Before the truth value of any proposition is known, metaphysical or otherwise, the meaning of the words must be known. For example, is the proposition "mbeya majipu" true or false ?

First, do the words have a meaning in the first place, and if they do, who or what determined their meaning ? And if their meaning has been determined, where is this meaning to be found ?

IE, the truth value of a synthetic proposition cannot be known empirically until the meaning of the words within it are known analytically.

No, I'm just unpacking what's already there. 'Snow is white' is true if and only if snow is white. I merely unpacked, pedantically really, the right side. Nothing is missing. — TonesInDeepFreeze

I believe that you are saying that the denotation of "snow" as snow and the denotation of "white" as white are already within the expression snow is white, waiting to be unpacked, waiting to be discovered.

However, if given fire is hot as the expression on the right hand side, this means that the denotation of "x" as fire and the denotation of "y" as hot are already within the expression fire is hot, waiting to be unpacked.

If that is the case, then what are "x" and "y" ?

I didn't say anything like that. — TonesInDeepFreeze

1) the denotation of 'snow' is: precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C)
2) the denotation of 'white' is: has the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum
3) 'Snow is white' is true in this interpretation if and only if precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C) has the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum.

The only conclusion that can be drawn from what you wrote is that the T-sentence "snow is white" is true IFF snow is white is missing a necessary condition on the RHS of the biconditional, otherwise you wouldn't have included items 1) and 2).

Of course the word 'snow' is not the word 'white'. And of course the word 'white' is not an adjective regarding the word 'snow'. — TonesInDeepFreeze

The meaning of "is"
It seems that most of our disagreement relates to the meaning of certain words that have multiple meanings.

For example, I wrote : But "snow" being "white" is not conditional on snow being white, as snow is of necessity white.

You wrote: That doesn't enter into it at all. Of course the word 'snow' is not the word 'white'. And of course the word 'white' is not an adjective regarding the word 'snow'.

When Tarski wrote "snow is white", this is obviously not intended literally, in that A is A, but rather that "snow has the property white". Similarly, when I wrote "Snow" being "white", my intended meaning was that of "snow" having the property "white".

Language is problematic when key words have multiple meanings.

Tarski's T-sentence
You wrote:
1) the denotation of 'snow' is: precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C)
2) the denotation of 'white' is: has the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum
3) 'Snow is white' is true in this interpretation if and only if precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C) has the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum.

From 1) Let S = precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C)
From 2) Let W = the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum
From 1,2,3) "snow is white" is true IFF i) S is W ii) where the denotation of "snow" is S and the denotation of "white" is W

I wrote: "Snow is white" is true IFF not only i) snow is white but also ii) snow has been named "snow" and white has been named "white"

Tarski's T-sentence is "snow is white" is true IFF snow is white

It seems that we both agree that the T-sentence is missing a necessary condition on the RHS of the biconditional.

(As an aside, I am of the opinion that i) snow is white is the condition of satisfaction, and ii) snow has been named "snow" and white has been named "white" is the condition of designation).

@Banno

What do "the domain of the metalanguage" and "the world of that metalanguage" refer to? — TonesInDeepFreeze

Metalanguage
I used to think that "For Tarski, the right hand side is a Metalanguage, which is not the world", however, @Andrew M made me rethink. I now believe Tarski's T-sentence is the Metalanguage (ML). As the truth cannot be found in either the RHS or LHS by themselves, but only in a combination, the T-sentence must be the ML.

The LHS is the Object Language (OL).

It seems sensible that the RHS is the world of the ML, where world is a synonym for domain, where the world of the ML is snow, apples, houses, white, mountains, etc. However, the world of the ML is not necessarily our world, though it could be.

A language itself doesn't have a domain nor a world. Rather, an interpretation of a language has a domain of discourse — TonesInDeepFreeze

In the OL, we can say that the domain of the wife is cooking, cleaning and housekeeping, where the set wife = {cooking, cleaning, housekeeping}

In the OL, "Terry left the bar and walked through a thick fog". In the ML we can say that the writer used the expression "thick fog" to symbolize Terry's state of mind. The OL is interpreted in the ML.

The domain of the OL on the LHS of the biconditional is "cooking", "cleaning", "bar", "fog", etc
The domain of the ML on the RHS of the biconditional is cooking, cleaning, bar, fog, etc

IE, the T-sentence relates the domain of the OL with the domain of the ML

Consider the sentence: 'Snow is white' is true if and only if snow is white. — TonesInDeepFreeze

Summarising @TonesInDeepFreeze (I hope correctly)
1) In the world is the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum. Designate this "white"
2) In the world is precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C). Designate this as "snow"
3) "Snow is white" is true IFF what has been designated "snow" has what has been designated "white"

Designating
Names are designated in Institutional Performative Acts and written up in the annals (metaphorically). For example, "apples" have been Institutionally named, but the object part my pen and part the Eiffel Tower hasn't (yet) been Institutionally named.

Tarski's T-sentence
I observe the world and see something cold, white and frozen and a relation between them, the relation snow.

If cold, white and frozen didn't exist in the world, then neither would the relation snow.

Let white be designated "white" and snow be designated "snow". It is also possible that white had been designated "green" and snow designated "apple". The world of the ML is not our world, and, in the world of the ML, anything is possible.

The T-sentence is a biconditional, meaning that the truth of the proposition "snow is white" is conditional on something.

But "snow" being "white" is not conditional on snow being white, as snow is of necessity white. Snow only exists as a mereological object having the parts cold, white and frozen. Snow doesn't exist independently of its parts, cold, white and frozen.

"Snow is white" is conditional on i) the existence in the world of cold, white and frozen and a relation between them, snow ii) snow being named "snow" and white being named "white"

Simplifying, it seems to me that the T-sentence becomes: "snow is white" is true IFF snow is white, snow has been named "snow" and white has been named "white".

The T-sentence is in the metalanguage, while the quotes name a sentence in the object language. — Andrew M

Considering Tarski's T-Sentence "snow is white" is true IFF snow is white, you are right that the T-sentence is the metalanguage, not the right-hand side of the biconditional.

Yes, but naming it doesn't affect what it is. 200,000 years ago, snow wasn't named "snow", and the color white wasn't named "white", yet snow was still white. — Andrew M

Certainly if the word "white" were used to denote the color green then the sentence, "snow is white" would be false (since snow is not green). — Andrew M

We agree that snow is white, and we agree that "white" could have been used to denote the colour green.

Assume that "green" was used to denote the colour white.
Given that snow is white, "snow" denotes snow, "white" denotes green and "green" denotes white, then "snow is white" denotes snow is green.
Also, "snow is green" denotes snow is white.
If snow is white, then "snow is green" is true.
IE, "snow is green" is true IFF snow is white.

In that event, doesn't this mean that Tarski's T-sentence would be false ?

Yes, but naming it doesn't affect what it is. 200,000 years ago, snow wasn't named "snow", and the color white wasn't named "white", yet snow was still white. — Andrew M

The truth of Tarski's T-Sentence depends on how snow and white have been named

Today, we have Tarski's T-Sentence "snow is white" is true IFF snow is white. The left hand side is the object language, the right hand side is the metalanguage.

In the metalanguage, snow is white, meaning that, in the domain of the metalanguage, snow is white, ie, in the world of the metalanguage, snow is white. The world of the metalanguage may or may not correspond with our world.

I agree that in our world snow is white. However, in the world of the metalanguage, snow may or may not be white.

Possibility One - in the world of the metalanguage, snow has the property white and apples have the property green

1) Let "snow" name snow, "white" name white
Then "snow is white" is true
2) Let "snow" name snow, let "white" name green
Then "snow is white" is false

1) Let "snow" name apple, "white" name white
Then "snow is white" is false
2) Let "snow" name apple, let "white" name green
Then "snow is white" is true

Possibility Two - in the world of the metalanguage, snow has the property green and apples have the property purple.

1) Let "snow" name snow, "white" name white
Then "snow is white" is false
2) Let "snow" name snow, let "white" name green
Then "snow is white" is true
3) Let "snow" name snow, let "white" name purple
Then "snow is white" is false

1) Let "snow" name apple, "white" name white
Then "snow is white" is false
2) Let "snow" name apple, let "white" name green
Then "snow is white" is false
3) Let "snow" name apple, let "white" name purple
Then "snow is white" is true

Summary

If snow is white in a metalanguage, "snow is white" may or may not be true dependant upon how snow and white have been named. Therefore, it is not necessarily true that "snow is white" is true IFF snow is white.

IE, the truth of Tarski's T-Sentence depends on how snow and white have been named, or as Kripke said, "baptised".

Tarski didn't think of the T-sentence as being a definition of truth and, I'd add, neither was his actual definition of truth circular. — Andrew M

I am curious why naming plays no part in Tarski's T-sentence, as naming seems to affect the truth or falsity of the T-sentence itself. Am I missing something ?

The problem of naming

Tarski proposed:

The T-sentence - "snow is white" is true IFF snow is white.
A definition of truth can be obtained in a very simple way from that of another semantic notion, namely, of the notion of satisfaction.
Satisfaction is a relation between arbitrary objects and certain expressions called "sentential functions." These are expressions like "x is white,"

A sentence such as "snow is white" is true if in the sentential sentence "x is white", x is satisfied by snow.

200,000 years ago snow had not been named. Today, snow has been named, whether "white" in English or "schnee" in German. Therefore, there must have been a point in time when snow was named "snow", ie, what Kripke calls "baptised".

Although the right hand side of Tarski's biconditional is a metalanguage, as he uses the example of the object snow and the property white, for the moment consider a world whereby snow is white. In a world whereby snow is not white, or we consider the general T-sentence "P is Q" is true IFF R is S, the same problem of naming occurs.

Before naming snow as "snow" and white as "white"
As "white" didn't exist, in the sentential function "x is white", there is no x that satisfies "white", therefore "snow is white" can never be true.

After naming snow as "snow" and white as "white"
As snow has been named "snow" and white has been named "white", in the sentential function "x is white", x is always satisfied by snow. Therefore, "snow is white" is always true.

In summary, the T-sentence is false before snow had been named "snow" and white named "white". The T-sentence is always true after snow had been named "snow" and white named "white". IE, the T-sentence itself may be either true or false dependant upon how its parts have been named.

If the parts exist, their collection necessarily exists too.........Collections in a spacetime can have causal relations between them — litewave

I don't see much difference between a galaxy posited as an abstract entity and me as an actual entity — universeness

Convention of quotation marks
Using the convention of Davidson's T-sentence "snow is white" is true IFF snow is white, where with quotation marks refer to language and the mind and without quotation marks refers to a world.

Sets (to my understanding)
A set is a collection of elements. A set with no elements is "empty", a set with a single element is a "singleton", elements can be numbers, symbols, variables, objects, people and even other sets. A set is an abstract, such that its elements don't have to be physically connected for them to constitute a set. An object is not a set, though it can be a set of objects.

Platonists vs Nominalists
A Platonist would argue that "galaxies" exist in a mind-independent world, whereas a Nominalist would argue that they don't. For the Nominalist, an apple in the world is a projection of the concept "apple" in the mind onto the world.

See SEP - Abstract Objects - https://plato.stanford.edu/entries/abstract-objects

I agree that galaxies exist in a mind-independent world, I agree that "galaxies" exist in the mind, but I don't agree that "galaxies" exist in a mind-independent world.

Argument Three against Platonism
A Platonist would argue that "apples" exist in a mind-independent world, a Nominalist would argue that apples exist in a mind-independent world.

It is argued that if two people observe the same world, and both independently perceive an "apple" then an apple exists in the world. However, I may observe the world and perceive a "duck", whilst someone else perceives a "rabbit".

IE, it does not necessarily follow that because we both perceive the same "object", then that object exists in the world.

Sets and Galaxies
@Kuro started the thread by asking about a set of all that exists. The word "exist" needs to be defined.

A Nominalist would argue that as sets are abstract, and as abstracts don't exist in a mind-independent world, neither do sets. Therefore, sets can only exist in the mind. A set of stars exists in the mind as a "galaxy". Galaxies exist in a mind-independent world.

A Platonist would argue that although abstracts exist in a mind-independent world, they are independent of any physical world. As abstracts exist in a mind-independent world, and as sets are abstract, then sets can exist in a mind-independent world. Sets can also exist in the mind. Therefore, "galaxies" exist both in the mind and in a mind-independent world. Galaxies also exist in a mind-independent world.

A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter. These physical parts are connected by physical forces, such as gravity.

A "galaxy" is an abstract entity of physical parts. These physical parts are connected, but not physically. If an object, such as a "galaxy", is a collection of parts, such as stars, there must be some kind of connection between the parts, otherwise it wouldn't be an object.

For the nature of connections see SEP - Relations - https://plato.stanford.edu/entries/relations

In summary, "galaxies" must be distinguished from galaxies.

I would say that all combinations exist regardless of the mind..........But who says that parts of an object need to be in causal contact? — litewave

In Mathematical Platonism, sets exist in the world as abstract entities. The parts don't need to be in causal contact. Yet the parts must be connected in some way in order for the set to exist. How exactly ? How are things in the world abstractly connected ? By what mechanism ?

Infinite number of objects doesn't seem sensible? — litewave

For a world to start off with 3 objects and end up with an infinite number of objects because of the ontological existence of sets doesn't seem sensible.

Tree's rocks and stars can exist as composites without the labels tree, rock, or star. — universeness

You write that trees, rocks, stars, solar systems, etc are combinatory systems that can exist
independently of a lifeform and can exist without the labels tree, rock, star, solar system, etc.
@Kuro wrote "Suppose that all that exists forms a set."

Taking the Milky Way Galaxy as an example, The Milky Way Galaxy is an object, a combinatory system, a collection of things. As an object it is a set of parts.

The Mathematical Platonist would argue that the Milky Way Galaxy as a set of parts exists as an abstract entity, independent of any mind. A Nominalist would disagree.

If the Milky Way Galaxy exists as an abstract entity, by what mechanism do you propose that the parts are connected, parts that could be 87,000 light years apart ?

Taking sets to exist is the most natural interpretation of the existential quantifier in set theory without awkward paraphrases — Kuro

I am sure that both Platonists and Nominalists agree that sets exist. The question is where, in the mind or mind-independent.

Frege argued for mathematical Platonism as the only tenable view of mathematics, yet objectors include Psychologists, Physicalists and Nominalists.

Quine-Putnam's Indispensability Argument argued for the existence of abstract mathematical objects, such as numbers and sets, yet persuasive objectors include Harty Field.

I agree that the Existential Quantifier, having the meaning "there exists", "there is at least one", "for some", is invaluable in logic. For me, however, the most natural interpretation of "exist" means within the mind.

IE, the most natural interpretation for one person may be different to another person's.

What doesn't exist only in the mind then? Non-composite objects? — litewave

Yes, a tree is a combination as is a grain of sand, a rock or a star. They need no lifeform to exist as combinations of fundamentals. — universeness

If combinations don't ontologically exist in a mind-independent world (aka relations) but do exist in the mind, then:
i) what exists in the mind-independent world are fundamental forces and fundamental particles. These fundamental particles may be called "objects", and are non-composite.
ii) a tree, which is a combination of parts, can only exist in the mind.

Argument One against sets as combinations existing in the world
From before, if only 3 things were introduced into a world, and if sets as combinations did exist, then an infinite number of other things would automatically be created. This doesn't seem sensible.

Argument Two against sets as combinations existing in the world
If combinations exist in the world, then an object such as an apple would exist as a set of parts. It would follow that one part 8cm distant from another part would be in combination.

The Earth would exist as an object, meaning that one part 12,000 km from another part would be in combination.

The Milky Way Galaxy would exist as an object, meaning that one part 87,000 lights years from another part would be in combination.

If being in combination was instantaneous, then the combination between two parts of the Milky Way Galaxy 87,000 light years apart would be instantaneous. But this would break the physical laws of nature as we know them, and would need to be justified.

If being in combination followed the physical laws of nature as we know them, then two parts could only be in combination once information had travelled between them at the speed of light. This raises a further problem.

If, during the 87,000 years it took for the two parts to become in combination, one or both of the parts ceased to exist, then a combination would come into existence without any parts. This doesn't seem sensible.

IE, Platonic Sets existing in a mind-independent world sounds fine until one considers the real world implications.

The apple exists as a set of parts in the mind. When the mind believes that it is observing an apple in the world, for the apple to also exist in this observed world as the same set of the same parts would be an example of overdetermination.

IE, an apple does not need to exist in the world in order for the mind to believe that it is observing an apple in the world.

Some people think of a set as being some abstract, Platonic entity that "exists" in some sense, distinct from its members? — Michael

The 'extra things' come from combination of the fundamentals — universeness

A set is a combination of things. I would accept that "combinations" exist in the mind. I would accept that the mind observes "combinations" in the world when observing the world. I would accept that there are forces between things in a mind-independent world, but the concept of force is different to the concept of "combination". A set of things does not require that there are forces between these things.

Q1 - do "combinations" exist in the world when the world is not being observed ?

Is there any persuasive argument that "combinations" do exist in a mind-independent world ? I have yet to come across one.

Suppose that all that exists forms a set — Kuro

In the world exists x, y and z.
Suppose x,y and z exist in the world.

This gives us 6 sets - (x) - ( y) - (z) - (x,y) - (x, z) - (y,z).

If sets exist in the world
You say that sets "exist".

Q1 - If sets exist in the world, we start off with 3 things that exist and end up with 6 things that exist. Where did the extra 3 things come from ?

But if sets do exist in the world it gets worse.
Let set F be (x), set G be ( y), set H be (z), set J be (x,y), set K be (x,z) and set L be (y,z).
This gives us the additional sets (F), (G), (H), (J), (K), ( L), (F,G), (F, H), (F, J), ((F,K), (F,L), (F,G,H), (F,G,J), (F,G,K), (F,G,L), (F,H,J), (F,H,K), (F,H,L), (F,J,K) - etc - a lot.
We can continue the same process and end up with the existence of an infinite number of possible sets.

Q2 - if sets do exist in the world, we start off with 3 things that exist and end up with an infinite number of things that exist. Where did the extra things come from ?

If sets don't exist in the word
If sets don't exist in the world, life is a lot simpler, and the only things that exist in the world are x,y,z.

The implication is, that as an object such as an apple is only a set of parts, as sets don't exist in the world, then apples don't exist in the world, which is my belief.

IE, set E (x,y,z) is the set of all that exists in the world.

That in another possible world snow is green, but 7+5 is 12 in all possible worlds................And is not obviously related to T-sentences. — Banno

T-Sentences
Consider the T-sentence "snow is white" is true IFF snow is white.

Note that "snow is white" is being used in the sense that white is one of the properties of the object snow, not that white is the only property of snow.

The right hand side of the biconditional
For Tarski, the right hand side is a Metalanguage, which is not the world.
For Davidson, the right hand side is the world, in that for Davidson, T-Sentences are laws of empirical theory. For Davidson, I can hear someone saying "schnee ist weiss" and see them pointing to white snow. A similar approach to Wittgenstein's Tractatus, in that the understanding of language is founded on what is shown rather than what is said.

Naming
In the world one million years ago, snow existed but the word "snow" didn't. Today, the word "snow" exists. Therefore, there must have been a moment in the past whereby snow was named "snow". This may be called a Performative Act.

Does snow exist in the world?
Yes, if relations ontologically exist in the world. No, if relations don't ontologically exist in the world.

Note that if relations don't ontologically exist in the world, then neither can the equation 7+5=12 exist in the world. In this event, the equation 7+5=12 cannot exist in all possible worlds, and therefore cannot be necessary.

As I have not come across any persuasive argument that relations do ontologically exist in the world, my belief is that they don't.

Assuming for the sake of argument that relations do ontologically exist in the world

Situation One - in the world, the properties cold, white and frozen exist

The properties cold, white and frozen exist as the mereological object snow.

Therefore, snow is white is true.

Let the property cold be named "cold", the property white be named "white" and the property frozen be named "frozen".

Let the properties cold, white and frozen be named the object "snow".

"Snow is white" is true IFF not only i) snow is white but also ii) snow has been named "snow" and white has been named "white"

"Snow is white" is false IFF not only i) snow is white but also ii) snow has not been named "snow" and white has not been named "white".

Situation Two - in the world, the properties cold, white and frozen don't exist

Then the mereological object snow doesn't exist.

Snow is white is false because the properties cold, white and frozen don't exist.

"Snow is white" is false because snow is white is false

Summary

"Snow is white" is true IFF not only i) snow is white but also ii) snow has been named "snow" and white has been named "white".

Anil Gupta says that Tarski's biconditionals are central to the concept of truth, yet introduce circularity, such that i) from "p is true" can infer p ii) from p can infer "p is true" iii) such that "p is true" is equivalent to p.

However, the biconditional given above is not circular, as the truth of "snow is white" depends on a contingency, namely, that of the Performative Naming of properties and objects observed in the world.

"Snow is white" is not analytic...Keep working on it. — Banno

Random searches on the internet agree that "snow is white" is not analytic. For example, from www.oxfordbibliographies.com: "The existence of analytic truths is controversial. Sceptics have sometimes argued that the idea of an analytic truth is incoherent".

I am still not convinced. The problem is one of logic. In what fundamental way is "snow is white" different to "seven plus five is twelve". I hope next time I will have a deeper understanding and a more persuasive argument. :smile:

The analytic.synthetic distinction makes not difference to the T-sentence; in works for both.............Your use of "designation" is nothing like Tarski's. It's closer to Austin's discussion of performative utterances — Banno

Hopefully, I'm not repeating myself too much.

Designation has at least two senses, one as used by Tarski, and one as used by Austin. Both are relevant to the T-Sentence.

Austin and designation
"I name this ship the Queen Elizabeth" is a Performative act, whereby the ship has been christened the "Queen Elizabeth". The performative utterance gives an unnamed object a name, a designation, by which it is henceforth known. There is a free choice as to what objects may be named. For example, snow may equally be named "white" or "black". If snow is named "white", then "snow is white" is true.

Tarski and designation, satisfaction and definition
Tarski sets out certain definitions in The Semantic Conception of Truth and the Foundations of Semantics

The expression "the father of his country" designates (denotes) George Washington.
Snow satisfies the sentential function (the condition) "x is white".
The equation "2*x = 1" defines (uniquely determines) the number 1/2.
Where the words "designates", "satisfies" and "defines" express relations between certain
expressions and the objects "referred to" by these expressions.
While the words "designates," "satisfies," and "defines" express relations (between certain
expressions and the objects "referred to" by these expressions), the word "true" is of a different
logical nature: it expresses a property (or denotes a class) of certain expressions, viz., of
sentences.

"All notions mentioned in this section can be defined in terms of satisfaction. We can say, e.g., that
a given term designates a given object if this object satisfies the sentential function "x is identical
with T" where 'T' stands for the given term.
Similarly, a sentential function is said to define a given object if the latter is the only object which
satisfies this function."

In other words:

Designation and satisfaction
As regards analytic propositions:
i) If snow satisfies "x is identical with white" then "is white" designates snow.
ii) If snow satisfies "x is identical with black" then "is black" designates snow.
Snow may be identical to "white" in the sense that snow has the property of being "white".

As regards synthetic propositions:
iii) If snow satisfies "x is identical with being on the ground" then "being on the ground" designates snow.
iv) If snow satisfies "x is identical with not being on the ground" then "not being on the ground" designates snow.
Snow may be identical to "being on the ground" in the sense that snow may be observed "being on the ground".

Definition and satisfaction
i) If snow is the only object that satisfies "x is white" then "x is white" defines snow. As many objects can be white, "x is white" doesn't define snow.
ii) If snow is the only object that satisfies "x is on the ground" then "x is on the ground" defines snow. As many objects can be on the ground, "x is on the ground" doesn't define snow.

Analytic proposition "snow is white"
During a Performative Utterance, a previously unnamed property is designated "white". Subsequently, a previously unnamed object with the property "white" is designated "snow"
As "snow is white" is always true, then "snow is white" is true.

During a Performative Utterance, a previously unnamed property is designated "black". Subsequently, a previously unnamed object with the property "black" is designated "snow"
As "snow is black" is always true, then "snow is black" is true.

Synthetic proposition "snow is on the ground"
Subsequently, during a Performative Utterance, a previously unnamed object is named "ground"

The object named "snow" may or may not be on the object named "ground"

If snow is on the ground:
"Snow is on the ground" is true IFF snow is on the ground
"Snow is on the ground" is false IFF snow is not on the ground

If snow is not on the ground:
"Snow is not on the ground" is true IFF snow is not on the ground
"Snow is not on the ground" is false IFF snow is on the ground

Summary
To my understanding, whether a proposition is analytic or synthetic makes a difference to the T-Sentence, because the truth of an analytic proposition is determined by a Performative Utterance, which is not the case for a synthetic proposition.

white is not a property but just the most commonly seen appearance of snow...Unfortunately this leads away from the OP topic which presumes truth for T-sentences. — magritte

In the dictionary, snow is defined as atmospheric water vapour frozen into ice crystals and falling in light white flakes or lying on the ground as a white layer. A property is defined as an attribute, quality, or characteristic of something. For example, the dictionary does not define snow as "as atmospheric water vapour frozen into ice crystals and falling in light flakes of various colours or lying on the ground as a layer of various colours".

To this reading, white is a property of snow.

It is also true that FH Bradley noted that the nature of an object's properties is problematic.

However, I do think that the difference between analytic and synthetic propositions is central to the nature of T-Sentences.

Snow is black shocks because it is contradictory to white and thus supposedly logically impossible. — magritte

Snow can appear black at night, can appear white in sunlight, can appear red at sunset and can appear grey at dusk.

All these are contradictory yet logically possible.

It seems unlikely that the fundamental nature of snow changes with the light.

Adding white to snow is a synthetic addition to my more modern understanding because on a dark night snow could be black instead. — magritte

The word "is" has many meanings. For example - i) "snow is black on a dark night", where "is" means "appears to be" - ii) "snow is white", where "is" means "has the property" - iii) "snow is angry", where "is" is being used metaphorically - iv) "snow is welcome", where "is" is being used ironically, etc.

Tarski in "snow is white" is using "is" to mean "has the property", in which case "snow is white" is analytic.

To say "snow is black on a dark night" is a synthetic proposition, as it can be expanded to "snow which has the property of being white appears black on a dark night"

So yes, the T-sentences are not a theory of truth, at least in that they do not tell us which sentences are true and which false, but which sentences have the same truth value. — Banno

Propositions may be either analytic or synthetic
I would move on to Davidson if it weren't for my confusion with Tarski's Semantic Theory of Truth (STT), in that it does not differentiate between analytic and synthetic propositions. For example, the proposition "snow is white" is analytic, whereas "snow is on the ground" is synthetic. Note that the word "is" does not mean "is a synonym of" but rather "has the properties of", thereby avoiding Quine's Two Dogmas of Empiricism problem.

The matter is complicated by the fact that Tarski himself used an analytic proposition "snow is white" to illustrate the T-Schema "p" is true IFF p which is dependent on synthetic propositions.

Tarski wrote in The Semantic Conception of Truth: and the Foundations of Semantics 1944 - "Consider the sentence ‘snow is white.’ We ask the question under what conditions this sentence is true or false. It seems clear that if we base ourselves on the classical conception of truth, we shall say that the sentence is true if snow is white, and that it is false if snow is not white. Thus, if the definition of truth is to conform to our conception, it must imply the following equivalence: The sentence ‘snow is white’ is true if, and only if, snow is white."

Analytic Propositions
Consider something in an Object Language (OL) that is "green, circular and distant". Still within the Object Language, I designate this something as "snow".

As long as "snow" has been designated "green, circular and distant", then it follows that not only is "snow" satisfied by the predicate "green, circular and distant" but also that "snow is green, circular and distant" is true.

"Snow" is therefore independent of anything that may or may not exist in the Metalanguage (ML). Similarly with all analytic propositions.

For example, as long as "snow" has been designated as "white" in the object language, then it follows that not only is "snow" satisfied by the predicate "white" but also that "snow is white" is true.

For example, as long as "unicorn" has been designated as "a horse with a single horn", then it follows that not only is "unicorn" satisfied by the predicate "a horse with a single horn" but also that "a unicorn is a horse with a single horn" is true.

IE, analytic propositions don't require a Metalanguage in order to be true. Analytic propositions are Theories of Truth using the Performative Speech Act.

"Designation" is a Theory of Truth
Designation is a Performative Speech Act, in that "I name this ship Queen Elizabeth" means the same as "I designate the name of this ship the Queen Elizabeth".

Designation as a Performative Speech Act is a Theory of Truth, in that "designation" establishes what is true. Once one knows what is true, it follows that one knows the conditions of satisfaction.

IE, designating something "green, circular and distant" as "snow" establishes that "snow is green, circular and distant" is true. It follows that the predicate "green, circular and distant" then must satisfy the subject "snow".

Synthetic Propositions
Consider the synthetic proposition "snow is on the ground" in the Object Language.

In the Metalanguage, either snow is on the ground or snow is not on the ground.

Let "snow" in the OL be designated snow in the ML, and let "ground" in the OL be designated ground in the ML.

Situation A) - in the ML, snow is on the ground.
i) The predicate "is on the ground" in the OL is satisfied by the predicate is on the ground in the ML
ii) "The snow is on the ground" is true IFF the snow is on the ground.
iii) "The snow is on the ground" is false IFF the snow is not on the ground.

Situation B) - in the ML, snow is not on the ground.
i) The predicate "is not on the ground" in the OL is satisfied by the predicate is not on the ground in the ML
ii) "The snow is not on the ground" is true IFF the snow is not on the ground.
iii) "The snow is not on the ground" is false IFF the snow is on the ground.

IE, as the T-Schema does not tell us whether snow is or isn't on the ground, Tarski's SST is not a Theory of Truth.

The STT is not a Theory of Truth
The IEP article "The Semantic Theory of Truth" notes that "STT as a formal construction is explicated via set theory and the concept of satisfaction. The prevailing philosophical interpretation of STT considers it to be a version of the correspondence theory of truth that goes back to Aristotle"

As to my understanding, the STT is not a Theory of Truth, including the Classical Correspondence Theory of Truth, it seems to me that the quote above from the IEP is incorrect.

"This sentence is false"
There are many possible Theories of Truth - Correspondence Theory of Truth, Evidence Theory of Truth, Performative Theory of Truth, Coherence Theory of Truth, Common Agreement Theory of Truth, Utilitarian Theory of Truth, etc. Tarski requires a Theory of Truth to be formally correct, ie to avoid paradox.

If a Particular Theory of Truth leads to paradox, the conclusion is that this particular Theory of Truth is not valid, not that there isn't a Theory of Truth that doesn't lead to paradox.

Summary
To my understanding, 1) Tarski's T-Schema "p" is true IFF p is not a Theory of Truth, but establishes the conditions necessary for a Theory of Truth for synthetic propositions.

2) Designation is a Performative Act which is a Theory of Truth for analytic propositions.

To my understanding: Tarski's Semantic Theory of Truth is not a Theory of Truth

Tarski in his Semantic Theory of Truth (STT) requires any Theory of Truth to be formally correct and materially correct. Formally correct means it does not lead to a paradox. Materially correct is formulated as Convention T, whereby the truth of the proposition "schnee ist weiss" in an Object Language is given in a Metalanguage as snow is white

In the Object Language are names of objects, such as "snow", "house", "government", etc, and names of properties, such as "red", "distant", "large", etc. In the Metalanguage are the same names, ie, snow, house, government, red, distant, large, etc.

Any name in the Object Language can be designated any set of names in the Metalanguage. For example, "snow" may be designated green, circular and distant.

But who designates "snow" as green, circular and distant? Either an individual or an Institution can designate a name, although generally this is done by Institutions.

And on what basis does an Institution designate a name? It could be designated in either a performative act, such that "truth is what I say it is", or by correspondence with the world, such that "snow" corresponds with snow.

Tarski's Semantic Theory of Truth is not a Theory of Truth, in that it doesn't specify which Theory of Truth should be used, only that a Theory of Truth must be used. The Semantic Theory of Truth is establishing the conditions under which a Theory of Truth may be used.

For example, if the Theory of Truth to be used is the Performative Theory of Truth, let "snow" designate distant, green, circular. As "snow" is satisfied by circular, then "snow is circular" is true. The T-Schema may be written "snow is circular" is true IFF snow is circular.

If the Theory of Truth to be used is the Correspondence Theory of Truth, let "snow" designate cold, white, frozen, As "snow" is satisfied by white, then "snow is white" is true. The T-Schema may be written "snow is white" is true IFF snow is white.

Within Tarski's Semantic Theory of truth, both i) "snow is circular" is true IFF snow is circular is true and ii) "snow is white" is true IFF snow is white is true.

Within the Performative Theory of Truth, only "snow is circular" is true IFF snow is circular is true. Within the Correspondence Theory of Truth, only "snow is white" is true IFF snow is white is true.

IE, Tarski's Semantic Theory of Truth is establishing the conditions under which a Theory of Truth may be used.

Tarski seems to be the theory in which folk are most interested — Banno

"Small moves, Banno, small moves"

This is how Tarski avoids the problem to which @Michael drew attention — Banno

My understanding is correct IFF my understanding is correct.

My instinctive belief is as @Michael wrote ""'p' is true iff p" isn't the definition of truth but something which follows from whatever the actual definition is". This leads into @Banno's quote that "Neither correspondence nor coherence are at work here. It's a formal language with truth defined in terms of satisfaction."

Consider "schnee ist weiss" is true IFF snow is white

What is "designation"
I perceive the word "snow" and designate it "schnee", such that "schnee" mean "snow". I perceive the word "white" and designate it "weiss", such that "weiss" means "white".

What is the mechanism of "satisfaction"
From the IEP: "The Semantic Theory of Truth"
Consider the open formula "x is a city", open because it has a free variable.
The formula is satisfied by London, so "London is a city" is true
The formula is not satisfied by The Thames, so "the Thames is a city" is false
Satisfaction turns an open formula into a true sentence, and non-satisfaction turns an open formula into a false sentence

Based on @Banno, an object o satisfies a predicate f IFF either the object o is snow and the predicate f is "is snow" or the object o is schnee and the predicate f is "ist weiss".

What is intensional and extensional
The quote marks around "snow is white" makes it intensional. Intensional means analytic, reasoning from abstract rules, what Quine calls "meaning" and what is necessary to make a concept.

P ↔ Q means biconditional, it means P IFF Q, it also means P implies Q and Q implies P. The meanings of P and Q are extensional. Extensional means synthetic, involves examples from the world, what Quine calls "reference" and what is contingent to a concept.

Replacing the T-Schema "schnee ist weiss" is true IFF snow is white by the equivalent T-Schema "snow is white" is true IFF snow is white

@Banno wrote: "Tarski gets past this for formal languages by developing the mechanism of satisfaction, so that he has extensionally transparent terms on both sides of the equivalence". This means that the extensional meaning of "schnee ist weiss" is the same as the extensional meaning of snow is white, because of the mechanism of satisfaction.

Because "schnee" has been designated as "snow", and as ""weiss" has been designated as "white", the intensional meaning of "schnee is weiss" is the same as the intensional meaning of "snow is white".

Therefore we can replace the T-Schema "schnee ist weiss" is true IFF snow is white by the equivalent T-Schema "snow is white" is true IFF snow is white.

Introducing extensional meaning
Tarski is saying that the extensional meaning of "snow is white" is equivalent to the extensional meaning of snow is white.

In this case, the T-Schema may be written as: the extensional meaning of "snow is white" is true IFF it is equivalent to the extensional meaning of snow is white.

The problem with the extensional meaning
The problem is, why should the extensional meaning of "snow is white" be equivalent to the extensional meaning of snow is white?

The T-Schema has become tautological. It may be written in full as: the extensional meaning of "snow is white" is true IFF it is equivalent to the extensional meaning of snow is white given that the extensional meaning of "snow is white" is equivalent to the extensional meaning of snow.

The core problem with the T-Schema as a definition of truth without circularity is that it is founded on a conditional, the conditional IFF, which is saying no more than x is true IFF x is true. The T-Schema is a tautology, it is analytic.

The truth tables reinforce the conditionality of the T-Schema
The truth table for material conditional uses the conditional, and the truth table for material biconditional uses the conditional.

A valid definition of truth cannot be founded on a conditional
A definition of truth cannot be founded on a conditional, as this leads to a tautology. A valid definition of truth must avoid the conditional. For example, i) "truth is what I say it is" is a valid definition of truth, ii) the performative act "I name this ship Queen Elizabeth" means that it is true that this ship is named Queen Elizabeth and iii) I perceive something in the world and name it "snow" means that it is true that "snow" is snow.

As an aside, my perception of something in the world that is cold, white and frozen and name it "snow" means that there is a correspondence between "snow" and snow. However such correspondence is not purely cognitive, but is founded on something visceral, thereby avoiding the problem of belief as a truth bearer.

Summary
The T-Schema is based on the conditional IFF, which is fixed by the mechanism of satisfaction. Yet the mechanism of satisfaction is itself based on another conditional, again leading to circularity.

It seems to me that a valid definition of truth cannot rely on a conditional, which Tarski's Semantic Theory of Truth does.

"Snow is turquoise with purple polkadots" is true IFF snow is turquoise with purple polkadots — Banno

I am attempting to understand Tarski's logic of of truth.

Tarski's T-Schema states "S" is true IFF S

Tarski's Semantic Definition of Truth establishes the T-Schema, whereby "S" is true IFF S, where "S" is in an Object Language, and S is in a Metalanguage.

The following T-Schema are all true:
"Snow is turquoise with purple polkadots" is true IFF snow is turquoise with purple polkadots.
"Snow is white" is true IFF snow is white
"Snow is a volcano" is true IFF snow is a volcano.

If S was not limited in some way, the T-Schema would be "S" is true

For every possible statement "S" in an object language, an S may be found in a metalanguage. For example, given the proposition "snow is a volcano", there is a true T-Schema such that "snow is a volcano" is true IFF snow is a volcano.

It follows that for every possible "S", a true T-Schema may be found, meaning that every possible "S" will be true.

If every possible "S" is true, the term IFF becomes redundant, and the T-Schema may be reduced to "S" is true.

What limits possible values of S ?

However, there is a term IFF in the T-schema, meaning that not all propositions "S" in an object language are true. It follows that there are limitations as to what S can be in the metalanguage.

My belief is that the S in the metalanguage is limited by correspondence with the world, in that I perceive something in the world that is cold, white and frozen, but I don't perceive something in the world that is cold, a volcano and frozen.

However, if S is not limited by correspondence with the world, yet S must be limited by something (otherwise the T-Schema would be "S" is true), then what does limit S ?

What prevents some values of S from being a possibility in the metalanguage ?

We want to add predication. To do this, Tarski developed satisfaction. — Banno

Quick question.

I perceive something in the world that is cold, white and frozen, and I name it "snow".
Therefore, "snow" means something in the world that is cold, white and frozen.

For Tarski, Convention T is "p" is true IFF p. Therefore, "snow is white" is true IFF snow is white.

Tarski's T convention assumes that in the object language the subject is satisfied by its predicate, in other words, the subject "snow" has the property "is white".

I perceive something in the world that is the ground and name it "the ground".

Therefore, Tarski's Convention T may be written as "snow is on the ground" is true IFF snow is on the ground.

But Tarski's T convention assumes that in the object language the subject is satisfied by its predicate. This would mean that "snow" has the property "is on the ground".

But is it true that "snow" has the property "is on the ground", as for snow, being on the ground is a contingent rather than a necessary fact ?

What am I missing ?

Yes, although the circularity perhaps only reflects the fact that definitions are unnecessary. The game asks for judgements, but not reasons.......But, as such, they all fail the sorites test, which requires some perfectly absolute intolerance, as well as tolerance.. — bongo fury

Truth rests on meaning - and meaning rests on definition

The Sorites Paradox asks that when on the removal of a single grain a heap becomes a non-heap.

In the dictionary, a "heap" is defined as a "large number of". "Large" is defined as "considerable". "Considerable" is defined as "large". In this case, circular. Does this mean that definitions are unnecessary? Society has determined that it is not necessary that a "heap" be defined within a single grain, as it has, or example, with the metre length, recorded on a bar of platinum - iridium in the Bureau International des Poids et Mesures.

The Sorites Paradox is only a paradox because it requires a definition that does not exist. It would be like asking if the proposition "a xyxxy swims in the sea" is true or false before the meaning of "xyxxy" had been defined.

The Sorites Paradox requires the definition "a heap has at least X grains and at most Y grains" without defining the meaning of X and Y.

In Tarski's terms, the proposition " a heap has at least X grains and at most Y grains" is in the object language. The truth or falsity of the proposition may only be proven in the metalanguage, whereby a heap has at least X grains and at most Y grains. Yet the meaning of X and Y has never been defined. Truth can never be proven in the metalanguage until meaning has been defined in the object language.

The Sorites Paradox shows that it is not the case that definitions are unnecessary, rather, that it is only a paradox because it is requiring a definition that doesn't yet exist.

An interesting puzzle, though, is how, relative to a language game, truth can be absolute as well as relative. — bongo fury

Given the Sorites Paradox, we have a heap of sand. A heap is defined as "a large number of". Large is defined as considerable. Considerable is defined as large. Definitions become circular.

The word "heap" is as vague as any concept - love, hate, government, the colour red, tables, etc. Yet we have one word for something that is imprecise, for something vague yet is recognizable.

I suggest that the brain's ability to fix a single name to something that is variable is fundamentally statistical. For example, I am certain I see the colour green, I believe it is green, I am probably seeing green, I think it is green, it could be green, it may be green. Such statistically-based concepts could be readily programmed into a computer. Complex concepts may be developed from a set of simple concepts.

You present an account of institutional facts, in which the direction of fit is word-to-world. and then jump to the non sequitur that all utterances are of this sort. They are not. — Banno

I agree that most of the time I accept the names given to things by society, such as ships, tables, governments, etc. However there are occasions when there are no existing words that fit the bill. For example, to make a philosophic point, two years ago I made the performative utterance: "a peffel is part my pen and part The Eiffel Tower".

I agree that most of the time the direction of fit is world to word, but there are occasions whereby word to world is also required.

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What is truth ?
I perceive in my world my pen and the Eiffel Tower. My pen and the Eiffel Tower are facts in my world.

Along the lines of the Tractatus, it is immaterial as to whether I believe in Idealism or Realism. Regardless, I know that my pen and the Eiffel Tower are facts in my world.

In a performative utterance, I name my pen and the Eiffel Tower a "peffel". A performative utterance is in a sense a christening, such as "I name this baby Horatio". I record my performative utterance in a (metaphorical) dictionary.

Before the performative utterance, in my world are the facts my pen and the Eiffel Tower. After the performative utterance, in my world are the facts a peffel, my pen and the Eiffel Tower.

In Searle's terms, a performative utterance is an Institutional activity. A performative utterance creates new Institutional facts, whether it is the fact that the bishop always stays on the same coloured squares, or a peffel is part my pen and part the Eiffel Tower. Institutional facts require a social obligation, whether I am obliged to move the bishop diagonally, or my listener is obliged to acknowledge the sense of the word peffel when used in conversation.

Under what conditions is the statement "a peffel is part my pen and part the Eiffel Tower" true ? Its truth value can only be known if its meaning is first known. The meaning of a "peffel" may be discovered in the dictionary, such that "a peffel is part my pen and part the Eiffel Tower". Knowing the meaning of a "peffel", and knowing that my pen and the Eiffel Tower are facts in my world, the statement "a peffel is part my pen and part the Eiffel Tower" is true.

It is said that dictionaries are not all that useful as meaning changes, but (metaphorical) dictionaries are foundational to knowing the nature of truth. It is true that definitions may change with time, in that Art as Postmodernism didn't exist before the 1960's, but as definitions change, our knowing what is true changes. Our knowledge of what is truth is not a fixed thing.

Under what conditions is the statement "A is X and Y" true. First, its meaning must be known. The meaning of "A" may be discovered in the dictionary, such that "A is X and Y". Knowing its meaning, and knowing that X and Y are facts in my world - the statement "A is X and Y" is true.

Therefore, a linguistic statement is true when, not only, the subject has been defined in a performative utterance as having the properties given in the predicate, but also, the predicate exists as facts in the world.

IE, rather than "snow is white" is true iff snow is white, I would suggest that "snow is white" is true iff not only has "snow" been defined as having the property "white" but also snow is white.

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You present an argument that language is arbitrary, which in a sense it is, then jump to the non sequitur that truth is relative — Banno

Some aspects of language can be arbitrary, and other aspects can be relative.

I perceive something white in my world. I have a free choice as to what I name it. In a performative utterance I give it a name, I christen it "X". In a sense, my choice of "X" is arbitrary.

As regards "the truth is what I say it is", truth refers to the statement "snow is X" rather than the fact in the world that snow is X.

Situation one: I christen "snow" as "white".
"Snow is white" is true iff "snow" has been defined as "white" and snow is white.

Situation two: I christen "snow" as "black"
"Snow is black" is true iff "snow" has been defined as "black" and snow is white.

In a sense, the truth of the statement is relative to my arbitrary choice of the name I use when christening what I have perceived in my world.

Sometimes something is true because you say it. You cannot apply the above reasoning to everything. — Michael

Agree. Most of the time I accept the names given to things by society, such as ships, tables, governments, etc. However there are occasions when there are no existing words that fit the bill. For example, to make a philosophic point, two years ago I made the performative utterance: "a peffel is part my pen and part The Eiffel Tower". For me, it is now true that the "peffel" is part my pen and part the Eiffel Tower.

And if the truth is what you say it is, does it follow that what you say is true, is true? Can you cast spells? — Banno

The truth is what I say it is
I perceive the world and observe something white. In a performative utterance, I name this something "black". Henceforth, for me, "something is black" is true iff something is white, and the truth for me is that "black" is white.

Unfortunately, those in authority within society had previously in a performative utterance named this something "white", such that society as a whole accepts that "something is white" is true iff something is white, and the truth for society as a whole is that "white" is white.

Truth is relative. There is no absolute truth. My truth is no more valid nor less valid than anyone else's. It may be true that I will have difficulty fitting in with society, but that is no judge as to what I know to be true. After all, in 1633, the Inquisition of the Roman Catholic Church forced Galileo Galilei, one of the founders of modern science, to recant his theory that the Earth moves around the Sun, and under threat of torture, Galileo so recanted.

Is what I say true, true
I make the performative utterance "I name this ship Queen Elizabeth".
I can then say that it is true that this ship is named Queen Elizabeth.
Is what I say is true, true ?
(What I say is true) is (this ship is named Queen Elizabeth)
So yes, (this ship is named Queen Elizabeth) is true

So yes, what I say is true is true.

Spells
A spell has magic power. Magic produces supernatural effects. The supernatural exists outside the natural world. The natural world is matter, energy, time and space. My belief is that there is nothing outside the natural world, though I don't know.

Therefore, I believe that I cannot cast spells, but I cannot say that I know that I cannot cast spells.

What is truth? — Pie

Consider the propositions "snow is white" and "the bird is blue". To know whether they are true or false, one must first know what they mean. We cannot decide whether a proposition is true or false until we know what it means.

There are two kinds of propositions
"Snow is white" is analytic necessary, as snow is white by definition. "The bird is blue" is synthetic contingent, as we need to observe the world.

The example of the Rosetta Stone
Ancient Egyptian was a coherent language that described the world in which the ancient Egyptians lived, yet couldn't be understood for thousands of years until the discovery of the Rosetta Stone. In Tarski's terms, ancient Egyptian is the object language. Something external to the object language was needed to give the object language meaning. In this case the Rosetta Stone was needed. In Tarski's terms, a metalanguage.

The meaning of "snow is white"
Go back to the beginning. I perceive in the world something that is cold, white and frozen. I name this something in a performative act "snow". I could equally well have named it "schnee". I record my performative act in a dictionary, where white is described as one of the properties of snow, in that white is a necessary property of snow. Austin discusses performative acts.

I utter the proposition "snow is white". In Tarski's terms, utterances are uttered in the object language. In Tarski's terms, performative acts are carried out in the metalanguage. Therefore, what does the utterance "snow is white" mean. It only has meaning if snow is white has been established during a performative act in the metalanguage. It has no meaning if snow is white has not yet been established by a performative act in a metalanguage.

Is "snow is white" true or false
The utterance in the object language "snow is white" is true if the predicate "is white" has been established as a property of the subject "snow" during a performative act in a metalanguage. The utterance in the object language "snow is white" is false if the predicate "is not white" has been established as a property of the subject "snow" during a performative act in a metalanguage.

Meaning of "the bird is blue"
For "the bird is blue" to have meaning as an utterance in the object language, the properties of the subject "bird" and properties of the predicate "is blue" must have been established during performative acts within a metalanguage. A bird, for example, having several colours, ability to fly and being an animal

Is "the bird is blue" true or false
The utterance in the object language "the bird is blue" is true if, first, the predicate "is blue" has been established as a possible property of the subject "bird" during a performative act in a metalanguage and second, if it is perceived in the world that the bird is blue. The utterance in the object language "the bird is blue" is false if, first the predicate "is blue" has been established as a possible property of the subject "bird" during a performative act in a metalanguage, and second, if it is perceived in the world that the bird is not blue

The analytic T-sentence "snow is white"
Under what conditions is the utterance "snow is white" true ? The T-sentence is "snow is white" is true iff snow is white. "Snow is white" is an utterance in the object language.

"Snow is white" is true if the predicate "is white" has been established as a property of the subject "snow" during a performative act in a metalanguage.

An analytic T-sentence may be generalised as "A is B" is true iff the predicate "is B" has been established as a property of the subject "A" during a performative act in a metalanguage.

The synthetic T-sentence "the bird is blue"
Under what conditions is the utterance "the bird is blue" true ? The T-sentence is "the bird is blue" is true iff the bird is blue. "The bird is blue" is an utterance in the object language. "The bird is blue" is true iff not only the predicate "is blue" has been established as a possible property of the subject "bird" during a performative act in a metalanguage but also if it is perceived in the world that the bird is blue

A synthetic T-sentence may be generalised as "A is B" is true iff not only the predicate "is B" has been established as a possible property of the subject "A" during a performative act in a metalanguage but also if it is perceived in the world that the A is B.

Quine and the analytic-synthetic divide
Quine wrote Two Dogmas of Empiricism 1950. He argued that analytic truths are problematic. He distinguished between logical truths, "no not-x is x" and truths based on synonyms, such as "a bachelor is an unmarried man". Synonyms are analytically problematic, in that although bachelor is a synonym for unmarried, they have a different senses, different meanings.

Consider the analytic proposition "snow is white", which is analytic because by definition snow is white. But note that the word "is" has different possible meanings. As a metaphor, "cheese is heavenly". As irony, "spinach is delicious". As identity, A is A. As description, "the Eiffel Tower is a wrought-iron structure erected in Paris for the World Exhibition of 1889 with a height of 300 metres". As definition, "a unicorn is a mythical animal typically represented as a horse with a single straight horn projecting from its forehead". As assumption, "drinking a lot of water is good for you".

The word "is" in "snow is white" is not used as an identity, but as a definition.

Where does meaning and truth exist
Consider the proposition in an object language "snow is white". To know whether it is true or not first requires knowing what it means. As with the example of Ancient Egyptian, meaning cannot be discovered within the language itself, no matter that the language is coherent, no matter that it describes the world within which it exists. Meaning is discovered external to the language itself, whether the Rosetta Stone, or a dictionary created in a performative act within a metalanguage.

The meaning of the object language exists within the metalanguage, not in the object language. Similarly, the truth of the analytic proposition "snow is white" exists not in the object language but in the metalanguage.

Consider the proposition in the object language "the bird is blue". The meaning of the object language exists within the metalanguage, not in the object language. The truth of the synthetic proposition "the bird is blue" requires not only its meaning which exists only in the metalanguage and not the object language but also a perception of the world that the bird is blue

Where is the world
I perceive something in the world. If I believed in Idealism, the world would exist in a mind. If I believed in Realism, the world would exist mind-independently.

My argument so far requires that I perceive a world, but whether this world exists in my mind or exists mind-independently makes no difference to either the meaning or truth of the analytic "snow is white" or synthetic "the bird is blue". As an aside, Wittgenstein's Tractatus may also be read independently of any belief in Idealism or Realism.

The creation of meaning and truth
I perceive in the world something that is cold, white and frozen. In a performative act I name this something "snow". Subsequent to this performative act, "snow" means something cold, white and frozen and it is true that "snow" is something cold, white and frozen.

Meaning and truth have been created in a performative act.

The problem of the nature of objects and properties
I perceive something in the world that is cold, white and frozen, and in a performative act name it "snow". Later I may discover that "snow" is not only cold, white and frozen but also H2O. How can the same object have different properties ? This raises the question of what "snow" is exactly. It raises the question of what any noun is, whether it be snow, table, the Moon, the Eiffel Tower, etc.

Bradley, for example, questioned the nature of objects and their properties. He starts with the example of a lump of sugar. He notes that there appears to be such a thing as a lump of sugar and this thing appears to have qualities such as whiteness, sweetness, and hardness. But, asks Bradley, what is this “thing” that bears properties? On the one hand, he thinks it is odd to assume that there is something to the lump of sugar beside its several qualities, thus implying that postulating a property-less bearer of properties is incoherent. On the other hand, he notes that the lump cannot merely be its qualities either, since the latter must somehow be united.

For Bradley, unity or “coexistence” of qualities presupposes relations, which is why he questioned our concept of relations, leading to questioning the ontological existence of relations.

IE, "snow" is not an object existing in the world. "Snow" is a name given to a set of properties that exist in the world.

A solution to the Liar Paradox
Consider the statement "this statement is false". Tarski diagnosed the paradox as arising only in languages that are "semantically closed", and to avoid self-contradiction, it is necessary to envisage levels of language, the object language and the metalanguage. The metalanguage is where truth and meaning are created in performative acts.

When I name this ship the Queen Elizabeth, the ship only has the name Queen Elizabeth at the conclusion of my performative act. At the conclusion of my utterance "I name this ship" it is not yet true that the words "I name this ship" refer to the proposition " I name this ship Queen Elizabeth".

Similarly, the statement "this statement is false" only has meaning at the conclusion of my performative act. At the conclusion of my utterance "this statement", it is not yet true that the words "this statement" refer to the proposition "this statement is false".

IE, within the performative act, "this statement" doesn't refer to the statement "this statement is false".

Summary
Truth is a creation of a performative act, in that, in naming this ship the Queen Elizabeth, it becomes true that this ship is named Queen Elizabeth.

My conclusion may be summed up by a line from that great film "The Shooter" - The Truth is what I say it is

Anyway, I agree that there must be "something deeper than mathematics". — Gnomon

:smile: :smile: :smile:

Perhaps those mathematical ratios & regularities tell us only that whatever happens is natural & logical — Gnomon

Given G as 6.67 * 10-11 Nm2/kg2, whatever follows is natural and logical, agreeing in this respect with Max Tegmark that the universe is mathematical.

The question remains, why is G the value it is in the first place. Either mathematics spontaneously caused itself, which I cannot accept, or there is something deeper than mathematics, meaning that the universe is not, at its core, mathematical.

"snow is white " is true iff s..........All we need to do now is work out what s might be. — Banno

My attempt:

I believe that I am observing something that is atmospheric water vapour frozen into ice crystals and falling in light white flakes or lying on the ground as a white layer

Rather than keep saying "I believe that I am observing something that is atmospheric water vapour frozen into ice crystals and falling in light white flakes or lying on the ground as a white layer" it is more convenient to say "I believe that I am observing snow"

Where "snow" is defined as "something that is atmospheric water vapour frozen into ice crystals and falling in light white flakes or lying on the ground as a white layer".

In other words, "white" is part of the definition of "snow".

I need no knowledge of the world to know that "snow is white", only knowledge of language.

In Tarski's terms, I can say "snow is white" and a German can say "schnee ist weiss". These are said within the object language

The metalanguage is where words are defined, in that "white" is part of the definition of "snow", "white" means "weiss" and "snow" means "schnee"

Therefore, we can replace "snow is white" is true iff s by "snow is white" is true iff "white" is part of the definition of "snow", "white" means "weiss" and "snow means "schnee"

Therefore s = the linguistic declaration that "white" is part of the definition of "snow", "white" means "weiss" and "snow" means "schnee".

Metaphorically, what we call "Logic" is simply mathematics with Words (Gk. logoi). And words are merely encapsulated & portable commonly-relevant meanings. — Gnomon

Mathematics tells us that the gravitational force between any two objects is F = GmM/r2, where G = 6.67 * 10-11 N m2/kg2. But mathematics does not tell us why G = 6.67 * 10-11 N m2/kg2, rather than 1 * 10-11 N m2/kg2, for example. Mathematics tells us what will happen, not why it will happen.

Mathematics is based on making logical inferences from observed regularities. If we measure the gravitational force between two objects numerous times and discover that G = 6.67 * 10-11 N m2/kg2, we believe that it is true that G = 6.67 * 10-11 N m2/kg2.

It is true that mathematics tells us that G = 6.67 * 10 -11 N m2/kg2, but mathematics doesn't tell us why G = 6.67 * 10 -11 N m2/kg2 is true. If mathematics cannot explain why something will happen, then in order to understand the nature of reality, we need to know more than mathematics.

IE, what does the mathematical symbol G mean to us ? It means that we can predict what will happen, it does not mean that we know why it will happen.

“the existence of consistent patterns that can intuitively be discerned and from which accurate deductions can be made which emulate the state of things as they are”. — Benj96

Consistency
If there was no regularity in what we observed, there would be no logic in what we observed.

For example, if one morning the sun rose in the east, the next day it rose in the west, and the following day it did not rise at all, we would say that there is no logic in the behaviour of the sun. We expect regularity in the laws of nature. If today 1 + 1 = 2, then we expect that tomorrow 1 + 1 = 2.

If we observe the sun has risen in the east for the previous 1,000 days, we logically infer that the sun rises in the east, where such an inference is based on an assumption of regularity in what we observe, an assumption of the regularity in the laws of nature.

Perhaps, rather than logic depending on regularity, perhaps logic "is" regularity.

Where is this regularity
We observe regularity, but where is this regularity - in the mind of the observer, or observer independent ?

Regularity requires the existence of a relation between two things or two events. But there can only be regularity in an observer independent world if relations ontologically exist in an observer independent world. As I have never come across a persuasive argument that relations do ontologically exist in a observer independent world, my belief is that relations don't ontologically exist in an observer independent world.

If relations don't ontologically exist in a observer independent world, then regularity, which depends on relations, cannot exist in an observer independent word. This means that regularity can only exist in the mind of the observer, meaning that logic can only exist in the mind of the observer

In fact, the world is only comprehensible to an observer because the observer imposes themselves on what they observe. We observe the world, and after observing regularities in the world, we logically infer that regularity exists in the world. Such logical inference is in the mind of the observer, not in what is being observed.

Therefore, logic doesn't exist independently of any observer.

The phrases "observer independent" and "observer dependent" should be treated as figures of speech rather than taken literally.

"Observer independent" refers to a conscious person having free will. "Observer dependent" refers to a non-conscious thing not having free will. Searle's inferred assumption is that free-will is a consequence of consciousness.

Consider two unobserved rocks on the moon. We have examples of i) information, in that there is a particular arrangement of things ii) numbers, in that 1 + 1 = 2 and iii) computation, as that of an abacus, in that 1 + 1 = 2.

In Searle's terms these are "observer dependent", in that there cannot be information, numbers or computation without a conscious observer, meaning that information, numbers and computation only exist in the mind, not in a mind-independent world.

Searle's observer independent refers to an animate system (such as a person) which, when experiencing identical inputs, may result in alternate outputs because it has consciousness.

Searle's observer dependent refers to an inanimate system (such as a calculator) which, when experiencing identical inputs, must result in the same output because it doesn't have consciousness.

However, the assumption that an animate system with consciousness (such as a person) when experiencing identical inputs may result in alternate outputs is unproven and needs to be justified.