You're providing the sentences involved with that connection, though. — frank

Well, yes. What of it?

We have the propositional content and we have the propositional attitude. Folk here say Kimhi thinks there is a "force" not captured by either of these. I'm asking what that force is.

He says that the act of assertion, which pins the meaning of a proposition down to the actual world, is secretly there: "smuggled in.". — frank

Secretly in the content? But you understand what "the sun rises in the south" is about, without asserting it's truth. If all that he means is that to understand "the sun rises in the south" is to understand what would be the case for it to be true or false, then yes, I agree.

Frege was saying that the above propositions haven't ever been asserted. His focus is on how one thought follows another, and thoughts which have never been asserted abound in the processing of the mind.

Kimhe says this way of thinking about propositions disconnects thought from the world as if there's some inner sanctum where they dance around isolated from the world of time and space. — frank

Yes, understood. But you do know what "the sun rises in the east" is about, as much as "the sun rises in the north" or "the sun does not rise". These are not disconnected from the world, isolated from time and space.

Kimhi's forces aren't quite illocutionary forces, we're not talking about speech act theory, by my reckoning we're closer to talking about logic — fdrake

Yeah, agreed, but it covers much the same territory. Instead of talking of illocutionary force we might talk of propositional attitude. What's at issue is the supposed difference between an attitude towards a proposition and an attitude within a proposition; Kimhi, on the accounts given here, thinks there is an force that is somehow a part of the content of the proposition, and not of what is being done with it.

But even that is unclear, and depends on which of the various versions one listens to.

My purpose here has simply been to set out how illocutionary force, propositional content, and propositional attitudes are usually seen, in the hope that it provides some background against which @J or someone might set out the issue.

As for engaging with the thread topic on its own terms, I don't see that those terms have been established to anyone's satisfaction.

Again, yes. And how does this relate to assertoric force? What is assertoric force? It's not the illocutionary force of making an assertion...? It's not what is involved in denoting this rather than that? It's something in between, but what?

This is just an application of the classical analytic "What do you mean by..."; but is there a satisfactory answer?

"It is true that the sky is blue" would be an example of something with assertoric force. — schopenhauer1

And of the illocution of making an assertion. So how does assertoric force differ from the illocution of making an assertion?

Yep, all that. We learn to use a language by using it.

So what is the force in assertoric force? Is what you are claiming that the assertoric force is how "The cat" denotes the cat? Than it's about denotation, and fine. But that's not 's "some kind of latent or dormant assertoric force which is inseparable from the sentence itself." It's picking stuff out.

I don't think the notion of assertoric force is clear enough to be understood, if it is something different from denotation or illocutionary force.

but the problem with phrasing it that way is that it closes the question that is supposed to remain open. — Leontiskos

Could that be becasue the question is muddled?

And presumably everyone is in agreement that you can remove the illocutionary force, without being in agreement on whether you can remove the assertoric force, which in itself shows that the two are different. — Leontiskos

Not everyone. Very few, I suspect. To remove the "assertoric force" is to remove whatever it is that makes a declaration into an assertion. And that is what the illocutionary force of does.

The question is subtle. — Leontiskos

Indeed. To the point of invisibility.

So it is making an assertion. Attaching an illocutionary force. Doing something with the proposition.

Kimhi says that the proposition "The orange is good to eat" has existence conferred upon it by someone affirming or denying that the orange is good to eat. — Srap Tasmaner

If this is so, then Kimhi is using "proposition" for what others call an "assertion".

And his argument reduces to his inability to distinguish what the sentence is about from what is being done with it. He is claiming that one cannot understand what a statement is about without deciding if it is true or false.

And here he is just wrong.

We can understand what it would take for a statement to be true or false, without assigning a judgement to the statement.

It would be interesting to ask him about how questions are to be understood. How does "Is that orange good to eat?" exist? Not by being affirmed or denied. How will he account for questions without admitting some alternative? How do questions differ from assertions in his account?

He defines three sorts of problems related to non-existence: (1) empty predicates; (2) vacuous singular terms; (3) problems that implicate the whole proposition — Srap Tasmaner

Ok, this might be informative. Firstly, there is a large body of literature for these issues, so it is not the case that these are ignored by logicians and others. Secondly, there are ways of dealing with these issues, indeed, many for each. It might be argued that there is no consensus, but why should there be? To think that there is one right way to deal with such things is to adopt logical monism, and there are good grounds not to do this.

...how do we think, falsely, that the world is how it is not; — Srap Tasmaner

Well, we don't. It's a confused notion. One response is also from Wittgenstein, and is close to Frege - that to understand (the content of) a statement is to understand what would be involved in it's being true as well as it's being false; to understand the difference between the cat being on the mat and the cat being on the lounge. There's a fair bit in the Tractatus on this, and it is one of the ideas carried into his later work.

So in what way does a proposition "exist"?
— Banno

Only as an abstract object, immanent in an actual use. What I think so far. — Srap Tasmaner

That's not what I am asking. Sure, propositions are abstract, for some notion of "abstract". But what does it mean to say they exist? Following the usual analytic approach, we might ask the contrary question, "what could it mean for a proposition to not exist?". I hope you see this as problematic. And if this latter question is problematic, so is the former. We might do something analogous to Quine's "to be is to be the value of a bound variable", using a second-order logic ranging over propositions, and here it might be clear what it is for a proposition to exist, but that does not seem to be the question being asked. And hence we might do well to approach the notion of propositions existing with some scepticism until it can be made clear what a non-existent proposition might be.

Last night turned into an early morning, so I am somewhat weary, and havn't been able to follow your point closely. But it seems you are pointing out that in order to say that snow is white, is the same as to say that schnee ist weiß, extensionaly, we would need the entire paraphernalia Tarski brings to his discussion of truth. We can't just take "schnee" and "snow" to meant he same thing; we have to show that they are extensionally equivalent, employing something along the lines of

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

...so that the metalanguage is talking about the same things as the object language. Where one arrives is at some variation of Convention T, that "schnee ist weiß" is true iff Snow is white.

Now it is not clear to me that we have made a judgement here as to whether snow is white, or even schnee ist weiß... Rather all we have succeeded in doing is setting out what would have to be the case for "schnee ist weiß" to be true. The judgement remains something further, something outside this logic.

Real life calls. I'll try to return to this later.

Thanks! So we are talking about illocutionary force - a force that

The adoption of the force / content distinction allowed them to construe that which is true / false or is / is-not the case (e.g., a thought, a sentence, a state of affairs) as having its own existence independent of that conferred upon it through the veridical use of the verb “to be.”

"...having its own existence..."? So in what way does a proposition "exist"? I can make sense of it's being treated as the value of a bound variable, "There is a proposition such that it has as it's subject the cat and the mat". Looks like it could be treated extensionally, too.

Analytic philosophy thus became completely unconcerned with the problem of non-existence associated with the propositional whole

What problem? The sort of thing addressed by free logic or possible world semantics? But then it would not be fair to say it was ignored...

Still puzzled.

I can't quite figure out if you want to claim that the notion of assertoric force is so obscure and muddled that we ought to entirely dispense with it or if you rather want to claim that it is so clear and well understood that you can't fathom what the problem might be with it. — Pierre-Normand

Nor can I. If it is just the illocutionary force involved in making an assertion, then it seems reasonably clear, but then what is Kimhi worried about? and if it is something different, then what? A force involved in denoting - what's that, then? Or something else?

You seem to treat it as fairly transparent. So what is it?

So we have Kimhi's proximate thesis: Frege mucked up assertoric force. — Leontiskos

What is Frege's notion of assertoric force, and how was it mucked up, and did subsequent developments of the notion of "force" not address those problems, and how is any of this so central to "Classical" analytic philosophy that it undermines it?

Frege's notion of assertic force is to do with the judgment stroke, it was further developed in different directions by model theory and Oxbridge linguistic philosophy, both of which became ubiquitous. It remains unclear what any problem with "classical" analytic philosophy might be.

The efficacy of false theses — Leontiskos

If the thesis is false, then there is a thesis. But, what is the thesis?

Since "assertoric force" remains obscure, it remains unclear what the problem with "assertoric force" might be.

it effectively closes out a 100+ year-long tradition in modern philosophy, namely, the classical Analytic tradition, — Robert Hanna,

It's not at all clear what "classical" analytic philosophy might be, nor what the argument(s) against it might be, and certainly not that they succeed. Nor is it clear that there is any substantial point here against formal logic as it now stands, nor what any alternative might look like.

And it remains unclear what sort of thing "assertoric force" might be.

In the end I remain unimpressed.

yep.

Putting this discussion in terms of thought rather than statements or propositions is problematic in all sorts of ways, to do with the sort of issues you raise here, and mostly avoided since the first half of last century by talking about language rather than thinking. Seems a retrograde step.

To be clear, Frank seems to be saying that since we do not know which cat is being spoken of, "the cat is on the mat" is not an example of a proposition. Might be OK to think of "The cat sat on the mat" as a variable ranging over propositions.

But you just did.

The only way I can make sense of Frege's idea of a proposition (a thought) that is disconnected from assertion is to imagine that we're looking at humans as if they're robots and we're examining the programming to see where the meaning is coming from. That's wild. — frank

I agree. Wild. But is this anything more than an odd piece of of biography?

If you are incapable of entertaining a statement without deciding if it is true or if it is false, then you and I are different. I can.

Folk seem too keen on claiming that one cannot understand what a statement is about without deciding if it is true or false.
— Banno

I don't think anyone has made that claim. You probably need to understand the truth conditions, but not whether it's true or false. — frank

This pleases me.

So "Put the cat on the mat!" is not truth apt, nor is "Is the cat on the mat?". They are not the sort of sentences that ordinarily might be considered true or false. But "The cat is on the mat" is.

It means it can be either true or false. — frank

...given the right circumstances.

How can it be truth-apt if we don't even know which cat it is? — frank

What do you think "apt" means?

If you like. I disagree. A proposition is best thought of as a sentence that is truth apt. "The cat is on the mat" can be given a truth value, and hence counts as a proposition.

On your account, a proposition's truth value must be fixed by context. I submit that there are propositions for which the truth value is unknown, and yet these count as propositions. Consider "There is life on other planets". I take this to have a truth value, but not one we know. I count it as a proposition. Do you? Is it only a proposition if one specifies which planet?

How could "the cat is on the mat" be truth-apt? — frank

Isn't it apt to be true, or perhaps false? Couldn't it be true, or perhaps false, in suitable circumstances? What more could you want?

A) An extensional analysis of rejection regarding a statement p( x ) must rely on the following claim: asserting the statement ¬p( x ) is equivalent to rejecting p( x ).
B) The equivalence in ( A ) requires that an asserter of p( x ) would commit themselves to all and only the same claims that a rejecter of ~p( x ) would. — fdrake

I appreciate the style here. Yes, in an extensional context, ⊢~p ≡ ~⊢p, so far as I can make out. And belief is not an extensional context. So for beliefs, ⊢~p ≢ ~⊢p.

One could also reject a claim like "abortion is a sin" in a manner which believes in sin and a manner which does not believe in sin. — fdrake

Yes, the first being within the "judgement stroke", the second outside it, and the whole not being amenable to extensional analysis. This is Frege's contribution, to see that setting the judgement stroke to the side permits extensionality. And keeping in mind, extensionality is what makes 'p' the very same thing in the various expresions within the scope of the judgement stroke. So in your example, the protagonists are not talking of the same thing in using the word "sin".

a symbol, such as when we show the modus ponens inference — J

My point was in part to show that "modus ponens inference" is not singular; it's at best a group of loosely related activities which are not fundamental to logic.

Isn't it apparent that treating logic as imperative is a consequence of, and motivation for, logical monism? That's @Leontiskos' game - who else is playing? (He hasn't been around for a few days - hope all is well).

The view from anywhere differs from the view form nowhere in an important respect: while the view from nowhere solipsisticly centres on the self, the view from anywhere is eccentric, looking to account for what others say they see, while seeking broad consensus. It's a variation of the Principle of Charity: we make maximum sense of the words of others if we interpret them in such a way as to maximise agreement. It replaces a focus on "I" with a focus on "Us". It acknowledges that what we are doing here is inherently embedded in a community and extends beyond the self.

Since my joke fell flat, I'll respond again.

Just to be clear, Martin claims that when one asserts the propositionally complex content ~p, one does not thereby engage in a separate act of entertaining the truth value of p (with its own force) separate from the special force that attaches to the overarching content ~p. Rather, on Martin's account, when one claims that ~p, p is presented for the sake of rejection within the overarching negative judgment. — Pierre-Normand

There's something quite amiss in this, to do with the absence of a clear account of "force". One simply can attend to the cat and the mat, and understand the predication, entirely without making a judgement as to the truth of "the cat is on the mat".

And second, the circumstances in which not being on the mat counts as a property of the cat would be, shall we say, quite extraordinary. Talk of cats and mats is what we do. Talk of properties is philosophic wordplay. Point geing that you seem to be tying a nice philosophical knot for yourself.

I appreciated 's "gubbins". Here's the thing: It remains very unclear what "assertoric force" is, and for my part I remain unconvinced, as the kids say, that "It is a thing".

Despite that it remains that we use names to denote, we use sentences to command, question and state, and we can understand what a statement says without making a judgement as to it's truth.

Note the careful absence of "force" in that last paragraph.

...special forces... — Pierre-Normand

A whole different level...?

The interplay between form-of-life relativity, extensional language, and the complexity of expressing de re thoughts highlights a tension between formal logic and the nuances of how we actually use language. In formal systems like first-order logic, negation is usually understood in purely extensional terms: if "the cat is on the mat" is false, then the cat has the complementary property of "not being on the mat." This is a standard binary treatment of predicates. But this way of modeling lacks the resources to capture the rich, context-dependent, and object-dependent (de re) features of thoughts we actually have in ordinary language. The idea that certain de re thoughts, like demonstrative thoughts about specific objects are tied to particular objects in a way that extends beyond simple formal predicates seems to align with a more Fregean perspective. For Frege, proper names and demonstratives carry what he called "singular senses," which directly connect to the object being referred to. First-order predicate logic, being extensional, can't accommodate this kind of object-dependent sense—it abstracts away from the individuality of objects, treating them only as elements of a domain of quantification. Moreover, the asymmetry between positive predicates (like "is-red") and their negations ("isn't-red") seems to invoke Wittgensteinian concerns about how our language practices, rooted in forms of life, inform meaning. The negation of "red" doesn't just refer to some bizarre alternative state of redness, but rather expresses a rejection of a particular way of seeing or classifying the object in question. In contrast, formal logic treats negation as purely symmetric and mechanical, but in actual language use, negation often relies on pragmatic and normative judgments about how things are appropriately described within our specific form of life. This gap between the abstract nature of formal languages and the more grounded, practice-based nature of our ordinary language practices raises a larger philosophical question: how much of what we express in language, especially about objects and properties, can ever be fully captured by formal logic? It's a tension between, on the one hand, the precise and consistent tools of extensional logic, and, on the other, the fluid, context-sensitive tools of natural language that are deeply embedded in our life practices and forms of life. Your point about first-order predicate logic is well taken. In formal systems like first-order logic, negation is usually understood in purely extensional terms: if "the cat is on the mat" is false, then the cat has the complementary property of "not being on the mat." This is a standard binary treatment of predicates. But, as you note, this way of modeling things lacks the resources to capture the rich, context-dependent, and object-dependent (de re) features of thoughts we actually have in ordinary language. The idea that certain de re thoughts, like demonstrative thoughts about specific objects (e.g., this apple), are tied to particular objects in a way that extends beyond simple formal predicates seems to align with a more Fregean perspective. For Frege, proper names and demonstratives carry what he called "singular senses," which directly connect to the object being referred to. First-order predicate logic, being extensional, can't accommodate this kind of object-dependent sense—it abstracts away from the individuality of objects, treating them only as elements of a domain of quantification.
Moreover, your reference to the asymmetry between positive predicates (like "is-red") and their negations ("isn't-red") seems to invoke Wittgensteinian concerns about how our language practices, rooted in forms of life, inform meaning. The negation of "red" doesn't just refer to some bizarre alternative state of redness, but rather expresses a rejection of a particular way of seeing or classifying the object in question. In contrast, formal logic treats negation as purely symmetric and mechanical, but in actual language use, negation often relies on pragmatic and normative judgments about how things are appropriately described within our specific form of life. This gap between the abstract nature of formal languages and the more grounded, practice-based nature of our ordinary language practices raises a larger philosophical question: how much of what we express in language, especially about objects and properties, can ever be fully captured by formal logic? It's a tension between, on the one hand, the precise and consistent tools of extensional logic, and, on the other, the fluid, context-sensitive tools of natural language that are deeply embedded in our life practices and forms of life. Building on this distinction between formal logic and natural language, let's explore further how this tension plays out, especially in light of how we use language in ordinary contexts. When you refer to form-of-life-relativity, you're pointing to something crucial that Wittgenstein emphasizes in his later work. Language isn't just a neutral tool for representing facts; it's deeply embedded in the ways we live, act, and interact with the world. The meaning of a word, including how we handle negation, depends not just on abstract rules but on shared practices—what Wittgenstein calls our "form of life." For example, the meaning of "The cat is not on the mat" isn't just the complementary truth of "The cat is on the mat." It draws on shared background assumptions about what it means for objects to be in certain spatial relations and how we typically describe such relations. Negation, in our everyday language, often carries with it an implicit reference to expectations, norms, and contrasts. For instance, to say "The apple isn't red" is not merely to state the absence of redness; it contrasts with an expectation that apples are often red, so the negation carries a subtle but important normative dimension. This highlights the asymmetry between "is-red" and "isn't-red," as the latter is not just the absence of the property, but often signals a failure or deviation from some expected or typical state of affairs. Extensional languages like first-order predicate logic treat negation purely mechanically. When we negate a predicate in such a language (e.g., "P(x)" becomes "¬P(x)"), we're simply saying that some object doesn't belong to the extension of that predicate. But this misses the richer pragmatic content involved in how we use language. Frege himself was aware of this limitation. He drew a sharp distinction between the sense (Sinn) and reference (Bedeutung) of expressions, arguing that formal systems must focus on reference—the extension of terms—while leaving much of the richness of sense unexplained. In first-order logic, a negated sentence like "The cat is not on the mat" is true if and only if "the cat is on the mat" is false, but this ignores the wider web of meaning that comes with natural language negation, where such statements might involve expectations, context, and shared understanding.De re thoughts are object-dependent in a way that resists formalization in purely extensional terms. Frege's notion of singular senses helps capture this. When we think or speak de re, we're not just quantifying over objects but referring to them in a way that depends on our direct relation to them. For example, the thought "This apple is not red" doesn't just express a truth about the apple's lack of redness, but also depends on our demonstrative relationship to the particular apple we're referring to in this context. This is where formal systems struggle, especially with demonstratives or indexicals (like "this" or "here"). In formal logic, "this apple" is usually modeled as some constant or variable in a domain, abstracting away from the unique, context-dependent way in which we actually engage with the object. But for Frege, the sense of "this apple" is tied directly to the speaker’s cognitive or perceptual connection with the object. This relationship—how we pick out an object in the world and form thoughts about it—is richer than what can be captured in purely extensional terms. The asymmetry between "is-red" and "isn't-red" is important. When we use a positive predicate like "is-red," we're asserting something affirmative about the object's properties in a way that reflects a positive categorization. But when we say "isn't-red," we're not simply placing the object in the complement of the extension of "red." Instead, we are rejecting a specific classification, often against a background expectation. This asymmetry reflects the way our language and our practices of classification are embedded in a shared world of expectations. When we describe something as "not red," it often implies that there’s something notable about this fact. In contrast, formal logic treats these as symmetric: "¬P(x)" is simply the negation of "P(x)," with no extra interpretative layers. But the actual use of negation in our form of life often involves rejecting a default classification or expectation, and this makes negation richer than simple complementation. Your earlier reference to simple language games involving demonstrative thoughts about apples points to something crucial: in ordinary language, the structure of these games allows for rich, context-sensitive thoughts that are difficult to capture in formal systems. In these games, we rely on shared practices for picking out objects and predicates, and our language reflects the complex ways we interact with the world. Formal languages like first-order predicate logic, while useful for modeling certain aspects of truth and inference, strip away much of the context and the interpersonal dimensions of language use. These games involve implicit understandings, normative judgments, and object-dependent references that go beyond the resources of extensional logic. In sum, while extensional logic is powerful for formalizing certain aspects of reasoning, it falls short in capturing the full richness of natural language—especially in cases involving negation, de re thoughts, and asymmetries in predicate use. Language, as used in our form of life, is embedded in practices, expectations, and interactions with objects in the world. It allows us to express thoughts that are dependent on these contexts in ways that formal logic, which abstracts away from this rich background, cannot fully account for. This tension between the two highlights a key philosophical problem: how can we reconcile the precision of formal systems with the expressive flexibility and context-sensitivity of natural language? The limits of extensional logic reveal the need for other approaches—perhaps more dynamic or pragmatically oriented systems—to better reflect the way we actually think, speak, and live.

Called in the nukes. Cheers.

I baulked at Martin's paper mostly because I found the notion of force used throughout to be unclear. Facetiously, again, it's worth noting that nothing (at least nothing physical..) is moved by an assertoric force. Further, the example in the conclusion, that p has no force while ~p has a force all it's own seems fraught:

The unembedded negative thought ~p must therefore be tied to a logical act with a non-assertoric negative force of its own, and judging that not p, accordingly, consists in rejecting the actualization of the possibility to judge that p.

I'm puzzled by what seems an unnecessary multiplication of p's... I'd understood Wittgenstien's notion to be that understanding p and understanding ~p amount to the very same thing, but that judging p or ~p was undertaking a further step. That step I would put in terms of intent, well before the much less lucid notion of force. So proceeding the judgement of the cat not to be on the mat is the separation of cats from mats within a suitable form of life, together with the intent of representing thing in that way.

That is, I'm not seeing "force" as overly helpful here.

Nice.

Well, I hope it's clear that I have more sympathy for game formalism than you have expressed, and also that I am sceptical that there is a thing that is the meaning of an utterance, such that it might be got at by the "full context principle" - not that I am too sure what that might be.

the full context principle assigns meanings (Fregean senses) to subsentential expressions (e.g. names predicates and logical connectives) not only in the context of whole sentences but also in the context the other sentences a sentence relates to in a language game — Pierre-Normand

Should we picture the meaning of a sentence as something we approach only asymptotically, as our comprehension of the context improves?

Though, to split the difference, I agree with ↪unenlightened — Moliere

Well, of course Un's right. @Unenlightened is always right, the bastard. Best just to ignore his posts, else he bring all these threads to an end, leaving us with no alternative but to engage with the real world.

"The overwhelmingly vast majority of truth cannot be expressed by language" is ambiguous. Is it to be understood, as I think Tarskian does, as saying that there are true statements that cannot be stated, (a contradiction), or is it to be understood as that while any particular truth can be stated, not every truth can ever be stated, which is a simple consequence of there being transfinite numbers. — Banno

Quoting myself. A bad sign. Might try this with an analogue.

Supose you are building a deck, which will have forty floor boards screwed to joists. You have four hundred floorboards.

Now it's true that the overwhelmingly vast number of floorboards cannot be screwed to joists. But it is not true that any one floorboard cannot be screwed to the joists.

We can see this by asking to be shown a floorboard that cannot be screwed to the joists. And the answer is, they all can.

Similarly, even supposing that it is true that the overwhelmingly vast majority of truths cannot be expressed by language, it does not follow that any particular truth cannot be expressed in language.

So we ask, show an example of a true statement that cannot be stated. And the answer is, they can all be stated.

I wouldn't sell him short. — J

Fair enough. I misspoke, since what I have at hand is not Kimhi's book but the reports of his book found hereabouts. The ambiguity may not be his. Similarly it's the discussion of PM on this thread that I found problematic, not the account given by Kimhi. I'm not sure what to make of the paragraph you quote, in particular the conclusion: " Therefore, Geach's understanding of Frege's observation conflates the two senses of propositional occurrence: symbolic and actual." Not at all sure what "symbolic and actual" is doing here.

If I were to comment it would be to point out the benefit of treating Modus Ponens as a rule of inference. We might do well to avoid trying to work out what an "actual argument of the form modus ponens" might be, apart from one that makes use of the rule of inference.

It's common for those versed in axiomatic or ealry logics to think in terms of "Laws Of Thought", such as Modus Ponens. It's worth seeing what "Modus Ponens" looks like in the Open Logic text. There's the rule of "→ elimination" for Natural Deduction,
This is understand as that if in a natural deduction you can write "φ" and you can write "φ→ψ" then this rule entitles writing "ψ". and

Proposition 12.19. If Γ ⊢φ and Γ ⊢φ →ψ, then Γ ⊢ψ. — Open Logic, p.180

or the subsequent Deduction Theorem: Γ ∪{φ}⊢ψ if and only if Γ ⊢φ →ψ. The first of these is about what can be written in Γ, the second about what happens when Γ is extended. In the sequent calculus, Modus Ponens is derived. Cut provides a generalisation of Modus Ponens, but the cut elimination theorem displaces it from any centrality. Modus Ponens is not any one expression, and is not always fundamental.

It's worth asking what sort of thing a "Law of thought" might be. Presumably a Law of thought must be such that it hold true in all cases. If there are such entities, then there is "one true logic", that which uses these Laws. Recent work has questioned this, asking why there could not be a variety of correct logics. And some investigation of the view that there might be no correct logics. Don't be too quick to reject logical pluralism. Given any system of rules, it is a simple question of imagination to set out what things would be like if those rules are contradicted.

But if logical pluralism is even a possibility, then the idea of "Laws of Thought" would be undermined, and with it, perhaps the psychologism that Kimhi would reintroduce into logic.

To this mix we might add more general questions about following rules. Language does not only function by observing convention, but also by rejecting convention, by hitting the nail right on the thumb, putting the cart before the hearse, or bringing your chickens home to roast.

We must give up the idea of a clearly defined shared structure which
language-users acquire and then apply to cases. And we should try again to say how convention in any important sense is involved in language; or, as I think, we should give up the attempt to illuminate how we communicate by appeal to conventions. — Davidson, A Nice Derangement of Epitaphs

In this regard it seems to me that Frege, Kimhi and others have a view of philosophy as seeking a closed, consistent and complete account of how things are. We know from other considerations that we can easily achieve completeness usually at the expense of coherence. I'll opt for coherence over completeness.

While I'm rabbiting on, it's worth taking a bit more. care with notions of objectivity. Einstein's great contribution wasn't to set out a view from nowhere, but to give an account that worked anywhere. He recast the Laws of physics so that they worked for anyone, regardless of their frame of reference. Objectivity is about finding explanations that work from multiple points of view; about having explanations that work regardless of where one stands, and so for the many rather than for the one. it's not about the view from nowhere, but about the view from anywhere.

Added: Frege's contribution was in this direction. By setting the assertive force aside he permitted wider agreement. Some might disagree that p is the case, while agreeing that if p were the case, q would follow. Logic allows us to examine the consequences of our options without commitment. Who was it said " "It is the mark of an educated mind to be able to entertain a thought without accepting it"?

...a member of the natural numbers/not being a member of the natural numbers, as based upon the unresolvable paradox. — ucarr

There's noting novel in the natural numbers not being enumerable. What this shows is that the list from which r is derived cannot be constructed.

What I would like is something that shows these unstatable truths to have some sort of significance. Trouble is, if they have significance (note the word), that significance is statable...

That there are unstatable trivialities is not significant.

"The overwhelmingly vast majority of truth cannot be expressed by language" is ambiguous. Is it to be understood, as I think @Tarskian does, as saying that there are true statements that cannot be stated, (a contradiction), or is it to be understood as that while any particular truth can be stated, not every truth can ever be stated, which is a simple consequence of there being transfinite numbers.

Hence my question - give an example of a truth that cannot be stated. "r is a real" is a truth that can be stated.

I suspect this underpins what was said by and . And sets a puzzle to 's restriction on thought - the paradox of being unable to tell us of something that cannot be said.

The paragraph expresses a number, not an unstateable truth.

Yes, yes, all that. So what? Give an example of one of these unstatable true sentences...

The overwhelmingly vast majority of truth cannot be expressed by language.

Oh, my goodness me. How shocking.

Now, can you give an example of one those the truths?

Just one will do. Then we will have an idea of what we are dealing with. Of the import of this startling, enigmatic observation.

Hmm.

I've no high aptitude for logic. Just a rough comprehension of the basics. But by all means keep up the flattery.

Coincidentally there is an article in a recent New Scientist lamenting the use of the word "force" in physics . "...language affects our wordless imaginations so deeply that it can’t fail to influence the way we think."

The notion of force being used in this thread is nothing to do with changing the motion of objects. I suspect this is misleading us.

Illocutionary "force" is not something that inheres in sentences, but what people do with sentences. Denoting is not something that inheres in names, but what people do with names. This performative aspect of language is hidden by talk of sentences having force.

(I) probably never should have wandered into speculations about different kinds or modes of “force,” even though Kimhi himself often seems to do that. — J

Well, it seems that when the notion of "force" is clarified, it doesn't do what Kimhi wants. He's reliant on ambiguity. But further, he seems not to consider the developments of logic and metalogic since Frege - and they are profound.

"Does a strong formalism such as Frege's invalidate whatever can be said or thought about p in ordinary language?" — J

There's an old adage concerning someone complaining about geneticists studying fruit fly when elephants were so much more important. But you can get more fruit fly into a laboratory, and they breed faster, so it makes sense to work with them. What is learned can then be appleid to elephants, if needed. Fruit fly simplify the process so that certain aspects can be examined in detail. Formal logic does much the same thing, but with language. It models certain aspects in a way that can be examined productively. If Kimhi wants to understand elephants, he could do worse than to start with fruit fly.

It is also a mistake to think that what Frege has to say is anything like the present state of play of formal logic. His discussion of truth is a case in point, his argument having been superseded by several generations of subsequent work.

And the discussion in this thread of modus ponens was just plain muddled.

It's hard to be sure, but there seems to be a profound misapprehension concerning what logic is, underpinning the Kimhi's work and much of the writing on this thread. I'm not inspired to go down that path.