The prosentential theory of 'true'

According to the prosentential theory of 'true, 'that is true' is a prosentence, and thus the same kind of thing as a pronoun, proadjective, proverb, proadverb, etc. We have it in our language because it is handy to have prosentences (just as it is handy to have the other proforms).

Here is a lazy use of it:
 John believes that [snow is white] and Mary believes that [that is true] too.

Like other proforms, 'that is true' has the same content as its antecedent expression. In this case its antecedent is the sentence 'snow is white' whose content is the proposition that snow is white  'that is true' expresses the same proposition.
Is the prosentential view plausible?

How plausible is it that 'that is true' is a prosentence?

If it is, we would expect it to be used like other proforms. Is it?

Does it have lazy uses? It seems so  we have already seen one above. Here are some possible others:
 It's a little surprising that [I won the race], but it makes me happy that [that is true].
 [Golf balls are dense], and it's because [that is true] that they sink in dams.
 [There are people on Mars]. [That is true].
 Bill claims that [there are people on Mars] and Mary knows that [that is true].

But note the following. According to prosententialism, instead of using the first sentence below we could equally well use the second:
 John asked if bananas are berries and Mary said that bananas are berries.
 John asked if bananas are berries and Mary said that that is true.
But is the second an accurate description of the situation?

Does 'that is true' have quantificational uses? Here are some possibles:
 Mary believes everything
 [Everything] is such that Mary believes [that is true]
 Don't believe anything Mary said
 If Mary said [anything] then don't believe [that is true]

Note that 'that is true' seems to have structure: 'that' seems to be a constituent expression that is used to refer to a proposition:
 A: John believes that snow is white and Mary believes that that is true too.
 B: Mary believes that what is true?
 A: That snow is white.
 John believes that snow is white and Mary believes that that is true too.
 John believes that snow is white and Mary believes that it is true too.
 John believes that snow is white and Mary believes that the thing John believes is true too.
 John believes that snow is white and Mary believes that what John believes is true too.
(It seems that we can replace 'that' by any expression that refers to the proposition that John believes.)
This is a significant difference from all other proforms. Why does this particular proform have structure while none of the others do?
(Note that Grover originally took ‘that is true’ to be a simple expression (i.e. has no structure)  this seems difficult to maintain.)

Enough about the expression 'that is true'  what about the following uses of 'true'?
 Goldbach’s conjecture is true.
 It is true that snow is white.
 The claim that grass is green is true.
According to prosententialists, each of these is also a prosentence. So as well as 'that is true' we have a whole bunch more prosentences.

We can form a prosentence in a couple of ways:

By taking an expression that refers to a proposition (e.g. 'Goldbach's conjecture') and adding 'is true' to it ('Goldbach's conjecture is true')  this gives us a prosentence that expresses the proposition that the first thing refers to.

By taking a sentence that expresses a proposition ('that snow is white') and adding 'is true' ('that snow is white is true', or 'it is true that snow is white')  this gives us a prosentence that expresses the propostion that the first thing expresses.
They call 'is true' a prosentence forming operator.

So the prosentences above express the following propositions:
 Goldbach’s conjecture is true.
 Every even number is the sum of two primes.
 It is true that snow is white.
 Snow is white.
 The claim that grass is green is true.
 Grass is green.
But is this right? This means that anyone who asserts the first is not talking about Goldbach's conjecture (they are talking about even numbers and primes), anyone who asserts the second is not talking about the proposition that snow is white (they are talking about snow), and anyone who asserts the last is not talking about the claim that grass is green (they are talking about grass). These all seem like the wrong results.
Also, why do we have this systematic way of forming prosentences, when we have no similarly systematic way of forming other proforms? (Or do we?)
Other prosentences?

If 'that is true' is not a prosentence, then what is? Or don't we have any? If not, why not?

Maybe the following have at least some prosentential uses: 'Yes', 'no', 'okay', 'amen'.

It would be interesting to see if other languages have any prosentences (other than their own version of 'that is true').
According to the Wikipedia article on prosentences, portugese speakers can talk in the following way:
 Is she at home? I believe that yes.
 She didn't leave home, but John yes.
Horwich’s minimalism

See Horwich, P. (1998), Truth, 2nd ed. (Oxford: Clarendon Press).

Horwich disagrees with nihilists when they claim that there is no such property as truth. He thinks that there is such a property, that we express it using the word 'true', and that when we say something like 'It is true that grass is green' we are predicating this property of the proposition that grass is green.

So he disagrees with the redundancy theory of 'true', Strawson's performative theory of 'true', and the prosentential theory of 'true'.

But he is a deflationist about truth, because he thinks that there is nothing more to truth than the following collection of facts:
 It is true that grass is green iff grass is green.
 It is true that snow is white iff snow is white.
 …

That is, the nature of truth is fully given by what he calls the ‘minimal theory’: the collection of all nonparadoxical Tpropositions:
 It is true that grass is green iff grass is green
 It is true that snow is white iff snow is white
 …

The collection of such propositions is uncountably infinite. It is in fact too large to be a set. So the theory cannot be fully given in a single language. In English, the portion that can be formulated is given by all instances of the schema:
It is true that # iff #
Where instances are obtained by replacing '#' by a sentence of English that expresses a proposition.

Note: Horwich's minimal theory is not the following single claim:
Every nonparadoxical Tproposition is true
(for that would be circular).

Rather, his minimal theory is an uncountably infinite bunch of claims (one for each nonparadoxical Tproposition).

What is it for someone to have the concept of truth? It would be too demanding to require that they do accept each of the uncountably many nonparadoxical Tpropositions. Horwich requires instead that they be disposed to accept each of the uncountably many nonparadoxical Tpropositions (which, presumably, is possible for creatures like us with finite minds).

But wait, if truth is a property then it is whatever all true propositions have in common. What is common about the propositions that Caracas is the capital of Venezuala, and the proposition that the Earth revolves around the Sun? Horwich says: they are both true  that's what they have in common.
But there is no common explanation of why they are true.
Perhaps truth is thus like the property of existing, and unlike the property of being a mammal.
A problem for Horwich

There seem to be some facts about truth that Horwich's minimal theory does not explain. (See Gupta, A. (1993), ‘A Critique of Deflationism’, Philosophical Topics 21, pp. 5781, esp. pp 657.)

Here is one such fact:
For every proposition p and q: the conjunction of p and q is true iff p is true and q is true.

Here are some instances of this generalization:

It is true that grass is green and snow is white iff it is true that grass is green and it is true that snow is white.

It is true that beer is tasty and coffee is yummy iff it is true that beer is tasty and it is true that coffee is yummy.
 ...

The generalization is not a Tproposition (it has the wrong form), so it is not part of the minimal theory.

Is it a consequence of the minimal theory? Here is an argument that it is not.

Each instance of the generalization is indeed a consequence of the minimal theory. Here is a derivation of the first instance above:

It is true that grass is green and snow is white iff grass is green and snow is white. (This is part of the minimal theory)

Snow is white iff it is true that snow is white. (This is part of the minimal theory)

Grass is green iff it is true that grass is green. (This is part of the minimal theory)

So, putting these three together, it is true that grass is green and snow is white iff it is true that grass is green and it is true that snow is white.

Since each instance of the generalization is a consequence of the minimal theory, so too is the conjunction of them all.

But that does not mean that the generalization itself is a consequence of the minimal theory. Why not? Because the generalization is not equivalent to the conjunction of all of its instances.

To see why not, consider a simpler example. Consider the following pair of claims:
 Everyone in this room is younger than 50.
 Wylie is in this room and is younger than 50 and Josh is in this room and is younger than 50, Moting is in this room and is younger than 50 and ... and Jeff is in this room and is younger than 50.
The second claim here is the conjunction of every instance of the first claim. But the two claims are not equivalent: it is possible for them to differ in truth value (someone older than 50 might have been in the room as well, in which case the first claim would have been false but the second claim would still have been true).
Here is another way to make the point: one might be in a position to know the second claim without being in a position to know the first (for example, by not knowing that Wylie, Josh, Moting, ..., and Jeff are all the people in this room).

So too, anyone who knows the minimal theory is thereby in a position to know the conjunction of every instance of the generalization. But she might not thereby be in a position to know the generalization, because she might be ignorant about whether the propositions covered by these instances are all the propositions that there are.

Why is this a problem for Horwich's minimal theory? Because then it would be possible for someone to have the concept of truth (understand the word 'true') and yet not know that the generalization is true. But that seems like the wrong result  anyone who does not know that the generalization is true does not have the concept of truth (does not understand the word 'true').
No exercise this week  time to catch up/polish up.