any conclusions here, just trying to make some sense of what turns out to be a surprisingly varied and lively debate.

If you noted Michael's support for indirect realism, it was based on science. — frank

As is the rejection of indirect realism from Austin.

Are you taking your own thread off topic?

In a way, the Cartesian self belongs to both religion and science. — frank

I don't agree with the latter. Science is also an essentially communal activity.

I'm sure there are more versions. Add on if you like. — frank

Neat topic.

Better to stop at Anscombe.

Notice how many of the threads here are about self, but take the first or second definition as granted? All that silly stuff about starting with perception and the thing-in-itself only has traction if one ignores the fact that we are ineluctably embedded in community.

Americans are being shafted.


OECD Doc

Trouble is the only narrative being used to explain this to them is the muddled myth of migrants and inflation. Bernie Sanders is correct.

You're dealing with ingrained human nature, to benefit oneself over that of another. Deception and unscrupulous behavior is a form of survival. — Outlander

So is trust. Those who indulge in deception as a matter of course will be rejected for the commonweal.

I think "bullshit" provides a better tool for analysis here than "post truth". Bullshit is what folk say in order to get what they want, regardless of truth. "Post truth" suggests we are done with truth. With bullshit, there are still truths, they are just denied for expediency. The truth will out: global warming will not go away because the GOP denies it's reality; tariff will fuck more than just the 'mercan economy; appeasing Putin will not end well.

there's no such thing as an uncountable recursive set. — TonesInDeepFreeze

Of course. Nice.

No, because that would be defining 'valid argument', not 'argument' in general. — TonesInDeepFreeze

Cool. So we have {p, q, r} with r designated as the conclusion, and that's an argument, and then in addition if it is a valid argument, r is also the logical consequence of {p, q}. Thanks for clearing this up.

You have a preference for the model-theoretic account of logical consequence, if I've understood aright. it has an intuitive appeal for me. On that, account, an argument is valid iff there are not counter-examples. The SEP article notes "One of the main challenges set by the model-theoretic definition of logical consequence is to distinguish between the logical and the nonlogical vocabulary" and suggests that this might be overlooked if we "limiting the admissible models for a language". This was my puzzle. What follows refers to that article.

Another issue is the difficulty that "the actual world is not accounted for by any model", but this seems to me to be misleading; sure "each model domain is a set, but the actual world presumably contains all sets, and as a collection which includes all sets is too ‘‘large’’ to be a set", but it doesn't follow that there are any particular things int he world that we cannot include in our model. That is, while we may not be able to model everything, we can model anything.

I take it that the "Tonk" argument undermines proof-theoretical accounts by showing them to be arbitrary. My realist tendencies play a role here.

Frankly I haven't yet been able to follow the argument for bringing proof-theoretic and model-theoretic perspectives together, but there is some appeal in that, and I gather that the result would be a win for logical pluralism.

None of this is 'tight" enough for a firm conclusion, but do you have any thoughts?

Your challenge could be taken as: Provide a definition such that any language is exactly one of: formal and informal. — TonesInDeepFreeze

Well expressed; and my hunch is that we cannot provide any such clear cut distinction. So we might stipulate that formal languages are those with recursive formation rules. I can imagine a contrarian logician developing a system that undermined some aspect of that - perhaps, by some novelty, having an uncountable number of formation rules, or some such oddity.

This speculation came about after struggling with two SEP articles. The first was Logical Consequence, which I read with a view to trying to get a handle on what the recent thinking is on what it is for a conclusion to follow from a premise. This led me to the article on Logical Form, were I ran afoul of differentiating Syntax, grammar and semantics. I might have been clearer if I had, after that article, asked what logical structure is.

An argument is a non-empty set of sentences with exactly one of the members designated as the conclusion. — TonesInDeepFreeze

Perhaps one might ask, is that designation arbitrary? Why this sentence rather that that one? Is there more, such that the designated sentence is in addition a Logical Consequence (whatever that is) of the others?

An example: supose we have the sentences {p, q, r} and designate r as the conclusion. Is that an argument, or is there something more, such that in addition, r is the "logical consequence" of {p.q}? This seems to be the sort of thing that relevant logic is chasing. If we have {"Sydney is in Australia", "Some swans are black", "The cat is on the mat"} and designate "The cat is on the mat" as the conclusion, do we then have an argument, albeit a very bad one? Or is there more to an argument than just a grouping of sentences with one designated as the conclusion?

Better after the edit.

Tones made the response I would have - what is "coherent"? The argument is coherent, in so far as it is consistent with propositional logic.

So again, you seem to want two types of validity, one formal and the other informal.

As in, "If I went to the store, I did not go to the store, and I went to the store, so I did not go to the store." That is valid, but meaningless. — Hanover

It isn't meaningless. We have an idea of what it would be to go to the store, and not to go to the store. Yep, you can't do both.

What would it be for an argument not to be "coherent", in your terms? Do you just mean "valid yet unsound"? I'm not seeing what the introduction of "coherent" adds.

Yep.

Now closer this thread.

I suspect you are not long for this forum.

Candidly, there can't be any sensible doubt that the argument in the OP is valid for formal propositional logic. So in order for those who claim it is invalid to be correct, there must be more than one form of validity, and hence logical pluralism follows.

I haven't seen a trusted media link. — Swanty

Then you haven't looked. You are begging for a fight here, seeing hostility where there is none. In that you are playing into the stereotype you supposedly reject.

So what's the problem with religious people not wanting to be forced to display a pride flag? — Swanty

That wasn't the issue. They would not allow others to display the pride flag, banning it from being flown on city property.

I provided fairly extensive argument earlier in the thread.

Thank you.

So I find myself back at some foundational questions. Is there always one and only one answer to the question of an argument's being valid? And closely related, what is the logical structure of an argument, in contrast to its syntax, grammar, and semantics.

In effect, those who claim that the argument in the OP is invalid are inadvertently suggesting that there is more than one way for an argument to be valid - that it is formally valid, in propositional calculus, but that in some other logic it is invalid. In some cases, maintain this goes against some folk's own view as expressed elsewhere.

Or they may be saying that the logical form of the argument is other than that shown by parsing it in propositional calculus. In that case, there would be more than one logical form for even such a simple argument.

There's a bit of all-or-nothing slight of hand going on in the idea that you either value the zygote or you don't, and the implied conclusion that if you value it then it ought not be aborted. Hence the strategic move of putting the argument in terms of a contrast between the cyst and Mrs Smith. Its not about which to value but what to do with those values.

And a repeat of the mistake of suggesting that values must be justified.

But I don't see any progress in the argument in the last week or so; just a different group of folk making much the same errors.

Might be interesting to adduce a formal sentence and demonstrate somehow that it can't be said in English alone (not just that all known attempts failed). — TonesInDeepFreeze

Yep.

Am I right in understanding that the definition you gave of formal languages is strictly syntactic? It is formal iff it follows some rule for being well-formed?

If not, how does it differ?

Bye.

Folk who are interested can gather an idea of why Lionino was off-track from the SEP article on logical consequences.

...can understand proofs... — Outlander

...not so much.

Saw what you did there. :wink:

What you wanted to say...

I didn't want to say anything about possible worlds, nor "causal implication", whatever that might be.

This horse is dead.

Oh yeah.

Cool. I will throw in the occasional beetroot.

Parsnips, I do. Not too keen on turnips.

If you get stuck I will pay you to weed my veggies.

Similarly, we might hunt for "logical consequence" or "consistency" as some sort of ur-concept upon which logic is built. — Srap Tasmaner

Whether we can specify a form for "logical consequence" that will apply universally is the bone of contention in Logical Nihilism

...replaced by AI...

By the way, I greatly enjoyed the video linked in the 'Logical Nihilism' thread. I have a lot of thoughts about it, and a lot of reading to do about it, but just not the time to put it together as a good post now. — TonesInDeepFreeze

Cheers. I've been thinking and reading for three years. Still reading and thinking.

...how would you say? — TonesInDeepFreeze

With difficulty... "For anything, there is something..." and beyond that it gets cumbersome and potentially ambiguous, but can we be sure it could not be put into a page of explanation in not-so-plain English? Is a software licence in a natural language or in a formal language? Should we ask @Hanover? He does lawyering, apparently. Or feed it into ChatGPT...

In simpler terms, the statement is saying: For every choice of x, we can find a y so that, for all z, if certain conditions about x, y, and other variables are true, then one of two broad cases must occur: Either a set of conditions that mostly focus on a specific chain of relations among various entities don’t hold together. Or, a different set of conditions, involving relationships among several other variables, do hold. — ChatGPT

:wink:

The reason we have formal languages is that they make such things easier and clearer; a mediaeval logician would be in great difficulty.

But is that natural? — TonesInDeepFreeze

Yep. We might stipulate a definition of natural language... is French a different natural language to English, or are both just dialects of one natural language? What about Lao?

I'm not offering an answer here, just pointing out that the difference between formal and informal languages is more intractable than it might appear.

A working hypothesis: anything that can be said, can be said in a natural language. But not anything that can be said, can be said in a formal language.

From what I've understood, Kripke also avoids being strictly paraconsistent becasue he does not use a third truth value, but just does not assign a truth value at all to oddities like the Liar.

Very clever.