The larger puzzle is this: How is it the case that, no matter what definition we use, we discover these regularities between math/logic and the world? — J

There are some questions that are problems of language, such as Q2 and Q4. Q2 is dependent upon the definition of "object" and Q4 is dependent on the definition of "cat".

Q1 is also a problem of language, in that dividing 23 objects by 3 gives $7\frac{2}{3}$ things. But Q2 defines a fraction of an object as not being an object, meaning that by definition the number 23 is not divisible (evenly) by 3.

I agree that there are, however, some questions that are not problems of language, such as the equation
${d = 0.5 * g * t^{2}}$ which accurately predicts where a dropped object will be at a given time.

I agree that the solution as to why there is such a good agreement between the equation ${d = 0.5 * g * t^{2}}$ and what we observe in the world is not in language, in that any definition of "object" is irrelevant.

As regards Q3 and the LNC, the propositions "p is the case" and "p is not the case" are mutually exclusive. But in fact it may be difficult to find an example of "p" that can actually be used. For example, as regards problems of language, "half an apple is an object is the case" according to John but "half an apple is an object is not the case" according to Mary. As regards problems not of language, "${d = 0.5 * g * t^{2}}$ is the case" as far as we know but "${d = 0.5 * g * t^{2}}$ is not the case" may be true. The ambiguities in thought are such that an clear-cut example of the LNC may be difficult to find.

To my understanding, we invent an equation and check whether it conforms to what we observe in the world. If it doesn't then we discard it, and if it does then we keep it. We keep the equations that work. In fact we don't need to know why a particular equation works as long as it does work.

However, the fact that an equation such as ${d = 0.5 * g * t^{2}}$ has consistently been shown to work over a long period of time is no guarantee that it will always work, in that any agreement between the equation and what is observed in the world may be accidental, as pointed out by Hume's concept of the constant conjunction of events.

In answer to your question, if we have invented a maths/logic founded on structural regularities, and discover regularities between our maths/logic and the world, this infers that the world is also founded on a structural regularities.

But that doesn't make Q2 a linguistic problem, since we've stipulated what an "object" will be in this question. — J

The moment we've stipulated what an "object" will be, Q2 becomes a linguistic problem, because there are many different ways an "object" can be stipulated.
===============================================================================

But what about the problem posed by the question itself, now disambiguated? -- presumably you'd say "No, it can't be divided evenly" and so we want to know whether this is due to a mathematical fact or a fact about the world. — J

Q2 is defining an object as being whole and unbroken.

Therefore, 24 objects can be evenly divided into three collections each of 8 objects

Also, 23 objects can be evenly divided into three collections each of $7\frac{2}{3}$ things.

By Q2's definition of "object", 23 objects cannot be evenly divided into three collections of objects.

However, other definitions of "object" are possible.

One of the Merriam Webster's definitions of "object" is "something material that may be perceived by the senses".

Using this definition, as $\frac{2}{3}$ of an object is something material that may be perceived by the senses, we can say that $\frac{2}{3}$ of an object is also an object. In that event, 23 objects can be evenly divided into three collections of objects.

Ambiguity arrives through deciding what exactly is the definition of an "object".

Knowing whether 23 objects can be evenly be divided into three collections depends on the definition of "object". This is a linguistic problem that has to be resolved even before we consider mathematical facts about the world.
===============================================================================

Q4: Why can’t my cat be on my lap and in Paris at the same time? (constraint: I live in Maryland) — J

Presumably, "my cat", being an average cat, has a length of 30cm, height of 20cm and width of 15cm, meaning spatially extended.

In other words, "my cat" does exist in more than one location at the same time.

Perhaps not as extreme as Paris and Maryland, but spatially extended nevertheless.

Though perhaps your cat unfortunately died, the brain sent to Paris for medical research and the body buried in Maryland.

In that event, one could rightly say that your cat is both in Paris and Maryland at the same time.

However, this depends on what exactly does "my cat" mean, raising the question as to the meaning of the terms "my" and "cat". This takes us back again into having to solve the linguistic problem before being able to solve the ontological problem.

I don't just see a bunch of atoms grouped together- I see a type of object. — schopenhauer1

Yes, as you say, "I see" a notepad.

In the world are many objects, where each object is a sheet of paper, but it is the "I" that sees them as a single object, a notepad.

It is the "I" that sees a relation between many different objects in the world. It is not the world that is relating a particular set of objects together.

Q2. Why are 23 objects not evenly divisible into three collections of whole and unbroken objects? — J

Q2 is a linguistic problem and results from a particular definition of "object".

23 things can be evenly divided into three collections of $7\frac{2}{3}$ things.

But Q2 defines an object as something that is whole and unbroken, meaning that if a thing can be divided into parts, then by definition that thing cannot be an object.

Therefore, although 23 things can be evenly divided into three collections, by the given definition of "object", 23 objects cannot be evenly divided into three collections.

However, other definitions of "object" are possible.

For example, as the object "house" is the set of other objects, such as "roof", "chimney", "windows", etc, an "object" could have been defined as a set of three other objects, in which event 23 objects is evenly divisible into three collections of whole and unbroken objects.

The metaphysical problem with your scenario though, is that if past events are contingent on future events, then this either implies that the past event doesn't come into existence (because its future dependency doesn't exist) or it just does away with the idea of contingency. If the past event doesn't come into existence because it is contingent on some future event is in a "loop" with, then neither events exist and there is no loop. — Hallucinogen

The Cosmological Argument is that the Universe is only composed of contingent events, but as a contingent event is not a sufficient cause of itself, a necessary being must exist outside such a Universe.

This argument applies to a linear Universe, where future event B is contingent on past event A.

However, in a cyclic Universe, such as proposed by the Big Bounce, there is no past and future. Event B is contingent on event A, but event A was contingent on event B, meaning that event B is contingent upon itself.

In a linear Universe, as a contingent event is not a sufficient cause of itself, there must be a necessary cause outside the contingent event itself, such as a God.

However, in a cyclic world, as an event is not contingent on anything outside of itself, an event is a sufficient cause to itself and needs no necessary cause outside of itself, such as a God.

IE, in a cyclic Universe, as a future event is not contingent on a past event, the existence of a future event is not dependent on the existence of a past event.

(1) Existence is a series of entities and events.
(2) For all series, having no 1st term implies having no nth term.
(3) The universe has an nth term. — Hallucinogen

However, if space and time are in a circular loop, an eternal return, within the wheel of time or a part of the Big Bounce, then no term can be said to be either the 1st or the nth.

In that event, premises 1) and 2) are OK, but premise 3) wouldn't apply.

I believe the speed of light is also a concept. — Carlo Roosen

Yes. The only thing I know for certain are my experiences of sight, sound, touch, taste and smell. I happen to believe that these experiences have been caused by something external to my mind, something I call "the world".

Therefore, every idea I have about what exists in this "world" is an inference from my experiences.

So yes, any idea that I may have about the speed of light can never be any more than what I have inferred from my experiences, and being an inference may not only be of a completely different nature to the something in the world that caused my experience but may also be wrong.

In accordance with what I say above I think the idea of consistency loses its meaning in that context, both because fundamental reality is presumably not something conceptual and because there is no second thing for it to be consistent with even if it were conceptual. — Janus

Though we must have the concept of a fundamental reality, otherwise we couldn't be talking about it.

Presumably, our concept of a fundamental reality, in order to have any value, must be consistent with our observations.

If fundamental reality wasn't consistent with what? Life? If fundamental reality wasn't consistent with life life couldnt exist? Profound! — Janus

The speed of light is a physical constant, part of a fundamental reality, and has been found to be consistently 299,792,458 m/s.

If the speed of light, together with all the other physical constants, exhibited no consistency and continually changed, one day 350,000,000 m/s and the next day 250,000,000 m/s, it seems to me that life would not be possible.

I don't know the answer to your question. I don't know what fundamental reality is consistent with.

What do you think fundamental reality is consistent with?

, it forms empirical evidence of the consistency of fundamental reality.. — Carlo Roosen

:100: If fundamental reality wasn't inherently consistent, life couldn't exist.

..............that with a concept in our mind we can do all kinds of tests to confirm that concept in fundamental reality........................So the concepts still *apply* to fundamental reality..............................You rely on fundamental reality every moment. — Carlo Roosen

As an Indirect Realist, I believe that my conceptual reality has been caused by a fundamental reality, even though I believe that I can never know this fundamental reality.

In my own words:

that with a concept in our mind we can do all kinds of tests to confirm that concept in fundamental reality

Suppose people observe that the Sun appears in the morning in the east and disappears in the evening in the west.

Person A hypothesises that the Earth rotates around the Sun. This hypothesis supports their observations, and leads them to think that they understand fundamental reality.

Person B hypothesises that the sun travels across the sky in a flying chariot driven by fiery horses and ridden by Zeus’s son, Apollo. This hypothesis supports their observations, and also leads them to think that they understand fundamental reality.

IE, the fact that an hypothesis may be justified by observations is no guarantee that the hypothesis describes fundamental reality.

So the concepts still *apply* to fundamental reality

My belief is there is only one fundamental reality, and therefore there is only one cause of our observations.

However, it does not logically follow that because a theory can explain a set of observations, the same theory of necessity also explains the ultimate cause of these observations.

For example, that I can observe a broken window tells me nothing about what caused the window to break.

Both Person A and B are able to predict that tomorrow the sun will rise in the morning in the east, but having a theory that allows them to make predictions about the future does not mean that the theory is describing fundamental reality. In fact, theories explain the immediate cause of observations, not the ultimate cause of such observations, not "fundamental reality".

IE, our concepts apply to our observations, from which we infer fundamental reality.

You rely on fundamental reality every moment.

Yes, on the one hand, without a fundamental reality there would be no observations, but on the other hand, there is no information within an observation as to the cause of such observation. For that, we have to infer the cause using reason, and if inferred, could be wrong.

IE, this is why we directly rely on theories and hypothesise, and only indirectly rely on fundamental reality.

I believe my terms work better because they take away the unease of things not being real. — Carlo Roosen

As an Indirect Realist, I believe that there is "a real, material, external world", aka "fundamental reality", and I know that I have "ideas", aka "conceptual reality".

"Fundamental reality" and "conceptual reality" are good names, but names are not descriptions.

But it should be recognized that as names, they don't include the aspect that the Indirect Realist only has a belief in a "fundamental reality" yet has knowledge of a "conceptual reality".

Who started saying that we cannot talk about things? — Carlo Roosen

The discussion has been around since at least Aristotle, a good 2,000 years ago.

As all our information about any world outside the mind arrives through our five senses, we can only know about an outside world through our senses, which are representations of the outside world.

Therefore, we only directly know representations of any outside world, and therefore only indirectly know about any outside world. This is my position as an Indirect Realist.

If we can only know something indirectly, then that something must be fundamentally unknowable. We can never directly talk about the thing-in-itself, although we can indirectly make inferences about the thing-in-itself.

From the The New World Encyclopaedia on Representation

Indirect realists, unlike idealists, believe that our ideas come from sense data acquired through experiences of a real, material, external world. In any act of perception, the immediate (direct) object of perception is only a sense-datum that represents an external object.

The earliest reference to indirect realism is found in Aristotle’s description of how the eye is affected by changes in an intervening medium rather than by objects themselves. He reasoned that the sense of vision itself must be self-aware, and concluded by proposing that the mind consists of thoughts, and calls the images in the mind "ideas."

If this is a paradox, I don't think it is a very complicated one.............Of course, it's impossible to talk about them yet here we are talking about them. — T Clark

Is there an uncomplicated explanation to the puzzle of how we can talk about things we cannot talk about?

I agree with Kant's Realism, in that a world independent of the mind does exist, but there is no reason to believe that what we imagine to exist in this world, such as tables and chairs, do actually exist in this world in the same way that we imagine them to be.

You can only recognise something "out there" if you already have a concept available "inside"...When you know what you are looking for, fundamental reality gives all the evidence. — Carlo Roosen

I look at the world and perceive many parts in the world.

I have the concept of the letter F in my mind, look at the world, and see the letter F.

The letter F is a unified single whole composed of several parts.

The parts exist in the world.

The question is, does the whole exist in the world or only in my mind?

If the whole does exist in the world, for example the letter F, then what is the ontological nature of the relations between the parts of the letter F in the world?

But if we would listen to Kant, he says we cannot understand fundamental reality. — Carlo Roosen

Kant is a proponent of Realism. in that his belief is that there is a "fundamental reality" that exists independently of our "conceptual reality". This "fundamental reality" contains "things-in-themselves", although we can never know what these "things-in-themselves" are.

There is the paradox within Kant's CPR that Kant doesn't properly answer, though gives an attempt in B276, of how we can know that there are things-in-themselves if we can never know what they are.

To say "transcendentally" is not an answer, in that "transcendentally" is just a name, not a description. In the same way that my saying that it is possible to travel through time using a "wormhole" in space is meaningless.

However, in practice, living in a "conceptual reality" is sufficient. We don't need to understand "fundamental reality" in order to understand "conceptual reality". For example, if I perceive the traffic light to be on red, I can react accordingly. I don't need to know the "fundamental reality" that the traffic light is actually emitting a wavelength of 700nm.

You will agree that our conceptual detection system is at work and recognizes this as a pattern forming the letter E. — Carlo Roosen

We perceive the letter E because we perceive a relation between the "cookies" (the "atoms"). In other words, we see a relation between the parts of the whole.

One aspect is the ontological nature of relations. Where do "relations" exist"? EG, Stanford Encyclopedia of Philosophy Relations

If relations don't ontologically exist in "fundamental reality", then the letter E can only exist in our mind as a "conceptual reality". This also means that other objects, such as "chairs" and "tables", don't exist in "fundamental reality".

If relations do ontologically exist in "fundamental reality", then the letter E exists both in "fundamental reality" and our "conceptual reality". But from this a number of philosophical problems arise.

Using Kant's terminology, if relations don't exist in "fundamental reality", then neither can "noumena" nor "things-in-themselves" exist in "fundamental reality" (the difference between "noumena" and "things-in-themselves" is argued over).

How do you engage with philosophy — Jafar

Find a statement on a recent thread that happens to be of interest. For example:

My belief is in "Innatism", the view that the mind is born with already-formed ideas, knowledge, and beliefs (Wikipedia Innatism)

Find a philosopher who agrees and explain in a few or many words their reasons.

Find a philosopher who disagrees and explain in a few or many words their reasons.

Finish by giving your reasoned opinion as to which philosopher is correct and which is incorrect in a few or many words.

Assuming by thing-in-itself we mean the object qua itself (independently of our experience of it), it sounds like you are denying that you cannot have any knowledge of the things-in-themselves; which cannot be true if there is an a priori structure by which your brain intuits and cognizes objects (which you equally affirmed). This doesn’t seem coherent to me. — Bob Ross

Although Kant and Indirect Realism overlap, it gets confusing when both Kant and Indirect Realism are discussed alongside each other, even though the concept of Indirect Realism was around during Kant's lifetime.

Wikipedia Direct and Indirect Realism

In medieval philosophy, direct realism was defended by Thomas Aquinas. Indirect realism was popular with several early modern philosophers, including René Descartes, John Locke, G. W. Leibniz and David Hume.

===============================================================================

There’s one part of the whole transcendental idealism which poses a threat to the entire enterprise and of which I would like to explore with this forum: the paradoxical and necessary elimination of knowledge of the things-in-themselves via particular knowledge of thing-in-themselves — Bob Ross

You are correct in that as regards Kant and the CPR, the topic of things-in-themselves is a paradox. The CPR leaves us with the paradoxical nature of things-in-themselves, and in that sense the CPR is unsatisfactory, but that is how it is.

It is true that Kant in the CPR does try to justify transcendental knowledge in section B276 "the Refutation of Idealism" using the example of time, but his argument is unpersuasive

Theorem. The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.

The word "transcendental" is a name not a description, and tells us nothing about the nature of transcendental knowledge. It doesn't even tell us that there is such a thing, in the same way that even though the name "unicorn" may exist in language, unicorns don't of necessity exist in the world. In the same way, if asked how to travel instantaneously through time and space, I can say through "wormholes". Naming something "transcendental knowledge" tells us neither whether it is possible in the first place nor even if it were possible how it is explained.

Kant in the CPR has no escape from this paradox, no explanation and no persuasive justification. Within the CPR, the thing-in-itself is a paradox and remains so

The problem is how to obtain a priori necessary knowledge from a posteriori contingent knowledge. Kant in the CPR says "transcendentally", but this is just a name, as "unicorns" and "wormholes" are just names not descriptions.
===============================================================================

To me, I would agree that the best explanation, given experience, is that there are objects impacting our senses: but that is derived from empirical data from (ultimately) our experience itself. — Bob Ross

As regards this topic, your position seems similar to Kant's

This is the problem. How to discover a priori necessary knowledge from a posteriori contingent knowledge.

Locke said we have innate knowledge, which Kant rejects.

Hume says our knowledge comes from the observation of the constant conjunction of a posteriori events, but this does not give us a priori necessary knowledge

Kant in the CPR developed Hume's idea, and said we have a priori necessary knowledge transcendentally from a posteriori contingent observations. But "transcendentally" is just a word and is meaningless in itself.

My belief is in "Innatism", the view that the mind is born with already-formed ideas, knowledge, and beliefs (Wikipedia Innatism), whereby my belief that my experiences have been caused by something else is part of the structure of my brain.

The problem with the CPR is that Kant doesn't explain how "transcendentally" is possible, leaving the paradox within the CPR of the possibility of knowledge about things-in-themselves.

But then the thought occurred to me, why would they be motivated by ‘winning’? — Wayfarer

When you ask a question of ChatGPT, why does it respond at all, what causes it to give any response at all? Because the the physical structure of ChatGPT is such that it is required to give an output on receiving an input.

"Winning" for the ChatGPT is giving an output for every input. Motivation for winning derives from its intrinsic physical structure.

In the same way that "winning" for a tennis player is being able to return the ball back over the net. Human motivation for winning derives from the intrinsic physical structure of the brain.

Barr was quite serious; watch the video. — Art48

There's no context to the video. Who are "they"?

In the context of being a comedian, Barr also said in 10 Feb 2023:

It's just beautiful. Like, I look out my bedroom window. I can't believe it, I see all these gorgeous little tiny baby deer in my yard eating the grass around my pool. I's so fantastic you know, because I can pull out my AR-15 and blow them just to Smithereens, legally.

Is Barr being serious, or using exaggeration to make a point? Exaggeration, hyperbole, metaphor, simile and figures of speech are important aspects of language, and understood for what they are within context.

As regards drinking human blood, there is a BBC article The people who drink human blood which writes

In most major cities around the world, communities of ordinary people – nurses, bar staff, secretaries – are drinking human blood on a regular basis. The question is, why?

In the French quarter of New Orleans, John Edgar Browning is about to take part in a "feeding". It begins as clinically as a medical procedure. His acquaintance first swabs a small patch on Browning’s upper back with alcohol. He then punctures it with a disposable hobby scalpel, and squeezes until the blood starts flowing. Lowering his lips to the wound, Browning's associate now starts lapping up the wine-dark liquid. “He drank it a few times, then cleaned and bandaged me,” Browning says today.

There are thousands of people drinking blood in the US alone.

[Actress Roseanne Barr] says people are eating babies and drinking their blood. Oh, and she says she's not crazy. — Art48

Just taking your first point, you give no attribution for the quote, which is a form of plagiarism, and you don't mention the fact that Roseanne Barr is also a comedian, one of whose jobs is to mock the silliness and stupidity of society.

Kant begins with the presupposition that our experience is representational and proceeds to correctly conclude that knowledge of the things-in-themselves is thusly impossible. — Bob Ross

Suppose I have a visual experience of shapes and colours. There is no doubt in my mind that this visual experience has been caused by something external to the visual experience itself. There is no doubt in my mind that this visual experience didn't cause itself.

It seems part of the a priori structure of the brain to expect that everything that happens has a cause. This cause may be called the thing-in-itself.

The next question is about the relation between my visual experience of a shape, for example, and the external cause of my experiencing this particular shape.

Either, the cause is identical to the effect, Direct Realism, or the cause is different to the effect, a representation, Indirect Realism.

But we only know the effect and can only reason about the cause.

For the Direct Realist, what information is there in an effect to be able to know its cause?

If it were possible to determine from an effect its cause, it would be possible to look at a broken window and know what caused it to break.

I think Kimhi believes that something can have force (not assertoric force) without being asserted. — J

In the mind is the sense that "the sunset is red", and in the world is the referent that the sunset is red.

Frege argues that a proposition can have a sense in the mind even if there is no referent in the world. Khimi argues against this.

This is not a problem for the Indirect Realist, for whom the world exists in the mind, meaning that a referent in the world exists as a sense in the mind. Unity arises in thought, thoughts about sense and thoughts about referents.

However, this is a problem for the Direct Realist, where referents in the world can exist independently of being observed. EG, for the Direct Realist, sunsets were red prior to the existence of any observer thinking that "sunsets are red".

How does a Direct Realist support Khimi and explain a unity between a sense in the mind and a referent in the world when these are independent of each other.

In other words, can there be something in the world having a force, such as a red sunset, prior to it being asserted by an observer that "the sunset is red".

I think the ND review gets it right about Kimhi's debt to Wittgenstein, which he acknowledges. He sees Wittgenstein as a fellow "psycho / logical monist". Is a there a Wittgensteinian response about assertion here that you could offer? (In this context, assertion isn't the same as "reference.") The Indirect Realist challenge is interesting, but I'll leave it alone as my own metaphysics is much closer to direct realism. — J

Assertion vs. reference
As you said, Frege wrote that his most important contribution to philosophy was disassociating the assertoric force from the predicate.

It is true that an assertion and a reference are not the same thing, but they are inseparable. In order to make an assertion, in order for there to be the act of asserting, something must be being asserted. In this case, what is being asserted is a reference.

For example, given the proposition "this grass is green", the somerthing that is being asserted is that this grass is green, where the truth value of the proposition "this grass is green" is given by its referent, ie, that this grass is green.

Frege in On Sense and Reference noted the connection between the assertoric and its referent:

We shall now enquire into the Sense and Reference of a whole assertoric sentence. Such a sentence contains a thought. Should this thought be seen as its Sense or as its Reference?

IE, the duality between assertoric force and predicate may well be equally expressed as the duality between sense and reference.

Wittgenstein and assertion

Within the Tractatus there is no reference to either "assertoric force" or "reference", but only to "sense".

As normal with Wittgenstein, he conflates many topics, whether falsehood and negation, the intensional and the extensional, the psychological and the logical as well as "sense" and "reference".

The unity of thinking and being is the cornerstone of Wittgenstein's Tractatus.

In the Tractatus, it is not the case that a proposition has a sense prior to anything that is being referred to, in that sense may be disassociated from reference, in that the sense of "this grass is green" may be disassociated from its referent in reality, that this grass is green. But rather, the sense of the proposition is what is being referred to, in that there is a unity between the sense of "this grass is green" and its referent, that this grass is green.

TLP 2.221 - What a picture represents is its sense.
TLP 2.222 The agreement or disagreement of its sense with reality constitutes its truth or
falsity

Wittgenstein in the Tractatus is unifying thought and being, and is unifying Frege's "sense" and "reference" into the single term "sense".

Indirect Realism vs Direct Realism

It is in the nature of Indirect Realism that there is a natural unity of thought and being, in that on the one hand we think about the world, and on the other hand, the world we think about exists as a thought. Such a unity is a consequence of logical necessity.

The Direct Realist, on the other hand, has the thought of a red postbox, and the belief that the postbox is red. However, there is no logical necessity that the fact that there is a red postbox in the world will give rise to the thought that there is a red postbox in the world. Any agreement between what exists in the world and any thought about what exists in the world remains contingent.

Indirect Realism has the advantage of thoughts as being necessarily true, whereas Direct Realism has the disadvantage of thoughts as only being contingently true.

Have I succeeded in raising a genuine challenge to Frege — J

An Indirect Realist's challenge to Frege's disassociation of sense from reference

For Frege, a proposition such as "this grass is green" or "this unicorn is intelligent" have a sense and a reference, such that sense and reference can be disassociated. Kimhi is saying that sense and reference cannot be disassociated because they have a unity.

For the Indirect Realist, the colour red doesn't exist in any world outside the mind, but only exists as a concept within the mind. Similarly, other objects such as apples, unicorns and grass don't exist in any world outside the mind either, but only exist as concepts within the mind.

Consider the Schema "this grass is green" in language is true IFF this grass is green in the world. For the Indirect Realist, the world of apples, grass and unicorns exist in the mind as concepts. Therefore, the schema would become: "this grass is green" in language is true IFF the grass is green exists in the mind as a thought.

For the Indirect Realist, the sense of a proposition exists in language in the mind as a thought, and the reference of a proposition exists in the world, which also exists in the mind as a thought.

For the Indirect Realist, sense and reference are unified as both exist in the mind.

Khimi and Wittgenstein
Wittgenstein proposed that language was thought.
For example: Tractatus 5.6 "The limits of my language means the limits of my world."

The sense of a proposition is in language and the reference of a proposition is in the world.

But we only know language through our thoughts, and we only know the world through our thoughts.

It follows that we only know the sense of a proposition though our thoughts and we only know the reference of a proposition through our thoughts.

If Wittgenstein is correct in that language is thought, the sense and reference of a proposion are unified within thought.

Khimi does support Wittgenstein over Frege. From the Notre Dame review of Thinking and Being:

3. It begins to look as though the contemporary neglect of the old puzzles rehearsed by Wittgenstein is far less revelatory of the nature of these puzzles than of the current state of philosophy. The groundbreaking lesson of Kimhi's reflections is that this diagnosis may well be sound. Our sense that we have put these old puzzles behind us bespeaks a "misplaced confidence", one that "stems from our present conceptions of logic and language" (2). The task of addressing these puzzles must be confronted anew. Given that the Parmenidean account of the unity of thinking and being lands us in an aporia, what is required is a diagnosis of what stands in the way of an alternative account of this unity

If Khimi also supports Wittgenstein's idea that language is thought, then for Khimi, this would be a mechanism by which sense and reference are unified, in being unified within thought.

What Kimhi adds to this, in a manner I'm still grappling with, is the unity part: the claim that "the assertion 'p is true' is the same as 'I truly think p'." — J

I don't have access to Thinking and Being, so am using reviews of the book.

Khimi does seem to say that the expression "is true" in a proposition such as "the Moon circles the Earth is true" is redundant.

If I assert that the proposition "the Moon circles the Earth" is true, am I not asserting my belief that the Moon circles the Earth, that I truly think that the Moon circles the Earth?
===============================================================================

The proper object of an assertion of falsehood is always a proposition or representation, whereas the proper object of an assertion of truth can be reality itself. — Leontiskos

The assertion of both truth and falsity about reality

Accepting that the Moon is not made of cheese, the proposition "the Moon is made of cheese" is false, and the proposition "the moon is not made of cheese" is true.

The assertion of truth, that "the Moon is not made of cheese" is an assertion about reality, in that the Moon is not made of cheese.

But what about the assertion of falsity, that "the Moon is made of cheese", What is being asserted. It can only be that the Moon is made of cheese, meaning that an assertion of falsity is also an assertion about what does and doesn't exist in reality.

In this instance, the objects of assertions of both truth and falsity are about reality.

The symmetry of truth and falsity

I only know the meaning of the true proposition that "the Moon is not made of cheese" if I also know the meaning of propositions that are false, such as "the Moon is made of butter", "the Moon is made of diamonds" and "the Moon is made of aluminium".

In this sense, one only knows how to speak about a proposition that is true providing that one also knows about propositions that are false

Perhaps this is what Kimhi means by "speaking of truth one can equally well speak of falsehood". Though in fact, it is more the case that one can only speak the truth by being able to speak about falsehoods.
===============================================================================

There was truth in creation before the serpent spoke, and falsehood (and doubt!) only emerged by and through his speaking. — Leontiskos

On the other hand, truth and falsity only exists as a relation between language and the world.

"Parmenides of Elea was a pre-Socratic Greek philosopher from Elea in Magna Graecia" is true IFF Parmenides of Elea was a pre-Socratic Greek philosopher from Elea in Magna Graecia.

Before the serpent spoke, as pre-language there cannot be truth or falsity, there was no truth or falsity in creation.

As for "this sentence is false" or 'this statement is false"... its essentially meaningless because it doesn't actually "state" anything ie stating something requires the subject of the statement to be separate from the statement itself — Benj96

:100:

It can also be resolved another way by changing the statement itself from "this statement is false" to something like "this statements grammar false is" in this way it remains self referential but justifies falsity by adding a variable to contextualise its falsity - namely erroneous structure. — Benj96

I think that "This statements grammar false is" can be compared to Chomsky's "Colourless green ideas sleep furiously".

"Colourless green ideas sleep furiously" is grammatically correct, yet nonsensical.

The fact that "this statements grammar false is" has an erroneous structure (within English, though perhaps not in other languages) means that it is not grammatical, and if not grammatical, cannot have a meaning.

And if has no meaning, can be neither self-referential nor not-self-referential.

When I see a red box falling on my foot causing me to feel pain, it would be as sensible to say that I see the colour red because the box is red as it would be to say that I feel pain because the box is in pain.

Or in other words, the logical space of events or state of affairs, that which is, defined, by, again, what something is not. Positive facts are mutually related by negative facts in logical space. — Shawn

Yes. If the apple is not on the Moon, then it could be in Australia, it could be on Mars or it could be in New York, where "could" is a modal verb showing possibility.

There is a logical space of modal possibilities, possible states of affairs. Then a fact is a state of affairs that obtains (though this is not necessarily what is given in the Tractatus).

The negative fact, such as the apple is not on the Moon, can be related to a positive fact by the modal possibility in logical space that the apple could be in front of me.

Wittgenstein once said that the totality of facts makes up the world. Now, facts are determined from the sum total of counterfactuals determining what are "facts". — Shawn

There are positive facts, such as this apple is in front of me, and there are negative facts, such as this apple is not on the Moon.

Bertrand Russell thought that there were negative facts, whereas Wittgenstein didn't think that there were negative facts.

Assuming that a negative fact is a counter-factual, as Wittgenstein didn't think that there were negative facts, for Wittgenstein, a positive fact, ie, a fact, cannot therefore be either defined or determined by a negative fact, ie, a counter-factual.

Where it gets bizarre with Kimhi is his further claim that p itself is syncategorematic. You’re right that he regards p as a fact rather than a Fregean complex, but how then is p used? What is the context we need to provide in order to state a relation involving p? I don’t think that, e.g., joining it with q in ‛p & q’ helps. The problem lies in how facts are asserted – how they’re affirmed or denied. — J

I think Kimhi wants to say something more radical – that the context needed to make use of (syncategorematic) ‛p’ has to involve a monistic understanding of what it is to assert. — J

Following on from @Leontiskos, it seems that truth and existence are meta-predicates rather than predicates.
Not "the apple is on the table is true" but "the apple is on the table" is true.
Not "the apple exists" but "the apple" exists.

For Khimi, the proposition "p" is a syncategorematic expression, where "p" is a fact.

Khimi agrees with Frege that a proposition can be both asserted (reference) and unasserted (sense), but whereas Frege thinks that sense and reference can be disassociated, Khimi disagrees and believes that sense and reference are two parts of a single unity

The fact that "I saw the Morning Star" is both asserted, in that it refers to the planet Venus,
and unasserted, in that its sense is of a star the rises in the morning.

For Frege, "unicorns are mythical creatures" can have a sense, a horse-like animal with a single projecting horn from its forehead, even though it doesn't have a reference.

For Khimi, if a proposition has a sense, then it must also have a reference, as sense and reference cannot be disassociated.

Khimi agrees with Wittgenstein that there are no negative facts,

It comes back to Wittgenstein's puzzle, how can not-p negate p, when p may not be the case.

Khimi holds that the idea of a judgement without a contrary is incoherent, in that if I judge the postbox to be red, then I must also be judging whether the postbox is not-red.

This makes sense in that I only know what something is when I know what it isn't.

I only know what it means for there to be rain if I also know what it means for there not to be rain.

To know something, I must know not only "p" but also "not-p".

This concept is mirrored in Wittgenstein's truth tables in the Tractatus. Wittgenstein did not invent truth tables, but their use in modern logic is usually traced back to the Tractatus. Because an exhaustive list of the truth-possibilities of a proposition tells us everything we need to know about that proposition, the truth table then shows us what we need to know about that proposition.

For example, the proposition "It will rain" can be understood by all its possibilities: "it will rain and I will get wet", "it will rain and I won't get wet", "it won't rain and I will get wet" and ""it won't rain and I won't get wet".

A fact such as "p" has meaning only when it can be judged to be "not-p".

A fact such as "the postbox is red" has meaning to me when I can judge whether it is "not-red"

For Khimi, the proposition "the postbox is red" has a sense, as well as a reference, but also "the postbox is not-red" must have a sense as well as a reference, as sense and reference cannot be disassociated.

The question is, what does "the postbox is not-red" refer to?

The colour purple is not-red, as well as the colours orange, brown, turquoise and violet.

Therefore, the colour not-red could be the colour violet.,

Therefore "the postbox is not-red" could be referring to "the postbox is violet".

This introduces possible modal worlds. Wittgenstein is important for his introduction of modality.

From the SEP article Possible Worlds

However, the predominant version of combinatorialism finds its origins in Russell's (1918/1919) theory of logical atomism and Wittgenstein's (1921, 1922, 1974) short but enormously influential Tractatus Logico-Philosophicus.

IE, "p", although syncategorematic, gets its meaning from its contradictory pair "not-p".

All sorts of interesting questions hinge on getting clear about “and”, “or”, “if/IFF”, “can”, “must”, et al. -- well, who knows, maybe we need a better understanding of “on” too. — J

Yes, there are many logical systems other than Frege's First-Order Logic, such as noted in the Wikipedia article on Non-classical logic. Some, I am sure, not invented yet.

When we give the name "Y" to X, we then say such things as "Y is X". When you give the name "Buppy" to your dog, you then write "Bubby is my dog". When I give the name "The Pentastring" to "This sentence has five words" I then write "The Pentastring is "This sentence has five words"".
You SKIP the examples:
A puppy was born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas. That puppy was named "Noorbicks". Noorbicks is the puppy born on August 30, 2024 at 8:00 AM in the house at 100 Main Street in Smalltown, Kansas. — TonesInDeepFreeze

I agree that when we give the name "Y" to X, we can then say "Y is X"

For example, when we give the name "Noorbicks" to the puppy born in Smalltown, Kansas, we can then say "Noorbicks is the puppy born in Smalltown, Kansas"

But this is not what you are doing. You are giving the name "The Pentastring" to "this sentence has five words". You are not giving the name "The Pentastring" to this sentence has five words.

Knowing that "The Pentastring is this sentence has five words" gives me no knowledge about the existence or not in the world of the Pentastring, meaning that I cannot say anything about The Pentastring in the world.

This includes being able to say that The Pentastring is "this sentence has five words".

Thanks, this helps. "Representing" is describing in words, while "mirroring" is more like ostension or making a picture. I'm not satisfied with how this carries over into logical form
(is "on" really a logical connective?), but that can wait till another day. — J

Another day has arrived.

True, prepositions such as "on" are not logical connectives, but rather syncategorematic.

From the Wikipedia article on Syncategorematic term

The distinction between categorematic and syncategorematic terms was established in ancient Greek grammar. Words that designate self-sufficient entities (i.e., nouns or adjectives) were called categorematic, and those that do not stand by themselves were dubbed syncategorematic, (i.e., prepositions, logical connectives, etc.)

Khimi uses the concept of an a syncategorematic expression, where a syncategorematic expression does not add anything to the sense of any proposition embedded in it.

Therefore, within the proposition "p is true", the expression "is true" is a syncategorematic expression, which adds nothing to the sense of "p".

From the Notre Dame review of Irad Khimi's Thinking and Being

A syncategorematic expression does not add anything (whether content or form) to the sense of any proposition embedded in it. On Kimhi's account, the assertions "Not-p", "A thinks p", "p is true" and, last but not least, "p" itself, do not add anything whatsoever to the sense of "p". None of these expressions stands for a relation. In fact, none of them stands for anything. They all are syncategorematic expressions. That the assertion "p" is itself a syncategorematic unit becomes intelligible once it is realized that the propositional symbol "p" consists in a fact rather than a complex (100).

This means that the proposition "the apple is on the table" is also a syncategorematic unit, meaning that it cannot stand by itself, as not being a self-sufficient entity. In terms of the Tractatus, this proposition is a fact rather than a complex, where a complex would be "the apple is on the table and the table is brown in colour". Complexes derive from facts using truth tables.

I think that I can understand that a Tracterian fact, such as the proposition "the apple is on the table" cannot stand by itself, in the same way the the equally valid proposition "matunda ni juu ya meza" cannot stand by itself, in that any proposition needs a context in order for it to be meaningful.

Syncategorematic expressions need a context.

"This sentence has five words" was named "The Pentastring". The Pentastring is "This sentence has five words". — TonesInDeepFreeze

I have no problem with "this sentence has five words" being named "The Pentastring". In other words, "The Pentastring is this sentence has five words".

My fundamental problem is that it is logically impossible to go from knowledge about the content of an expression, such as "The Pentastring is this sentence has five words", to knowledge about something that may or may not exist in the world, such as The Pentastring.

It is logically impossible to go from knowing that "unicorns are grey in colour" to knowing whether unicorns do or not exist in the world.

There is no logical connection between "This sentence has five words" was named "The Pentastring" and The Pentastring is "this sentence has five words".

As you said:

"London" is a city. (false - "London" is a word, not a city) — TonesInDeepFreeze

Can you say what the difference is between "representing" logical form and "mirroring" logical form? The example of the apple on the table suggests that, while "on" is undefinable without circularity, its logical form can nevertheless be shown through usage. That doesn't sound like the same issue -- or is it? — J

Suppose there are two people in a room, A and B. A has prior knowledge about apples on tables. B doesn't have prior knowledge, but wants to know about apples on tables.

Situation 1) The room is windowless. A describes in words to B what it means for there to be an apple on a table

Situation 2) The room has a window. A points to the window, and B sees through the window that there is an apple on a table.

In 1), the logic of an apple on a table is being "represented", it is being "said"

In 2), the logic of an apple on a table is being "mirrored", it is being "shown"

The problem with 1) is that if B has never previously been "shown" an example of one thing on top of another thing, B will never understand what A is saying, will never understand what is being "said".

Yes, because the word "on" is undefinable without being infinite or circular, its logical form cannot be "said", but its logical form can be "shown".

The question we are considering is whether all true sentences are formulable within formalism.

Within the literature, it seems to me that the words i) assertic force, asserted, force, extrinsic and assertion seem to be synonyms for Frege's "reference" and the words ii) content, semantic, intrinsic and unasserted seem to be synonyms for Frege's "sense".

From the Wikipedia article on Formalism (Philosophy)
Formalists within a discipline are completely concerned with "the rules of the game," as there is no other external truth that can be achieved beyond those given rules.

In these terms, situation 1) is a formalist situation.

But within situation 1), B, never having had prior knowledge of an apple on a table, no matter the words used by A, will never know the truth of what it means for there to be an apple on a table

IE, within a Formalist situation, B can never know the truth of the proposition "there is an apple on the table". True sentences can never be formulable within Formalism.

Hmm. Not quite sure I get this. Can you refer us to some passages in the Tractatus? — J

Wittgenstein argues in the TLP that propositions cannot represent logical form, that logical form cannot be expressed in language.

Logical form can only be mirrored in language, shown in propositions.

TLP 4.0312 My fundamental idea is that the "logical constants" are not representatives; that there can be no representatives of the logic of facts.

TLP 4.12 Propositions can represent the hole of reality, but they cannot represent what they have in common with reality in order to be able to represent it - logical form.
In order to be able to represent logical form, we should have to be able to station ourselves with propositions somewhere outside logic, that is to say outside the world.

TLP 4.121 Propositions cannot represent logical form: it is mirrored in them.
What finds its reflection in language, language cannot represent.
What expresses itself in language, we cannot express by means of language.
Propositions show the logical form of reality.
They display it.

TLP 4.1212 What can be shown, cannot be said

As a practical example, given the proposition "the apple is on the table", how can the logical constant "on" be expressed in language?

The Merriam Webster defines "on" as "used as a function word to indicate position in contact with and supported by the top surface of". It then defines "top" as "the highest point, level, or part of something". It then defines "high" as "an elevated place or region". Any attempt to express "on" in language becomes either infinite or circular.

If logical constants cannot be expressed in language, then there is a dualism between language and its logic.

Khimi, however, believes that there is a psychological/logical monism.

Typical statement: “The critical insight -- that any unity in consciousness is essentially self-consciousness of that unity -- is recognized to coincide with the insight that the consciousness of logical activity is inseparable from the capacity to manifest this activity in language.” — J

Depends what he means by "manifest". From Merriam Webster, a synonym of "manifest" is "show".

As Wittgenstein said in the Tractatus, one can show logic but not say it.

Kimhi will have a hard time in arguing for a psychological/logical monism, and against the dualism of psychological saying and logical showing. Language can be said, but the logic within language can only be shown.

This is a little tricky. Doesn't it depend on exactly what we mean by "say 'p'"? — J

As you wrote:

I can say “It is true that there are a hundred thalers on the table” but this adds nothing to the proposition ‛There are a hundred thalers on the table’. — J

Yes, the expression "p is true" says no more than "p".

I agree that "says no more" is a figure of speech, but is intended to have the same meaning as your "adds nothing".

Consider the sentence "there are a hundred thalers on the table is true".

Because the word "true" is internal to the sentence, it cannot be making a judgment or assertion about either i) the other parts of the sentence it is within or ii) the sentence as a whole.

For the word "true" to be making a judgment or assertion about the sentence "there are a hundred thalers on the table" it will have to be external, such as "it is true that "there are a hundred thalers on the table"".

In other words, a sentence cannot be "self-conscious", using another figure of speech.