OK, but then "actual" has no real meaning. The world we live in isn't distinct as "the actual world", all the possible worlds are actual worlds, and there is no point to calling the world we live in "the actual world", because it's just one of many, which are more properly called possible worlds. — Metaphysician Undercover

On the keyboard in front of you are several keys. The key “t” is an actual key on the keyboard. The key “k” is an actual key on the keyboard. Because there can be more than one actual thing does not make the word “actual” meaningless.

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That the world I live in and provides my empirical experience is "the actual world" must be an illusion........................Now this produces the age old metaphysical question of why do I experience this world, and not some other......................But we still have the same sort of question, why am I in this world, not in one of those others. — Metaphysician Undercover

Because there are more than one actual keys on the keyboard in front of you does not mean that each key is an illusion. We can also ask the question, when you are pressing the actual “t” key why are you not pressing the actual “k” key instead. One answer is that you can only press one key at a time. Not a metaphysical problem but just the nature of time.

Similarly, because there are more than one actual possible worlds does not mean that each actual possible world is an illusion. We can also ask the question, when you are looking at actual possible world 5 why are you not looking at actual possible world 9. One answer is that you can only look at one actual possible world at a time. Not a metaphysical problem but just the nature of time.

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If all the possible worlds are equally "actual", how could one be presupposed and the others theoretical? Doesn't this give unequal status to their actuality? — Metaphysician Undercover

For Lewis and Concretism, we know the actual world we live in and theorise that other possible worlds are also actual.

It is true that there is an unequal status in that we inhabit one of these worlds and theorise about the others, but there is no unequal status in that all these worlds are actual

I didn't see that coming! — frank

A thought:

It seems that it is impossible to understand something from the inside. One has to step outside in order to understand something.

For example, language cannot be understood using language, it can only be understood using a meta-language.

Similarly, modal logic cannot be understood using modal logic. Lewis’s Concretism was attempting this, even though it seems he failed.

SEP - Possible Worlds
Furthermore, because worlds are (plausibly) defined entirely in nonmodal terms, the truth conditions provided by Lewis's translation scheme themselves appear to be free of any implicit modality. Hence, unlike many other popular accounts of possible worlds (notably, the abstractionist accounts discussed in the following section), Lewis's promises to provide a genuine analysis of the modal operators.

Therefore, what is needed is another way to understand modal logic without using modal logic.

Yes that's exactly the problem. What we know as the independent, physical world, source of empirical observations, can no longer be accepted as such. It gets barred off as a sort of unreal illusion, and what we're left with is an extreme idealism where the ideas (possible worlds) are the reality. — Metaphysician Undercover

Davis Lewis in his Concretism presupposes an “actual world” that we live in and theorises about possible worlds where our counterparts live in. These possible worlds are also as “actual” as our world.

However, it is not part of his theory how we have knowledge of our “actual world”.

An Indirect Realist, such as Descartes, Locke, Leibniz, Hume and Russell, or a Phenomenologist, such as Husserl, would disagree that we can know an independent, physical world independent of empirical observations.

For the Indirect Realist and Phenomenologist, an independent, physical world is not barred off as an unreal illusion, and we are not left with an extreme idealism. The Indirect Realist is a believer in the concept of Realism, and the Phenomenonologist never doubts a reality behind the phenomena.

Wikipedia - Direct and Indirect Realism
Indirect perceptual realism is broadly equivalent to the scientific view of perception that subjects do not experience the external world as it really is, but perceive it through the lens of a conceptual framework

SEP - Phenomenology (Philosophy)
The epoché is Husserl's term for the procedure by which the phenomenologist endeavors to suspend commonsense and theoretical assumptions about reality (what he terms the natural attitude) in order to attend only to what is directly given in experience. This is not a skeptical move; reality is never in doubt.

For Lewis’s Concretism, it is not a problem as how we know the "actual world” that we live in, as this knowledge is presupposed, and outside the scope of his theory about possible worlds.

It is also not a problem as to how we can know possible worlds, as this is a theory. In the same way what we know about quarks is a theory, something that has such explanatory power that it is axiomatically assumed to be true.

SEP - Possible Worlds
His theory of worlds, he acknowledges, “does disagree, to an extreme extent, with firm common sense opinion about what there is” (1986, 133). However, Lewis argues that no other theory explains so much so economically.

Lewis’s Concretism attempts to analyse modal operators in non-modal terms using the theory of possible worlds. These possible worlds are as real, actual and concrete as the world we actually live in. The “actual” world we live in is presupposed and the possible worlds are theoretical.

SEP - Possible worlds
Furthermore, because worlds are (plausibly) defined entirely in non-modal terms, the truth conditions provided by Lewis's translation scheme themselves appear to be free of any implicit modality…………………Lewis's promises to provide a genuine analysis of the modal operators.

True, although isn't there an extra conundrum with direct realism: that if it's true, then it must be false (by virtue of what we observe about how the senses work). — frank

Even though quarks cannot be directly observed through the senses, they are accepted as being real because they explain so much and so economically.

Lewis is also saying that his theory, even if not empirically verifiable, because it is so elegant and explanatory should not be dismissed because it initially seems to be against common sense.

The problem being that the possible worlds model produces a separation between the possible worlds and the actual ontological world. Then one has to be selected as the real. — Metaphysician Undercover

As I understand it, for Lewis, it is not necessary to select one of the possible worlds as real, as all possible worlds are as real as each other. All possible worlds are real concrete worlds, actual ontological worlds.

SEP - Possible Worlds
But, for the concretist, other possible worlds are no different in kind from the actual world

As an analogy, the world you live in is more than likely very different to the world I live in (the people you know, the history of your country, the local climate, the geography, the architecture), but it would be wrong to say that your world is more real than my world.

As a science fiction fan, the idea of modal realism doesn't seem all that strange. — frank

His theory of worlds, he acknowledges, “does disagree, to an extreme extent, with firm common sense opinion about what there is” (1986, 133). However, Lewis argues that no other theory explains so much so economically. SEP Possible Worlds

Just a thought, but Lewis’s approach seems very similar to that of Direct Realism.

Lewis argues that because the concept of concrete possible worlds explains so much and so economically, this overcomes any common sense objections we may have to it.

Similarly for the Direct Realist, who argues that the tables and chairs we perceive are ontologically real, rather than indirect representations, because this explains so much and so economically.

Right so given rigid designation the extension of Aristotle is Aristotle in all PWs where Aristotle exists. The extension of "Aristotle" in PW 5 is different than the extension of Aristotle" in PW 6 because the name "Aristotle" refers to different entities if there is no rigid designation....................So the person predicated by "is a man named Aristotle" is a different individual or "entity" in each PW. This individual that has that predication does not change in that PW. — NotAristotle

Rigid designation
The person in PW 5 predicated by “is a man named Aristotle” is the same person as the person in PW 6 predicated by “is a man named Aristotle”.

Non-rigid designation
I agree that the person in PW 5 predicated by “is a man named Aristotle” Is a different person to the person in PW 6 predicated by “is a man named Aristotle”

I agree that the person in PW 5 remains the same person within PW 5.

So it may be that there are no rigid designators across possible worlds........................These entities can have different predicates, but like I said, the things that belong to those predicates, per each PW, will not change. — NotAristotle

In possible world 5 - “Babe is a pig and pigs cannot fly”
In possible world 6 - “Babe is a pig and pigs can fly”

Assuming rigid designators, then as I understand it is true that “These entities can have different predicate, but…………………the things that belong to those predicates, per each PW, will not change”. This means that Aristotle is necessarily Aristotle in all possible worlds, and Babe is necessarily Babe in all possible worlds.

But you are saying, given non-rigid designators, it is also true that “These entities can have different predicate, but…………………the things that belong to those predicates, per each PW, will not change”. This also means that Aristotle is necessarily Aristotle in all possible worlds and Babe is necessarily Babe in all possible worlds.

But then how is modal logic using non-rigid designators different to modal logic using rigid designators?

we're ready to move on to section 2, right? — frank

:up:

But the thing that belongs to the predicates enumerated does not itself change. — NotAristotle

My current understanding taken from various sources:

Suppose in possible world 5 “pigs cannot fly” and in accessible possible world 6 “pigs can fly”.

Modal languages using rigid designators
There are modal languages using rigid designators, such as Modal Logic K, Kripke’s standard modal logic.

These reference the same individual in all possible worlds, in that Aristotle is Aristotle necessarily.

These exhibit de re modality because it is about the modality of the thing. For example, all cyclists are necessarily bipedalists. All swans are necessarily white. All pigs necessarily cannot fly.

In Naming and Necessity Kripke showed that names are rigid designators. Therefore the pig in different possible worlds is the same pig. It is necessarily the same pig, it has the same intension, it has the same meaning and it is the same thing. It may be that possible world 5 is the Earth where pigs cannot fly, and possible world 6 may be Mars where there a low gravity allowing pigs to fly.

Modal languages using non-rigid designators
There are also modal languages using non-rigid designators, such as Epistemic Logic (knowledge and belief) and Temporal Logic.

These can model context dependent references, such that “the current president” can change across possible worlds, in that George Washington was the president accidentally. In other worlds he could have been a soldier.

These exhibit de dicto modality because they are about the modality of the proposition. For example, it is necessary that all cyclists are bipedalists. It is necessary that all swans are white. It is necessary that all pigs cannot fly.

Russell in his 1905 essay On Denoting developed his theory of descriptions. Therefore, what a pig is is determined by its context within the world it exists. It could be that in possible world 5 a pig = {domesticated, omnivorous, mammal, cannot fly} and a pig in possible world 6 = {domesticated, omnivorous, mammal, can fly}.

Therefore, the thing that belongs to the predicate, such as “the pig”, can change dependent on which system of modal logic is used, one with rigid designators or one without.

Yes, but there's a bit more. It's also intensional as it sets out the conditions under which something is a swan, not a list of the swans. I guess properly we should write x:x is white ∧ x is flighted ∧ x is a waterfowl. — Banno

Does my understanding make sense?

Am I right that:
1 - An extensional definition must include everything that falls under the definition.
2 - An intensional definition must include everything that is necessary and sufficient for the definition.

On my walks, I observe the set {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}.

I am also thinking about Wittgenstein and JL Austin.

I perceive that the elements of this set have a family resemblance.

I cannot describe this family resemblance, but I can name it X, such that the family resemblance between the elements of the set is X.

If I were the King, I could make it a law of the land such that X was henceforth given the name “swanness”, along the lines of a JL Austin performative utterance. Then “swanness” becomes the official name of the family resemblance between the elements of the set {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}

Note that “swanness” does not refer to the elements of the set {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}, but refers to the family resemblance between the elements of the set {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}.

As regards an intensional definition, the intensional definition of “swanness” is the family resemblance between the elements of the set {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}.

Therefore:
1 - On the one hand, I know in my mind that there is a family resemblance. The public word for this can be “swanness”, which I can use in my daily life.
2 - On the other hand, even though I know in my mind that there is a family resemblance, I cannot put my knowledge into words.
3 - Therefore, I can use words such as “swanness” in a public language because I know what “swanness” means, even though I cannot put my knowledge of what “swanness” means into words.

It is those additions which introduce subjectivity. The subjectivity being the intentional products of the mind which enter due to the variance in purpose, and are allowed to contaminate judgement, rendering "truth" as fundamentally subjective. — Metaphysician Undercover

In our world, the proposition “pigs cannot fly” is true. This is an objective fact. My judgement that “pigs cannot fly” is not a subjective judgement.

Modal logic K developed by Kripke introduced the concepts necessary and possible. He introduced possible world semantics, not just any possible world but accessible possible worlds.

What are accessible possible worlds?

Intuitively, an unknown world cannot be an accessible possible world.

Not “all” possible worlds are accessible, because some worlds will be unknown to us.

I could say that possible world 5 is accessible because it follows the logic of our world, such that it is possible in world 5 that “pigs can fly” is true. Or I could say that possible world 5 is accessible because it follows the natural laws of our world, such that “pigs can fly” is false but “pigs can vote” is true.

Suppose I use the model that a possible world is accessible because it follows the logic of our world. Then in possible world 5, pigs can fly.

Then in possible world 5 the proposition “pigs can fly” is true is not a subjective judgement, because in possible world 5 pigs can fly, which is an objective fact within possible world 5.

(I am willing to be corrected about my knowledge of modal logic).

IF logic did not apply to Middle Earth, the books would be unreasonable. Our logic ought apply in such cases. And indeed it does. — Banno

I feel that there is some truth in the following, but cannot clearly see it. Hopefully it adds something.

JL Austin’s performative and constative utterances is relevant to Wittgenstein’s Language Games

Suppose in Possible World 5 there is a form of life and a language game.

Before any performative utterances by an authority

JL Austin discussed performative and constative utterances.

Suppose in this world people see a family resemblance between the elements of the set {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}

We can then say that there is something X that the elements of this set have in common. In other words, the elements of this set are part of the domain of X

As regards X = {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}
1 - This is not an extensional definition, as the set does not include every element that falls under the definition.
2 - This is not an intensional definition, as the set does not include necessary and sufficient elements to be analytically valid.

Suppose in this world people also see a family resemblance between the elements of the set {waterfowl, flighted, white}

We can then say that there is something Y that the elements of this set have in common.

As regards Y = {waterfowl, flighted, white}
1 - This is not an extensional definition, as the set does not include every element that falls under the definition.
2 - This is not an intensional definition, as the set does not include necessary and sufficient elements to be analytically valid.

We now have two sets. Set X whose elements are concrete things and set Y whose elements are abstract properties.

But people also observe the following:
“This swan in Hyde Park” = {waterfowl, flighted, white}
“That swan on the Thames” = {waterfowl, flighted, white}
“Those swans on the Serpentine” = {waterfowl, flighted, white}

As regards “This swan in Hyde Park” = {waterfowl, flighted, white}
1 - This is not an extensional definition, as the set does not include every element that falls under its definition
2 - This is not an intensional definition, as the set does not include necessary and sufficient elements to be analytically valid.

From this we can say that there is a concrete something X that has the properties Y.

After performative utterances by an authority

What X is is unknown, but for linguistic convenience it can be given a name, and in a performative act someone in authority names it “swan”.

As regards “swan” = {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}.
1 - This is not an extensional definition, as the set does not include every object that falls under the definition.
2 - This is not an intensional definition, as the set does not include necessary and sufficient elements to be analytically valid.

Both the intensional and extensional definition of “swan” are still unknown, but what is known is that the elements of the set have a family resemblance. This means that “swan” is the name of a family resemblance between the elements of the set.

What Y is is unknown, but for linguistic convenience it can be given a name, and in a performative act someone in authority names it “swanness”.

As regards “swanness ” = {waterfowl, flighted, white}.
1 - This is now an extensional definition, because a performative utterance by an authority, and as the set does include every object that falls under the definition
2 - This is now an intensional definition, because a performative utterance by an authority, and as the set does include necessary and sufficient elements to be analytically valid.

Therefore, if something is observed that is {waterfowl, flighted, black} then by definition it has no "swanness".

As regards swan = {swanness}
1 - This is an extensional definition, because swanness is an extensional definition
2 - This is an intensional definition, because swanness is an intensional definition.

In summary, in a language game before performative utterances, sets of concrete and abstract elements can be neither extensional nor intensional definitions, but within a language game, performative utterances can create extensional and intensional definitions

Possible world 8, Tolkein's Middle Earth

“Creatures who walked into Mordor” = {Frodo, Samwise} was a performative rather than constative utterance by Tolkein.

Therefore, it is not an extensional definition, because the set does not include every element that falls under its definition. I am sure other creatures than Frodo and Samwise walked into Mordor.

Neither is it an intensional definition, because although Tolkein tells us that Frodo and Samwise necessarily walked into Mordor, that Frodo and Samwise walked into Mordor is not sufficient to the truth of the expression “creatures who walked into Mordor”.

Question

Before any performative utterance by an authority, X = {this swan in Hyde Park, that swan on the Thames, those swans on the Serpentine}.

Does X refer to the set of elements or does it refer to the family resemblance between the elements, ie, does it refer to the elements as part of the domain of X?

This leaves "truth" as either completely arbitrary, or rescued from arbitrariness by subjectivity. — Metaphysician Undercover

The truth tables are important in Tarski’s First Order Logic. For example, the material implication truth table, whereby:

P.....Q.....if P then Q
==================
T.....T..........T
T.....F..........F
F.....T..........T
F.....F..........T

Kripke extended First Order Logic into Modal Logic K adding necessity and possibility, where the truth table shown above remains applicable to each accessible world.

Therefore truth, as expressed by truth tables, cannot be said to be arbitrary and is in this sense objective rather than subjective.

ruth is evaluated by what is meant, which can change between speakers or speakers in different possible worlds..............On the other hand, I would think that truth would not be relative in an extensional sense. — NotAristotle

In possible world 5
Let the word “swan” have both the intension and extension {waterfowl, flighted, white}
Let the word “frog” have both the intension and extension {short bodied, protruding eyes, strong hind legs}
Then
It is true that “swans” are white
It is true that “frogs” have strong hind legs
It is false that “swans” have strong hind legs
It is false that “frogs” are white

In possible world 6
Let the word “swan” have both the intension and extension {short bodied, protruding eyes, strong hind legs}
Let the word “frog” have both the intension and extension {waterfowl, flighted, white}
Then
It is true that “swans” have strong hind legs
It is true that “frogs” are white
It is false that “swans” are white
It is false that “frogs” strong hind legs

Therefore, what is true in possible world 5 is false in possible world 6, and what is false in possible world 5 is true in possible world 6

Truth is relative in both an intensional and extensional sense.
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I don't think artifacts like houses have an essence. — NotAristotle

Then what makes a house not a table?
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It seems to me that: knowing that something has an essence, and for example that the essence of a dog is different from that of a swan, is not the same as knowing what those essences are. — NotAristotle

If you don't know the essence of a dog, and you don't know the essence of a swan, then how do you know that they are different?

I do not understand what the problem is; can you elaborate? — NotAristotle

How can one ever know what is essential to something.

For example, what is essential to something being a “game”.

What is essential to “a table”, “love”, “pain”, “a house”, etc.

What we have is a rigorous account of what it is for "Swans are white" to be true. But it doesn't tell us if swans are white...................To work that out we are gong to have to go out and take a look. — Banno

Hopefully summarising your posts correctly and adding my own understanding.

In possible world 5 (England)

Step one - First we start with many observations of things that are waterfowl, flighted and white. We accept that somewhere hidden could have been a solitary black flighted waterfowl.

Step two - Someone in authority, along the lines of JL Auston’s performative utterance, officially declares that “swans” are {waterfowls, flighted, white}. This fits in with Russell’s and Kripke's idea that proper names are descriptions, and not references to Aristotelian essences. Such an authority could be a person, such as a King, or general consensus.

Step three - In the event that a solitary black flighted waterfowl was discovered, by definition, it could not be a “swan” but must be something else.

Step four - At least there is now a foundation for Wittgenstein's language game, enabling a public language with a measure of agreement as to the meaning of words used.

It is clear that an extensional definition as found in a public dictionary can never give us the intensional meaning of a word. It may be that “Swan” = {waterfowl, flighted, white}, where “white” = {low saturation, reflects almost all wavelengths of light}. But then “light” = {electromagnetic radiation, composed of photons}, ad infinitum

For Wittgenstein, on the one hand, all thoughts are spoken and on the other hand there can be no private language. This implies that all thoughts are necessarily part of a public language. Thereby, there is no separation between the private concept of a swan and the public word “swan”. Such is the consequence that the meaning of swan, the intension of swan, becomes knowable within a public language game. In summary, private concepts are not particular to the individual but general within the public language game and necessarily apply within the language game.

But, is it really the case that Wittgenstein enables a public understanding of the intensional meaning of words!?

In possible world semantics, linguistic truth is not arbitrary. In possible world 5 (England) there may be a language game whereby “swans are white” is true, and in possible world 6 (Australia) there may be a different language game whereby “swans are black” is true. Truth is relative between different language games, between different possible worlds.

In possible world semantics, logical truth is not arbitrary. As it is true that the number 3 is a prime in all possible worlds, the material truth tables are true in all possible worlds, even though the particular forms of life expressed within these material truth tables may be different in different possible worlds.

I think if you have defined "swan" correctly by reference to its essential properties, your definition may change by addition, but the essential properties you have identified will not have changed. — NotAristotle

That’s the problem. What are the essential properties of a “swan”. This sounds like Aristotle’s essences.

The web site - https://birdsology.com/25-fascinating-characteristics-of-swans/ - lists 25 characteristics of swans, including 1 distinctive long necks 2 powerful flight capabilities 3 pristine black and white plumage…….. 25. Limited Global Species but Wide Range

Are these necessary or contingent properties of being a “swan”?

If Paul talks about x, what guarantees that Paul knows what his words mean? — frank

At this exact moment in time, when I write “swan”, I know without doubt what my concept of a swan is.

However, with time, as I learn new things about swans, my concept of a swan will change. However, I will still use the same word “swan”.

IE, what I mean when I write “swan” will inevitably change with time.

Therefore, one can say that Paul knows without doubt what he means when he talks about "x", even though what he means by "x" must inevitably change with time, as he learns new things about "x".

If what I mean by “swan” inevitably changes with time and what Paul means by “swan” inevitably changes with time, it is perhaps surprising that communication using language is possible at all.

Platonism is common in mathematical interpretations. The Idea of "two" for example, is supposed to have real meaning, independent from human minds, so the symbol stands for that intensional package of meaning, as an object. — Metaphysician Undercover

As you say, an extensional definition is trapped by limited empirical observations.

Suppose there is an extensional definition of S, where S = {two red books, two green trees, two black thoughts}

You say that the elements of the set S are there because they are part of the Platonic “Idea” of S, where the “Idea” is the intensional meaning of S, and is objective and independent of the human mind.

The problem is, how can you go from the extensional definition of S existing in your mind to an intensional definition of S existing independently of your mind?

IE, what is the intensional definition of S?

You can see the problem of having no intensional criteria. — Metaphysician Undercover

On the other hand.

Suppose you are given the extensional definition of the foreign word “livro”, where “livro” = {Pride and Prejudice, The Terminal Man, The Great Gatsby, In Cold Blood}

I am sure you could make a good guess as to the meaning of “livro” just from its extensional definition.

Once you have the concept of “livro” in your mind, you could then apply your concept to include other objects, such as {Harry Potter and the Chamber of Secrets}

IE, we can only ever observe extensional definitions, as intensional definitions only exist within our minds.

Foundation? — frank

I didn't say it was a personal thing. I said the matching of members of the domain and predicates is part of the model or interpretation. — frank

In my model, “swan” = {waterfowl, flighted, white}
In John’s model, “swan” = {waterfowl, flighted, black}

I agree that the matching of members of the domain and predicates is part of the model or interpretation.

But what judges whether white or black is part of the domain of a “swan”?

If any judgement is not a personal thing, what is the source of any impersonal judgement?

I think the simple answer is that it doesn't. You have to provide that. You build a model with a domain and predicates. You have to know what the things you're filling the domain with are and how the predicates relate. It's like you're building a little world. Truth is defined in a certain way. — frank

I am sure that truth in possible world semantics is not down to personal preference, though I am definitely no expert in modal logic.

From SEP Possible Worlds

Consequently, there was no rigorous account of what it means for a sentence in those languages to be true and, hence, no account of the critical semantic notions of validity and logical consequence to underwrite the corresponding deductive notions of theoremhood and provability. A concomitant philosophical consequence of this void in modal logic was a deep skepticism, voiced most prominently by Quine, toward any appeal to modal notions in metaphysics generally, notably, the notion of an essential property. (See Quine 1953 and 1956, and the appendix to Plantinga 1974.)

The purpose of the following two subsections is to provide a simple and largely ahistorical overview of how possible world semantics fills this void.

In my words, the article is saying that in traditional modal logic there was no rigorous account of what it meant for a sentence to be true. This led to a deep scepticism. However, this void of what it means for a sentence in modal logic to be true was filled by possible world semantics.

IE, possible world semantics do somehow give a rigorous account of what it means for a sentence in modal language to be true.

In other words, in modal logic, truth is not a personal thing, in that I think that it is true that "swans are white” whilst you may think that it is true that “swans are black”.

The section you posted from the SEP mentions the concept “true”, but does not specify “true for whom”.

For the modal operators. □X, that is, necessarily X, is true at a state if X itself is true at every state that is relevant to that state (at all accessible states).

But what is the foundation for truth in modal logic?

I think all of this is correct. — frank

Continuing the quest for truth.

The SEP article Possible Worlds writes:
1 - Modal logic, by contrast, is intensional.
2 - In an intensional logic, the truth values of some sentences are determined by something over and above their forms and the extensions of their components.

This initially makes sense.

Consider the sentence “swans are white”. The truth value of this sentence cannot be known just from the sentence itself

Consider the extension of “swan”. For example {that swan in Hyde Park, this swan on Ullswater}. Knowing what a “swan” is is impossible from a finite number of examples.

As the article writes, the truth value of the sentence “swans are white” can only be determined by something over and above the form of the sentence “swans are white” and over and above the extension of its component “swan”.

Suppose I observe something X having the properties {waterfowl, flighted, white}.

I obviously cannot know whether being white is internal (necessary) or external (contingent) to X without knowing how X has been defined, and that it has been named "swan".

Suppose a “swan” has been defined as having the properties {waterfowl, flighted, white}. Then I know I am seeing a swan, and being white is an internal, necessary property. Given this definition of “swan”, swans are necessarily white in all possible worlds

From Wikipedia Extensional and intensional Definitions
Intensional definition = gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used.
Extensional definition = listing everything that falls under that definition

However, it is not necessarily the case that the same definition obtains in all possible worlds.

For example:
In possible world 5, “swan” may have been defined as {waterfowl, flighted, white}
In possible world 6, “swan” may have been defined as {waterfowl, flighted, black}

The SEP article suggests that the truth value of the sentence “all swans are white” must be determined over and above its form and over and above its extension.

From the Wikipedia article Modal Logic, ☐ P is true at a world if P is true at every accessible possible world. In other words, necessarily “swans are white” is true at a world if “swans are white” is true at every accessible possible world.

However, in modal logic, this something over and above cannot be a definition, so what could it be?

How does modal logic determine truth values?

By defining necessity as f(x) being true in all possible worlds, we have extensionality within possible worlds, but not across them. In this case, necessity is a quantifier. It's telling us how many. — frank

Does the following make sense:

In possible world 5 - a chess set = {64 squares, made of stone}
In possible world 6 - a chess set = {64 squares, made of ivory}

But some of these properties may be necessary and some may be contingent.

But chess has to be defined.
Therefore, ☐ ∃x(B(x)), where x is the subject “a chess set”, and where B is the predicate “has 64 squares”
Then, it is necessarily the case that the proposition “a chess set has 64 squares” is true.
Therefore, having 64 squares is necessary.
Therefore, the proposition “a chess set has 64 squares” is true in all possible worlds.

But this definition says nothing about material.

Therefore ◊∃x(B(x))
Then, it is possible that a chess set is made of ivory.
Therefore, being made of ivory is contingent
Therefore, being made of ivory is possibly true in some possible world.

As you say, i) defining necessity as being true in all possible worlds and where ii) necessity is a quantifier (meaning “all”).

But is it not the case that:
1 - We have intentionality across all possible worlds (because necessary meaning is an intension and the necessary meaning is the same across all possible worlds)
2 - We have extensionality within each possible world (because contingent properties are an extension and contingent properties are particular to each possible world).

Hey, how badly can we mangle it? — frank

An actual possibility, but hopefully not.

This thread is for a read through of two SEP articles on possibility and actuality. — frank

I admire your confidence in being willing to tackle 60 intricate SEP pages about a generally controversial and deeply complex topic.

Do you have any idea what "noumena" is? — ProtagoranSocratist

What does Kant in the CPR mean by noumena, transcendental object and thing in itself?

The problem of exegesis
An exegesis of Kant’s CPR is problematic because his ambiguity of language makes it often difficult to determine the exact meaning of his text. Therefore, rather than trying to directly interpret his given text, and on the assumption that his underlying ideas are sensible, it may be a better approach to first establish one’s own opinions about the subject and then confirm that your own opinions are a valid interpretation of the given text. Unfortunately, following this approach, there is the real possibility that two different valid interpretations may be discovered about the same given text. A problem with David Hume, who may be read either as an Empiricist or Rationalist.

The noumenon and thing in itself in the two world view
It is clear that our concept of a red postbox may be very different from the reality of a red postbox. For example, we perceive the colour red, yet science tells us that the postbox actually emits a wavelength of 700nm. This begins to lead into the two world view, in that there are two types of object, the object as we conceive it in our mind having the colour red, a noumenon, and the object as it really is in the external world emitting a wavelength of 700nm, a thing in itself.

Even though a wavelength of 700nm is still another concept, we can reasonably conclude that what we perceive may or may not exist in the external world. In the external world what may exist may be the colour red, may be a wavelength of 700nm or may be something else altogether, say X.

The transcendental object in the two aspect view
There is also the two aspect view, where the object as we conceive it in our mind and the object as it really is in the external world are but two aspects of the same object. For a single object, having the colour red may be thought of as a different aspect of the external reality X. In other words, we start with the premise that seeing the colour red is another aspect of the emission of the external reality X. We see the colour red. We conclude that our seeing the colour red is another aspect of the external reality X. Our conclusion that seeing the colour red is another aspect of the external reality X is a justification for our premise that seeing the colour red is another aspect of the external reality X.

This is a transcendental argument. Therefore, the object that has one aspect of having the concept of the colour red and another aspect of an external reality X may be named a transcendental object. Being a transcendental object, there is a necessary and universal connection between the colour red and the external reality X.

The background to the transcendental object
All we directly know are our thoughts (concepts, ideas, reasoning, judgements, understanding) and appearances (phenomena, sensibilities). Kant wrote his Refutation of Idealism in defense of Realism, the idea that there is an external ground for these appearances. If there is an external ground for these appearances, then these appearances are determined externally and not by any human observer of them. Therefore, these appearances must have an internal reason and internal logic that mirrors their ground. Not an internal reason and logic determined by the human observer, but an internal reason and internal logic determined by the external ground. It is up to the human observer using their own reason and logic to discover within these appearances the internal reason and internal logic that already exists. It is therefore through human reason and logic that the human has a direct pathway to an external reality. Not a direct literal pathway, but a direct metaphorical pathway, where a metaphor creates a relationship between two different entities by stating that one is the other.

My explanation
Thing in itself = an object as it exists in the external world independently of our perceptions. I can think about the concept of a thing in itself, in the same way that I can think about the concept that there are things that I don’t know. However, I can never know what a thing in itself is. It is part of the two world view.

Noumenon = an object as it exists as a concept in our mind, such as our concept of a red postbox. Our concept may or may not be the same as the thing in itself, but this is unknowable. It is part of the two world view.

Transcendental object = an object as it exists in the two aspect view. The first aspect is as a noumenon, a concept in the mind. The second aspect is as a thing in itself, the ground of appearances. As knowledge of the object is synthetic a priori, which is transcendental, such knowledge is both necessary and universal.

Stephen Pinker and others have described innate language acquisition. It's not that they have innate knowledge, what you call content, it's that they have the capacity to gather and process that content–to think in structured and organized ways. — T Clark

I agree. Another example. I cannot see the colour red when I close my eyes, but have the ability to see the colour red when there is something red present in my field of vision.

The thing that jumped out to me when I read about the critique of pure reason was that Kant identified space and time as being known a priori. These strike me as exactly the kind of structured principles I described above. Time and space are not what you call "content," they are principles that allow us to organize and process content provided by our senses. — T Clark

I agree that we are born not so much with innate knowledge but with innate ability.

Carrying this idea forward, we could say that we are not born with an innate knowledge of space and time, but have an innate ability to recognise space and time in our sensibilities. In today’s terms, we could say that my innate ability to recognise space and time is a priori, where a priori is being used in a temporal sense.

However, as I understand it, this is not how Kant uses the term a priori. Kant is not using the term a priori in a temporal sense. It is being used to describe the relationship between two events that are simultaneous, contemporaneous. The concept of a cause that is contemporaneous with its effect is called "simultaneous causation”. Stephen Mumford argues that causation is always simultaneous. Aristotle’s material cause is in a sense about simultaneity. For Kant, our pure intuitions of space and time don’t originate temporally before our particular sensibilities (observations, experiences) but originate transcendentally from the very same sensibilities that they are needed to make sense of.

For Stephen Pinker, we are born with certain innate abilities that allow us to make sense of the experiences we have today, and in this sense a priori. For Kant, the abilities we have that allow us to make sense of the experiences we have today derive in a transcendental sense from the very experiences themselves, and in this sense a priori.

Because our a priori pure intuitions of space and time have transcendentally derived from our synthetic experience of space and time, these pure intuitions are necessarily necessary and universal. This is different to Hume’s observation of regularities in our synthetic experiences which are necessarily contingent and particular.

Kant believes there is something external that is causing our observations, from which we transcendentally derive our pure intuitions of space and time, but this external something, like the thing in itself, must forever remain unknown. This external something may in fact be exactly the same as our concept of space and time, but then again, it may not. We will never know.

However, as a personal opinion, there must be a real relation between our pure intuitions of space and time and the something external and unknowable, which may or may not be the same as our pure intuitions. Because our pure intuitions have been transcendentally derived from appearances, these pure intuitions must be necessary and universal as Kant proposes, even if only metaphorically necessary and universal.

I disagree with this. Maybe we could read through the Transcendental Aesthetic together and come to agreement. Who's up for that? — frank

You may be right, my wording may not have been the best.

The concept of the transcendental is important to the CPR, and is important to Kant’s principle of synthetic a priori. The Transcendental Aesthetic is 21 pages long, from A19/B33 to B73, so would be a major project.

To my understanding, for Kant, only the synthetic a priori can give knowledge. The synthetic by itself (the intuition of sensibilities, observations, appearances, experiences) cannot give knowledge. The a priori by itself (pure intuitions of space and time, pure concepts of understanding ( the Categories), pure logic, pure reason, pure judgement) cannot give knowledge. Knowledge may only be gained when the synthetic is spontaneous with the a priori.

For example, we make an observation which we make sense of using the Categories. But in Kant’s transcendental sense, these Categories did not exist temporally prior to the observations, but spontaneously came into existence at the same time as making the observations necessarily in order to make sense of the observations. Without the Categories we could not make sense of our observations, and without our observations we could not have any categories making sense of our observations.

In a transcendental argument, a strong premise about a situation leads to a reasonable conclusion. This reasonable conclusion then becomes a valid justification for the strong premise.

Perhaps the following wording would be better:

Therefore , transcendental Idealism is the idea that a strong premise (the a priori, such as the Categories) about a situation (the synthetic, such as our sensibilities) leads to a reasonable conclusion ( knowledge). This reasonable conclusion (knowledge) then becomes a valid justification for the strong premise (the a priori, such as the Categories).

Push on PDF with text then download to your files. — T Clark

:up:

Unless I’ve misunderstood you, this is not how I understand what Kant was saying. — T Clark

What does Kant mean by “a priori”?

Reason must have content, As Kant said "thoughts without content are empty, intuitions without concepts are blind”. Reason must be about something. Pure reason, which is reason without content, is impossible. Kant’s Critique of Pure Reason is a critique of pure reason, not an acceptance of the existence of pure reason.

For Kant in the CPR, all knowledge must be synthetic a priori, meaning that there can be neither purely synthetic knowledge nor purely a priori knowledge.

5+7=12 is an example of synthetic a priori mathematical knowledge, and the syllogism that all humans are mortal, Socrates is human, therefore Socrates is mortal is an example of synthetic a priori logical knowledge.

For Kant, the conscious reasoning about content is not innate in humans at birth. Children have to mature a certain number of years before being able to consciously reason about content.

If all knowledge must be synthetic a priori, which derives from reasoning about content, and there can be neither purely a priori knowledge nor purely synthetic knowledge, then reasoning can neither be temporally before nor after content. Reasoning must be contemporaneous with its content. Synthetic refers to the content and a priori refers to the reasoning, but as reasoning is contemporaneous with its content, the term “a priori” must also be considered in an atemporal sense. Atemporal in the same sense of Aristotle’s material cause (edited) rather than Hume’s temporal causation.

Kant’s synthetic a priori uses a transcendental argument, whether a Transcendental Deduction or a Transcendental Idealism.

In the Empiricism of Hume, some concepts, such as one billiard ball hitting another causes a movement, are derived using reason temporally after particular observations. Within Empiricism, these concepts are therefore contingent and accidental to particular observations, and are the basis of modern science.

In the Rationalism of Descartes, some concepts are innate, and temporally precede particular observations. Within Rationalism, these concepts, such as “there is a God”, are therefore necessary and universal.

Kant’s principle of synthetic a priori knowledge uses a transcendental argument that is neither Empiricism nor Rationalism. Within Kant's synthetic a priori, some concepts, such as the Categories, are necessary and universal because they create the very experiences that they derive from.

For Kant, in the CPR, the term “a priori” means neither innate nor inherent, in the sense of temporally preceding something else. It is meant in a transcendental atemporal sense, in that some concepts, such as the Categories, are a priori to the very experiences that they are derived from.

In case you’re interested, here’s a link to an article by Lorenz—“Kant's Doctrine Of The A Priori In The Light Of Contemporary Biology.” — T Clark

Do you have access to a clean copy of the article. From the Internet Archive, the “full text” comes out as:

This f^^ ^
is due to hereditary dl f chir -
acteristic of the ^f^ in U* 0~
disposes ^;J ncepti onof the'apri-
must realize th ^^ destr ^tion of the
orf as an organ means
concept: something natural
tionary adaptation to the laws otu«
external world has evolved a posteriori in a
certain sense, even if in a way entirely differ-
ent from that of abstraction or deduction from
previous experience.

I agree when the paper writes “In view of the indubitable fact of evolution”. The question is, did Kant mean by “a priori” what today is meant by “a prioiri”?

Again, this is not my understanding of what a priori means. As I wrote previously, I see it as knowledge we have as part of our human nature. It’s built into us. — T Clark

Many people believe that “knowledge results from biological and neurological Darwinian evolution”, as do I. In this context, the term “a priori” has a particular meaning.

However, if we are talking about Kant, this is not what Kant meant by “a priori”. In this different context, the term “a priori” as used by Kant has a different meaning

I am certainly not a Kant scholar, but it’s my understanding that he did see a priori knowledge as coming before any sensory input. It’s part of our human nature. Konrad Lorenz claims that that knowledge results from biological and neurological Darwinian evolution. That makes a lot of sense to me. — T Clark

Today it makes sense to talk about innate knowledge in the brain built up through 3.5 to 4 billion years of evolution. However, Kant in the 18th C did not regard a priori pure intuitions of space and time and a priori concepts of the categories as innate as we would understand them today. Kant's a priori is part of his Transcendental Idealism.

Kant is not using the term “a priori” to indicate the passage of time, and is more in line with Aristotle’s material cause (edited) than Hume’s causation. In Latin, “a priori” means “from the former” and can be used in an atemporal sense about something that exists outside any considerations of time.

Therefore, the relationship between a priori pure intuitions of space and time and a priori pure concepts of the categories and the phenomenology of experiences, a person’s sensibilities, should be thought about without any regard to the passage of time.

As I wrote before: “Kant did not propose that we have knowledge prior to our sensibilities, which we then apply to our sensibilities. Kant proposed in Transcendental Idealism that a priori knowledge is that knowledge derived from our sensibilities that is necessary to make sense of these very same sensibilities.”

As an analogy, suppose you fly over an island about which you have no previous knowledge. You observe stones on the beach in the form of the letters SOS. You may have the thought that these stones rolled into that position accidentally through the forces of nature, whether the wind or waves, but find such a thought almost impossible to believe. The only sensible explanation for your observation would be the existence of a human agency, even if you have no direct knowledge of such human agency.

Your belief in the existence of a human agency doesn’t transcend your observation, but is transcendental to your observation.

Your phenomenological experience is not proof of the existence of a human agency external to your observation, but neither is Kant’s Refutation of Idealism proof of his two world view. However, it clearly shows his belief in a two world view and his determined attempt to prove two realms of existence, the phenomenal and the noumenal.

Neither the desert island analogy nor Kant's Refutation of Idealism prove the two world view, but both are strong justifications for the two world view.

As I see it, as regards Kant, the intuitions of space and time and the concepts of the categories that are needed to make sense of phenomenological experiences are determined a priori (atemporally) by the very same phenomenological experiences that they need to make sense of.

Then you lose your reason for denying the possibility of non sensible or sensible intuition as an infallible source of knowledge. I recommend you to check the Critique of Pure Reason. — Sirius

Kant's Critique of Pure Reason discusses a priori pure intuitions of time and space and a priori pure concepts of the Categories. This is knowledge, but not innate knowledge that precedes our sensibilities. This is knowledge that derives from the very sensibilities that it needs to make sense of, ie, Kant’s Transcendental Idealism.

This is why I wrote “All our knowledge comes from sensory experience”.

Kant did not propose that we have knowledge prior to our sensibilities, which we then apply to our sensibilities. Kant proposed in Transcendental Idealism that a priori knowledge is that knowledge derived from our sensibilities that is necessary to make sense of these very same sensibilities.

It's useless to tell us whether this or that is unverifiable until you tell us your criteria for verification. — Sirius

A statement has been verified if the statement is discovered to be true.

It has been asked “what is metaphysics?”. One characteristic of metaphysical questions is that they are never verified to be true. For example, does anyone know the true answer to the metaphysical question “why is there something rather than nothing” or “do we have free will” or "what is the nature of reality”. In fact, if a statement can be verified, such that the speed of light is 299,792,458 m/s, then by definition it cannot be a metaphysical statement.

Not only that, you will also have to justify it. — Sirius

It is sufficient justification that metaphysical statements are not verifiable by pointing out that no metaphysical statement has been verified to be true.

Of course, if language is a tool, then it cannot be the subject matter of any science which aims to discover truths. This was known to Aristotle. — Sirius

Science is always concerned about the tools it uses. A faulty tool will give faulty answers. For example, when studying cells, the microscopes being used are constantly being tested for optical quality, resolution, etc.

But the [neo-] positivists you are echoing actually disputed this. They regarded language as unveiling the structure of the world & mind. — Sirius

Truth cannot be found within language. Truth transcends language. It is not the case that “Paris is in France is true” but rather “Paris is in France” is true IFF Paris is in France.

The neo-positivists (aka logical positivists, logical empiricists) followed the verification principle, in that a statement can only be meaningful if either empirically verifiable or a tautology.

As regards the world, a statement such as “Paris is in France” can be empirically verified, and therefore is meaningful, but as regards the mind, a statement such as “this painting is beautiful” cannot be empirically verified, and is therefore meaningless.

For the neo-positivists, language was very limited in its ability to unveil the structure of the world and mind, as not only was it forced to reject any statement that could not be empirically verified but also was forced to reject all poetic, metaphorical and emotive language.

What is metaphysics?

One aspect is that metaphysics is not verifiable, as metaphysics is undertaken using language, and truth cannot be discovered within language. Truth transcends language.

It is not the case that i) “everything within the empirical realm is in constant state of actuality (what it is now) versus potentiality (what it could be) is true” but rather ii) “everything within the empirical realm is in constant state of actuality (what it is now) versus potentiality (what it could be)” is true IFF everything within the empirical realm is in constant state of actuality (what it is now) versus potentiality (what it could be).

As Collingwood said, absolute presuppositions are not verifiable, because, as Hume pointed out, even though all our knowledge comes from sensory experiences, we can only directly observe the regularity of events, never the cause of these regularities. Through reason and logic we hypothesise a speculative cause for these regularities, and we can only reason about our sensory observations. In the absence of any sensory observation, there would be nothing for reason to reason about.

The speculations of metaphysics are not verifiable, and can only be supported by empirical observation. In physics, it is a supposition that the speed of light is 299,792,458 m/s, and in metaphysics it is a supposition that stealing is wrong. These suppositions cannot be arrived at by reason alone. The supposition of the speed of light is supported by empirical observation of astronomical events and the supposition that stealing is wrong is supported by empirical observation of human behaviour.

As with Kant, there must be a unity between what the mind observes, empirical sensory observations, and the mind’s comprehension in what it observes, logical reasoning. Also with Aristotle, there is unity between passive intellect, receiving and processing of sensory information, and active intellect, thought and reasoning.

Reason may be used to generalise the particular. From the particular, that his stealing that woman’s bag is wrong, to the general and universal, that stealing is wrong. Reasoning about empirical observations enables generalisations about particulars. Only particulars can be empirically observed. Last year in Paris the speed of light was measured as 299,792,458 m/s. Last week in Seattle, the speed of light had the same measurement. This morning, here in Copenhagen, the speed of light also had the same measurement. That the speed of light is universally 299,792,458 m/s cannot be empirically observed. It is only through reason that particular facts in the world may be universally classified. It is not only in physics that the speed of light is 299,792,458 m/s, but also in mathematics that 1+1=2. In chemistry, water is H2O, in ethics stealing is wrong, in religion that God exists and in psychology humans have free will.

Even logic cannot be thought about in the absence of reference to facts external to the thinker. The logic of the syllogism that i) all x are y, ii) z is x, iii) therefore z is y is part of linguistic thought, and as Wittgenstein pointed out, language cannot be private. Logical thought is founded on elements such as “all”, “x” and “therefore”, elements that can only be known to the thinker within a public language, and being public only accessible through sensory empirical observations.

All knowledge is speculative, whether that of physics or metaphysics, as knowledge is contained within language, and truth transcends language. Such speculation is founded on the unity between the passive intellect, empirical sensory observations, and the active intellect, reasoning, thought and logic. The only difference is the degree of public consensus. A more general consensus is that the speed of light is 299,792,458 m/s, and a more limited consensus is that stealing is wrong. All knowledge requires a fusion of reason with observation. Yesterday’s metaphysical knowledge might be today’s physical knowledge.

Metaphysics is not physics.

For example, the speed of light is a fundamental constant in nature, and is known to be 299 792 458 m / s. Physics knows that the speed of light is constant and is universal. Physics may ask why a constant and why a universal, but in order to undertake physics, physics does not need to know the answers to these questions. Metaphysics is concerned with those questions about the nature of reality that physics does not need to know the answer to.

Metaphysics asks questions, such as why does light exist, why does it have the specific value it has, why is its speed universal throughout the Universe, what does it mean to be universal, what exactly is a space encompassing 299 792 458 metres, what exactly is a time of one second, what does the number 299 792 458 mean and how does the mind know about things such as space, time, numbers and universals.

So we can ask these metaphysical questions, such as “do universals exist”, but as FH Bradley wrote "metaphysics is the finding of bad reasons for what we believe on instinct" and as Wittgenstein wrote "most of the propositions and questions to be found in philosophical works are not false but nonsensical".

Metaphysical questions and answers only exist in language, and the truth of a proposition can never be discovered within language. It is not the case that “the apple is on the table is true” but rather “the apple is on the table” is true IFF the apple is on the table. Truth transcends language. Not only is it the case that it is logically impossible to discover the truth of a metaphysical answer within philosophical language, it is also logically impossible to know whether the metaphysical question itself is valid. As both Bradley and Wittgenstein infer, truth, including metaphysical truth, cannot be discovered within language.

If metaphysical truth cannot be discovered with philosophical language, then we need to look elsewhere for metaphysical truths.

What is metaphysics?

Metaphysics asks those questions we don’t need to know the answer to, but which we are curious to know the answer to.

All WH questions are open ended and used to gain knowledge, but some WH questions are metaphysical and some aren’t. Metaphysical questions ask questions that we don't need to know the answer to because they have no import on our ability to live our lives, but only ask out of intellectual curiosity.

1 “Where is Paris?” is not a metaphysical question, as we need to know that Paris is in France when planning a holiday.

2 “When does the train arrive?” is not a metaphysical question, as we need to know this when trying to get to work.

3 “How does a rocket get off the ground?” is not a metaphysical question, as the rocket scientist needs to know the answer.

4 “What is the time?” is not a metaphysical question, as we may need to know the correct time when catching a train, but "what is time?” is a metaphysical question, as knowing the nature of time is irrelevant to the question “what is the time?”.

5 “Who is Aristotle?” is not a metaphysical question if the answer is “Aristotle was an ancient Greek philosopher”, but is a metaphysical question if the questioner is wanting to know his underlying philosophical identity, as knowing his underlying philosophical identity is irrelevant to knowing his philosophy.

6 “Why does a rock fall to the ground?” is not a metaphysical question if the answer is “because if follows the law of nature that d = 0.5 f t²”, but it is a metaphysical question if the questioner is wanting to know “why is d = 0.5 f t²”, as knowing why d = 0.5 f t² is irrelevant to knowing that d = 0.5 f t².

As described, metaphysics is over and above the axioms of physics. Physics only needs to know that certain axioms work, whereas metaphysics wants to know why these particular axioms work. Knowing why certain axioms work is not something that Physics needs to know.

Unfortunately, the very name metaphysics contains the seeds of its own destruction. For example, the fundamentals of language can only be understood using a meta language, something external to language itself. But when this meta language uses language itself, an impossible conundrum results. Similarly, the fundamentals of (physical) concepts can only be understood using meta concepts, something external to the concepts themselves. When these meta concepts use the same concepts as the concepts being investigated, another impossible situation arises.