Do propositions exist?

[aquinothomas]

A friend of mine who teaches philosophy at a college in my area asserts that propositions exist (as ontological entities). As a metaphysical theory, I’ve heard of this before, but it has never made sense to me. Asserting this seems to make for a very top heavy ontology. Aquinas addresses this issue very briefly in the Summa (ST I 86 1), and the view in the ST seems to make sense but I wanted to get other opinions on this. According to Aquinas, the mind forms propositions when a person remembers via phantasm or directly senses a particular. So, according to the view in the ST, the mind forms propositions, they don’t exist apart from minds. My friend says that propositions would exist even if there were no minds. For the sake of clarity, an example of a proposition would be the meaning behind a sentence such as “The chair is in the room.” The sentence I formed is not the proposition: the content and meaning of the sentence, which could be verbalized in any language, is the proposition.

Any thoughts, ideas or suggestions on this?

 

[ateista]

I had some good conversations about this subject with john doran. He also maintains that propositions are abstract objects, existing independetly of our mind. I think that he does not mean that they exist as “possibilities”, which might be something I could entertain.

To me this is sheer nonsense. To say that the “Hamlet” exists in another possible world without conscious entites, or with conscious entities who speak no English, makes no sense to me. To say that Shakespeare did not create the “Hamlet”, rather he discovered it is unacceptable.

As to the word “meaning”: there is no such thing outside a communication channel. The “meaning” of a sentence (or proposition) is whatever the recipient of communication “makes of it”. In case of a miscommunication, the “intended” meaning can be totally different from the “perceived” meaning.

 

[The_Truthinator]

I think it’s universally agreed that propositions do *exist * at least dependently on the mind.

But independetly, they exist only assuming the proposition’s validity, I think.

Does that make sense? The proposition “the chair is in the room” exists independetly IF the chair really is in the room; if it does not, it is a faulty proposition that cannot exist independently.

I realize this is a simplification, but I think it is somewhat sufficient to address your concerns.

Hope it helps.

Pax

 

[Leopard]

Do propositions exist?

Are you proposing that they may not?

 

[john_doran]

A friend of mine who teaches philosophy at a college in my area asserts that propositions exist (as ontological entities). As a metaphysical theory, I’ve heard of this before, but it has never made sense to me. Asserting this seems to make for a very top heavy ontology.

and what’s wrong with a “top-heavy” ontology?

aquinothomas:

My friend says that propositions would exist even if there were no minds. For the sake of clarity, an example of a proposition would be the meaning behind a sentence such as “The chair is in the room.” The sentence I formed is not the proposition: the content and meaning of the sentence, which could be verbalized in any language, is the proposition.

Any thoughts, ideas or suggestions on this?

there are a number of basic reasons for thinking that propositions exist as abstract objects:

A) something must be the bearer of truth values, i.e. truth or falsity. but if it’s sentences or beliefs or some other concrete objects, then there would be nothing true in possible worlds without language-users or thinkers. in other words, the proposition “there are no language-users” is true in all possible worlds without language-users, and it will be true in*** this*** world once all of the language-users perish. the same can be said for an infinite number of other true propositions, e.g. of mathematics: they are all true, irrespective of their being believed by anyone or uttered by anyone.

but if*** that’s*** true, then concrete entites cannot be the bearers of truth-values.

B) when i and my german friend Sarah both share the belief that “the earth is round”, we are believing the same thing. but then we can’t be believing a linguistic entity, since i speak no german and she speaks no english (and what language would our common belief be in?). and the belief cannot be a brain-state, since our brain-states are ***different ***(and thus not identical). so the proper objects of belief must not be concrete.

C) logically speaking, quantification over propositions (and other abstract objects) seems to be ineliminable. that is to say, translation of sentences about propositions into first-order logic requires that references to propositions be existentially quantified, and, as quine said, “to be is to be the subject of a variable”.

D) there are an infinite number of true propositions, e.g. of math. but there are only (and*** can*** only ever be) a finite number of concrete objects (e.g. beliefs, sentences, utterances). therefore propositions cannot be concrete.

 

[aquinothomas]

Are you proposing that they may not?

I’m suggesting that propositions are logical beings, not real beings. In other words, propositions do not exist in rerum natura (in nature, apart from the mind). Propositions seem to be ens logicum and/or ens rationis (logical being) as opposed to ens reale (real being). Propositions seem to describe states of affairs, and thus, since they are dependent on the created mind, can be true or false.

For those who think that propositions do exist in rerum natura, can they be true or false? If they do exist apart from the mind, then it seems as though there can never be a false proposition. Only with God, it seems, can propositions always precisely correspond with reality, and in fact be “creative”. But even in that case, propositions are still dependent upon a mind for their being. And even in the case of God, the proposition still does not exist in rerum natura (apart from God’s mind), despite the fact that in God’s mind, all propositions correspond to reality (or possible reality).

Returning to the case of propositions related to the human mind, propositions seem to me to be more of a “half way house” between reality and the mind. They are the mind’s formulation or understanding of reality (a representation of reality), and a relation between ideas, and are thus ens logicum. Propositions can then be formulated into language and expressed to another mind, but ultimately they have no being apart from a mind.

I hope that makes sense. I just noticed that John Doran replied and I may have more to say after I read his response.

 

[aquinothomas]

and what’s wrong with a “top-heavy” ontology?

It seems to me that with a more Platonic ontology, one begins to run into absurdities. With an extreme realist ontology, where do you draw the line concerning what exists ens reale? Do all universals (such as the color red, the relation of “father-to-son”, the essence of being a “horse”, “to the right of” or “to the left of”, the number 7) possess ens reale and subsist on their own? What about happiness, love or justice? It seems absurd to me to talk about love in possible world where there are no beings who love one another.

A) something must be the bearer of truth values, i.e. truth or falsity. but if it’s sentences or beliefs or some other concrete objects, then there would be nothing true in possible worlds without language-users or thinkers. in other words, the proposition “there are no language-users” is true in all possible worlds without language-users, and it will be true in*** this*** world once all of the language-users perish. the same can be said for an infinite number of other true propositions, e.g. of mathematics: they are all true, irrespective of their being believed by anyone or uttered by anyone.

I agree with you that something must be the bearer of truth values: an intellect. A being that possesses an intellect must exemplify truth or falsehood according to whether or not their propositions correspond to reality. Truth (and falsehood) relate primarily to minds (the intellect) and in created minds to the degree that the created mind corresponds to the world as it exists. Something is true in an absolute sense if and only if it corresponds to the Divine mind. If something fails to correspond to the Divine mind, then it is not true in an absolute sense. I’m firmly in the camp of the Aristotelian / Thomistic camp on the issue of truth, so there is no possible world in which there are no minds, but if there were and that world contained intelligible beings (sentient or not), then truth would not exist because it would be an oxymoron to speak of absolute truth in a world without God and other minds.

B) when i and my german friend Sarah both share the belief that “the earth is round”, we are believing the same thing. but then we can’t be believing a linguistic entity, since i speak no german and she speaks no english (and what language would our common belief be in?). and the belief cannot be a brain-state, since our brain-states are ***different ***(and thus not identical). so the proper objects of belief must not be concrete.

A language is simply the expression of a proposition using a different linguistic structure. We can express the same proposition in both German and English. Regardless of whether I express the proposition in English as “I’m at home” or in German as “Ich bin zu Hause”, it’s the same proposition. The intentional objects are the same in both sentences, there is identity between the meaning in both sentences, and the relations are the same. So, it’s one proposition expressed using two languages. The truth of the proposition depends on whether or not, when it’s uttered, I am in fact at home.

C) logically speaking, quantification over propositions (and other abstract objects) seems to be ineliminable. that is to say, translation of sentences about propositions into first-order logic requires that references to propositions be existentially quantified, and, as quine said, “to be is to be the subject of a variable”.

By “existentially quantified”, do you mean existing in the real world? Existing in a possible world? Also, wasn’t Quine a logical positivist? If he was, then the quote you gave would require that to be “existentially quantified” would mean to exist such that the state of affairs in question be empirically verifiable, which would exclude the existence of propositions per se wouldn’t it? Let alone other abstract objects such as love, justice and beauty…

D) there are an infinite number of true propositions, e.g. of math. but there are only (and*** can*** only ever be) a finite number of concrete objects (e.g. beliefs, sentences, utterances). therefore propositions cannot be concrete.

This seems to be a bit of question begging. You’re assuming as a premise that propositions must exist per se. If propositions exit only in the mind, then there will never be the possibility for there to be an actually infinite number of propositions.

Thanks very much for the substantial response. This is very helpful.

 

[aquinothomas]

But independetly, they exist only assuming the proposition’s validity, I think.

But, what do we mean when we say that a proposition exists “independently”? Are we referring to a state of affairs? And, if a proposition is true in that the state of affairs to which it refers obtains, is there ever a possibility for a proposition to be false? If so, what does it mean for a proposition to be “false”?

 

[IvanKaramozov]

I had some good conversations about this subject with john doran. He also maintains that propositions are abstract objects, existing independetly of our mind. I think that he does not mean that they exist as “possibilities”, which might be something I could entertain.

What do you mean, exist as possabilities? Do you mean in a Wittgensteinian sense "world is the collection of facts not things’ functions etc, or something else?

To me this is sheer nonsense. To say that the “Hamlet” exists in another possible world without conscious entites, or with conscious entities who speak no English, makes no sense to me. To say that Shakespeare did not create the “Hamlet”, rather he discovered it is unacceptable.

“Hamlet” is not a proposition

As to the word “meaning”: there is no such thing outside a communication channel. The “meaning” of a sentence (or proposition) is whatever the recipient of communication “makes of it”. In case of a miscommunication, the “intended” meaning can be totally different from the “perceived” meaning.

Can you back this up a bit?

 

[john_doran]

It seems to me that with a more Platonic ontology, one begins to run into absurdities. With an extreme realist ontology, where do you draw the line concerning what exists ens reale? Do all universals (such as the color red, the relation of “father-to-son”, the essence of being a “horse”, “to the right of” or “to the left of”, the number 7) possess ens reale and subsist on their own? What about happiness, love or justice? It seems absurd to me to talk about love in possible world where there are no beings who love one another.

one “draws the line” wherever one has good reason to believe an abstract object exists…

while i think that numbers and sets probably exist as abstract objects, i doubt that spatial relations or love (or ‘running’, or ‘eating’) exist as abstract objects - there seems to be no good reason to suppose otherwise.

aquinothomas:

I agree with you that something must be the bearer of truth values: an intellect. A being that possesses an intellect must exemplify truth or falsehood according to whether or not their propositions correspond to reality.

hold on a second - first you posit the intellect as the bearer of truth values, but then say that the truth-values exemplified by such an intellet depend on the truth or falsity of “its” propositions. but then propositions are still the bearers of truth-values…

aquinothomas:

Truth (and falsehood) relate primarily to minds (the intellect) and in created minds to the degree that the created mind corresponds to the world as it exists.

this seems almost self-evidently false: talk about truth and falsity is (almost) always talk about the truth or falsity of statements, or sentences, or utterances. i mean, we speak about the possible truth of golbach’s conjecture, not of the truth of the mind thinking about that conjecture, right?

more ordinarily, i ask you, “is it true that it’s raining outside?”, or “i think that he’s wrong when he says that love is an abstract object”; truth and falsity in each of these examples is predicated of an utterance or sentence (or, by my lights, the proposition expressed by the sentence or speech-act).

aquinothomas:

Something is true in an absolute sense if and only if it corresponds to the Divine mind. If something fails to correspond to the Divine mind, then it is not true in an absolute sense. I’m firmly in the camp of the Aristotelian / Thomistic camp on the issue of truth, so there is no possible world in which there are no minds, but if there were and that world contained intelligible beings (sentient or not), then truth would not exist because it would be an oxymoron to speak of absolute truth in a world without God and other minds.

even if you’re right (and i think you are) that propositions (and all other abstract objects) are actually thoughts of the divine mind, all that follows from that is something about the nature of abstract objects, but not that propositions aren’t abstract objects…

aquinothomas:

A language is simply the expression of a proposition using a different linguistic structure. We can express the same proposition in both German and English. Regardless of whether I express the proposition in English as “I’m at home” or in German as “Ich bin zu Hause”, it’s the same proposition. The intentional objects are the same in both sentences, there is identity between the meaning in both sentences, and the relations are the same. So, it’s one proposition expressed using two languages. The truth of the proposition depends on whether or not, when it’s uttered, I am in fact at home.

exactly my point: but then it follows that the proposition being expressed is an abstract object, since there are no identical concrete objects in the situation you describe…

aquinothomas:

By “existentially quantified”, do you mean existing in the real world? Existing in a possible world?

i mean “existing”. period.

aquinothomas:

Also, wasn’t Quine a logical positivist? If he was, then the quote you gave would require that to be “existentially quantified” would mean to exist such that the state of affairs in question be empirically verifiable, which would exclude the existence of propositions per se wouldn’t it? Let alone other abstract objects such as love, justice and beauty…

quine’s empiricism is a separate issue from his claim about the ontological commitments required by first-order logic.

 

[john_doran]

aquinothomas:

This seems to be a bit of question begging. You’re assuming as a premise that propositions must exist per se. If propositions exit only in the mind, then there will never be the possibility for there to be an actually infinite number of propositions.

not at all: i am saying simply that there are an infinite number of mathematical truths. but then the bearers of mathematical truth cannot be concrete objects, since there are only a finite number of concrete objects…

 

[aquinothomas]

while i think that numbers and sets probably exist as abstract objects, i doubt that spatial relations or love (or ‘running’, or ‘eating’) exist as abstract objects - there seems to be no good reason to suppose otherwise.

What good reason is there to assert that numbers and sets “exist”? By exist, do you mean existence in the same manner that you and I exist? What I mean is: do they subsist independently?

hold on a second - first you posit the intellect as the bearer of truth values, but then say that the truth-values exemplified by such an intellet depend on the truth or falsity of “its” propositions. but then propositions are still the bearers of truth-values…

Yes, but with a dramatically important difference: you and my friend are asserting that propositions exist apart from the mind and I am sceptical that such a position can be adequately defended. I’ve no problem with propositions being the bearers of truth values if they are part and parcel of the mind. But, when someone asserts that they are independent of the mind, that they subsist in some manner even apart from the real things that they describe (that they are more than just states of affairs), that they are ontological entities (some call them intentional entities that are mind independent), then I need to understand why someone would assert such an extreme realist position. To assert that an entity such as a number exists, not as a category of being (‘quantity’), but as an independent ontological being, seems to demand some explanation. I’m hoping that someone can explain to me why it makes more sense to assert that numbers and propositions and their ilk are ontological beings that exist (subsist) in their own right, as opposed to only being accidental properties of real beings.

aquinothomas;3136795:

Truth (and falsehood) relate primarily to minds (the intellect) and in created minds to the degree that the created mind corresponds to the world as it exists.

this seems almost self-evidently false: talk about truth and falsity is (almost) always talk about the truth or falsity of statements, or sentences, or utterances. i mean, we speak about the possible truth of golbach’s conjecture, not of the truth of the mind thinking about that conjecture, right?

I agree with you that truth and falsehood do relate directly to judgments that the mind makes about reality. But, when we talk about the truth of something like Goldbach’s conjecture (of which I know nothing), aren’t we asking the question: are our ideas relating to this issue corresponding to reality or not? This is assuming of course that we understand the true meaning of Goldbach’s conjecture. When we say: is the conjecture (correct / true / veracious) what we mean is to ask whether the conjecture squares with the real world. We aren’t really asking: do our propositions about the idea(s) concerning Goldbach’s conjecture correspond with reality. That almost seems like a path to infinite regress.

When we talk about propositions, what we really seem to be talking about are judgments about ideas in our mind. And, if those ideas square with reality, then the ideas and judgments are true. If they don’t, then they are false.

more ordinarily, i ask you, “is it true that it’s raining outside?”, or “i think that he’s wrong when he says that love is an abstract object”; truth and falsity in each of these examples is predicated of an utterance or sentence (or, by my lights, the proposition expressed by the sentence or speech-act).

But, here again, to take your rain example, what we are referring to with the question is whether someone’s judgment about the rain is true or false. When we ask a question like this, we’re asking someone to make a judgment. Whether their judgment is ultimately right or wrong will depend on whether their ideas are in good order, and that they in fact correspond to reality. We’re not asking their intellect to grasp two or more propositions, “it is raining outside” and “it is not raining outside”, let alone “it is snowing outside”, “it’s 90 degrees outside”, etc. which are as real as the rain or the snow. We’re asking them to make a judgment which takes the form of a proposition, and that proposition will be formulated into a sentence of a certain language in order to communicate that proposition to our mind. The truth or falsehood of the judgment communicated to our mind will depend ultimately on the correspondence between the ideas and judgments of their intellect and reality. When we’re asking someone a question about the weather, it seems superfluous to posit that they not only need to consult the rain but also a set of propositions that exist in the world independently of any mind.

 

[aquinothomas]

even if you’re right (and i think you are) that propositions (and all other abstract objects) are actually thoughts of the divine mind, all that follows from that is something about the nature of abstract objects, but not that propositions aren’t abstract objects…

It might be helpful to make another ontological distinction here. When we’re talking about truth and correspondence with a created mind, the created mind depends upon the existence of the thing about which truth is asserted. But, it’s the other way around with the divine mind. The existence of that which corresponds to the divine mind depends upon the divine mind. In other words, God’s thoughts are creative, but our thoughts are passive (to a certain extent). But, in either case, there seems to be a dependence upon mind for the existence of propositions. In other words, it seems impossible to me that propositions would exist in a world without minds. And, it would be superfluous to talk about truth or falsehood in such a world, because there would be no need for there to be a correspondence between thought and reality.

aquinothomas;3136795:

A language is simply the expression of a proposition using a different linguistic structure. We can express the same proposition in both German and English. Regardless of whether I express the proposition in English as “I’m at home” or in German as “Ich bin zu Hause”, it’s the same proposition. The intentional objects are the same in both sentences, there is identity between the meaning in both sentences, and the relations are the same. So, it’s one proposition expressed using two languages. The truth of the proposition depends on whether or not, when it’s uttered, I am in fact at home.

exactly my point: but then it follows that the proposition being expressed is an abstract object, since there are no identical concrete objects in the situation you describe…

I’m not sure I understand what you mean by “concrete objects” in this instance. The point I was trying to make here was that the truth of the proposition depends upon the correspondence of reality with my mind when I utter “I’m at home”. Again, it seems to me that by introducing the existence of propositions, we’re adding an epistemological layer that isn’t necessary. Why isn’t it sufficient to say that someone is wrong as opposed to a proposition being true or false?

i mean “existing”. period.

OK, understood. But, then why does the “translation of sentences into first order logic” require that “references to propositions” exist? What does this mean? (sorry, I’m not an analytic philosopher)

quine’s empiricism is a separate issue from his claim about the ontological commitments required by first-order logic.

Ah, I see. I thought that perhaps, following Wittgenstein, Quine might think it to be nonsense to talk of something we cannot directly “sense”. I think there was something about that in the Tractatus.

not at all: i am saying simply that there are an infinite number of mathematical truths. but then the bearers of mathematical truth cannot be concrete objects, since there are only a finite number of concrete objects…

Here’s why it seems like question begging to me. By “mathematical truths”, in this context I think you’re referring to an infinite number of mathematical propositions which are true. In other words, they exist, extra-mentally, and thus, are actual and not possible, propositions. And, an infinite number of these propositions cannot be contained in a finite set of minds. Therefore, propositions must exist apart from the mind.

You seem to be assuming, first of all, that there is an actual infinite set of true propositions, in existence, regarding mathematics. But if the set were only potential, and not actual, it allows for the possibility that the created mind could formulate that set over an infinite amount of time. Secondly, there is the issue of whether or not quantification (mathematics in general) is an accidental property of being or is being itself. If it’s only an accidental property, then it’s moot to talk about actual infinite sets of mathematical truths. I lean toward the former explanation, but I’m open to arguments to the contrary.

 

[ateista]

Oh, my… looks like retirement does not mean “more” time to participate in such discussions. While I was working I could steal a little time here and there from a boring activity called “work” (and as we know work is a 4-letter word). Now I have to balance time among equally fascinating activities,

But, be as it may, I suggest we ponder the “truth” and “falsity” of propositions. I submit that there are two meanings to the meta-proposition “a proposition ‘A’ is true”, depending on the type of ‘A’.

If ‘A’ refers to physically existing objects, then the proposition ‘A’ is true if and only if it reflects reality. The “chair is in the room” is true, if a physical chair is in a physical room, and the sentence specifically talks about these entities.

If ‘A’ refers to mathematical concepts, then the propostion ‘A’ is true, if it can be reduced to the axioms. Since there are infinitely many propositions about numbers, at first glance it seems obvious that their “truth” cannot be material object since there are only finite number of them. But that view is unnecessarily complicated. Every one of those infinitely many true propositions can be reduced to a few axioms, and we accept - by definition - that axioms are “true”.

If ‘A’ refers to abstractions like imaginary objects, then it is not sensible to speak of their “truth” or “falsity”. If the sentence “the chair is in the room” appears in a novel, it has no true value associated with it. It just “is”.

Anyhow… just a suggestion. And Happy New Year to all of you! (Question: was that a proposition? )

 

[john_doran]

What good reason is there to assert that numbers and sets “exist”?

i have presented a number of such reasons in my first post…

aquinothomas:

By exist, do you mean existence in the same manner that you and I exist? What I mean is: do they subsist independently?

they exist independently of us.

aquinothomas:

Yes, but with a dramatically important difference: you and my friend are asserting that propositions exist apart from the mind and I am sceptical that such a position can be adequately defended. I’ve no problem with propositions being the bearers of truth values if they are part and parcel of the mind.

but if propositions are simply mental entities, then when there are no minds thinking them, there are no truths or falsehoods. which seems absurd.

i mean, the proposition “there are no thinking things” will be true after the heat- or cold- death of the universe, right? as will the proposition “1+1=2”, and “nothing can fail to be self-identical”, and…

so how does one explain that if propositions (and thus truth and falsity) are mind-dependent?

aquinothomas:

But, when someone asserts that they are independent of the mind, that they subsist in some manner even apart from the real things that they describe (that they are more than just states of affairs), that they are ontological entities (some call them intentional entities that are mind independent), then I need to understand why someone would assert such an extreme realist position.

i keep giving you reasons to think that my position is true…

look, what do you think that the number 7 is? do you think that it will be false that “7+1=8” when no one is thinking about the number 7 or the number 1 (or 8, or the plus function)?

i need a reason to believe that numbers and sets and propositions are not abstract entities: why would anyone believe that the things that are true and false, or that are referred to in math and logic, are - what? - simply marks of ink on a page, or electrical impulses in a brain, or sound-waves in air, or…? why should anyone believe that? what sense does it make to say that a collection of chalk particles on a blackboard is “true” or “false”? and what happens to that truth and falsity once one erases the board?

aquinothomas:

To assert that an entity such as a number exists, not as a category of being (‘quantity’), but as an independent ontological being, seems to demand some explanation. I’m hoping that someone can explain to me why it makes more sense to assert that numbers and propositions and their ilk are ontological beings that exist (subsist) in their own right, as opposed to only being accidental properties of real beings.

see above…

i can make no sense of the alternative.

aquinothomas:

I agree with you that truth and falsehood do relate directly to judgments that the mind makes about reality. But, when we talk about the truth of something like Goldbach’s conjecture (of which I know nothing), aren’t we asking the question: are our ideas relating to this issue corresponding to reality or not?

no, we’re not: we’re asking “is the following proposition true: ‘every even number is the sum of two primes’?”.

my “idea” of goldbach’s conjecture is simply a token of the proposition of the conjecture - my idea is not true or false, but the proposition expressed by my idea.

aquinothomas:

This is assuming of course that we understand the true meaning of Goldbach’s conjecture. When we say: is the conjecture (correct / true / veracious) what we mean is to ask whether the conjecture squares with the real world. We aren’t really asking: do our propositions about the idea(s) concerning Goldbach’s conjecture correspond with reality.

you’re right, this is definitely not what we’re asking. we are asking simply if a certain proposition is true.

 

[john_doran]

But, here again, to take your rain example, what we are referring to with the question is whether someone’s judgment about the rain is true or false. When we ask a question like this, we’re asking someone to make a judgment. Whether their judgment is ultimately right or wrong will depend on whether their ideas are in good order, and that they in fact correspond to reality. We’re not asking their intellect to grasp two or more propositions, “it is raining outside” and “it is not raining outside”, let alone “it is snowing outside”, “it’s 90 degrees outside”, etc. which are as real as the rain or the snow. We’re asking them to make a judgment which takes the form of a proposition, and that proposition will be formulated into a sentence of a certain language in order to communicate that proposition to our mind. The truth or falsehood of the judgment communicated to our mind will depend ultimately on the correspondence between the ideas and judgments of their intellect and reality. When we’re asking someone a question about the weather, it seems superfluous to posit that they not only need to consult the rain but also a set of propositions that exist in the world independently of any mind.

you’re missing the point…

when we say that “it is raining” and “il pleut” have the same meaning, what are we referring to that is “the same”? it cannot be the brain-states of the speakers thinking the thoughts, since those brain-states are not the same; and since the languages are obviously different, what is left?

i agree with you about the way in which judgment occurs in the intellect, but that’s got nothing to do with the (un)reality of propositions as abstract objects…

what i would say is happeing when we make judgments about things people say, is that we are judging whether the sentences or speech-acts they employ express true propositions.

and just because it is possible that propositions are not always required to explain what we’re doing when we make judgments about the world (e.g. i don’t think, “the proposition ‘my knee is itchy’ is true”, when i decide to scratch it), doesn’t mean that we never need them (how do i understand “1+1=2 is necessarily true” without propositions?).

 

[john_doran]

Here’s why it seems like question begging to me. By “mathematical truths”, in this context I think you’re referring to an infinite number of mathematical propositions which are true. In other words, they exist, extra-mentally, and thus, are actual and not possible, propositions. And, an infinite number of these propositions cannot be contained in a finite set of minds. Therefore, propositions must exist apart from the mind.

forget propositions. think of it this way:

the proposition “every even number is the sum of two primes” is either true or false. but what makes it true (or false)? if numbers are simply thoughts or sentences or speech-acts or groups of natural objects, then how can a statement about an infinite number of such objects ever be true if the only available referents for the statement are finite in number?

but there are an all kinds of things-that-are-true like that in math - all kinds of references that we make to infinite quantities and sets with infinite numbers of members, and so on. but how can any of those claims be true (or false) if they fail of reference? i mean, if there aren’t an infinite number of things in the world, then i am not actually referring to anything when i talk about infinite sets, or “every number”, etc.; and if that’s true, then any claims i make about those things can’t be true or false, right or wrong. but that’s absurd…

aquinothomas:

You seem to be assuming, first of all, that there is an actual infinite set of true propositions, in existence, regarding mathematics. But if the set were only potential, and not actual, it allows for the possibility that the created mind could formulate that set over an infinite amount of time.

but statements about infinite quantities are true or false now.

aquinothomas:

Secondly, there is the issue of whether or not quantification (mathematics in general) is an accidental property of being or is being itself. If it’s only an accidental property, then it’s moot to talk about actual infinite sets of mathematical truths. I lean toward the former explanation, but I’m open to arguments to the contrary.

statements of logic and math are generally considered to be necessarily true; but if they are true-only-when-thought-by-a-thinker, then they can’t be necessarily true…

so. it seems to me that you either give up your belief in modality, or the belief that there are no abstract objects…

 

[aquinothomas]

but if propositions are simply mental entities, then when there are no minds thinking them, there are no truths or falsehoods. which seems absurd.

It isn’t absurd if the definition of truth is the correspondence of the intellect to reality. In that case, in order for there to be truth, there must be a mind.

i mean, the proposition “there are no thinking things” will be true after the heat- or cold- death of the universe, right? as will the proposition “1+1=2”, and “nothing can fail to be self-identical”, and…

I suppose this is as good a time as any to raise this issue. If I’m understanding the theory of propositions that you are asserting, there are two potential “truth relationships”. The first relationship is between a proposition, and reality. If the proposition corresponds to reality, then it is the bearer of “truth”. If it does not, then it is the bearer of “falsehood”. The second relationship is between our minds and propositions. If our mind has as its intentional object a true proposition, then we might say that the mind knows truth. If the intentional object is a false proposition, then the mind does not know truth (in that specific case). For reasons I’ll address later, I’m having a hard time understanding why it is necessary to have the extra ontological baggage when there are other, simpler, and seemingly more valid, notions which sufficiently explain how we know the truth. More on this later, but it seems to me that the “proposition”, along with “facts” and “states of affairs” are extra ontological entities that are not necessary to explain the relationship of the mind to veracity.

so how does one explain that if propositions (and thus truth and falsity) are mind-dependent?

We can explain this by the definition of truth as the correspondence of the mind with reality (being). You seem to be saying that propositions are necessary in order to explain truth in possible worlds where minds do not exist. But, if truth is the correspondence of mind with reality (nothing more, and nothing less), then it’s moot to talk about truth in a world without minds. The ancient Latin definition of what I’m talking about is adequatio rei et intellectus - an equality between mind and reality. This isn’t idealism, it’s realism, but the definition of truth is the measure of mind in accordance with reality.

With this definition, I’m assuming that as a precondition of truth, that reality is intelligible. It seems contradictory to talk about truth apart from intelligibility. But if reality is inherently intelligible, then it was designed to be that way. And, if there is teleology, then there is a divine mind, whose knowledge is in fact creative. Therefore, it’s contradictory to speak of an intelligible universe without any minds. Because of this, we can speak of reality thus: omne ens est verum; ens et verum convertuntur - every being is true, and the true and being are interchangeable.

 

[aquinothomas]

look, what do you think that the number 7 is? do you think that it will be false that “7+1=8” when no one is thinking about the number 7 or the number 1 (or 8, or the plus function)?

The number 7 is an accidental category of being - it is a quantity. That doesn’t mean that we actually need 7 somethings in rerum natura (in actuality) to have the idea of seven in our minds. We could be thinking of seven potential beings, or seven potential pounds of something. In that case we’re referring to logical beings, but not actual beings. Both are still ens reale - they are real, but in one case they may be actual and in another potential. If the thing can possibly exist in rerum natura, though, it’s real. We could be thinking of seven candy mountains, and it would still be real because it is possible. The idea of quantification has been abstracted from reality by the mind. Therefore, in world with no minds, it would be gratuitous to talk about 7+1=8 being true. By the way, I don’t think we every think of numbers per se - we think of a number of “somethings”. Try thinking of 7, and you’ll either think of the symbol for seven somethings (“7”) or seven somethings - the reference to being seems implicit in every mathematical enumeration. Imaginary numbers, prime numbers, and their ilk are all derivative of the category of quantity.

no, we’re not: we’re asking “is the following proposition true: ‘every even number is the sum of two primes’?”.

This statement is a logical proposition based on mathematical definitions and the relation of those definitions combined with quantity as a category. I’m not saying that it isn’t true, but it’s true based on definitions that we apply, which are in turn based on our idea of quantity (which was in turn abstracted from being in rerum natura). It seems to me that the truth of this proposition can be sufficiently explained via reference to logical being and mental deduction. It doesn’t seem necessary that the truth of the proposition depend on it being an abstract entity separate from us.

when we say that “it is raining” and “il pleut” have the same meaning, what are we referring to that is “the same”? it cannot be the brain-states of the speakers thinking the thoughts, since those brain-states are not the same; and since the languages are obviously different, what is left?

You’re right, we’re referring to a proposition. We’re referring to a proposition that can be expressed using whatever language we want to use. But, you’ve hit the nail on the head when you say “meaning” - the proposition has as its referent ideas which the mind contains. Those ideas are essences, which have been abstracted from being, and are now part and parcel of the mind. In order for communication to take place, regardless of language, the two minds communicating need to have the same essence in them which was abstracted from a trans-subjective (read “objective”) being. When we say “it’s raining” - we’re making a judgment about water (a substance) falling from above (a location), and if I try to communicate that to someone who doesn’t understand the essence of water, they will have no clue what I’m talking about. So, a proposition, it seems to me, is the communication of a judgment involving ideas (essences). So, “what is left” is an arrangement of ideas expressed in the form of a proposition.

what i would say is happeing when we make judgments about things people say, is that we are judging whether the sentences or speech-acts they employ express true propositions.

I agree with you, that we are judging the truth of a proposition: we are judging whether or not the judgment that took place in the other mind actually corresponds with reality. It doesn’t seem to me that we are judging whether or not a person has latched onto a true or a false proposition that is independent of both of our minds. We’re judging whether or not that person has connected with reality or not, not whether or not they’ve connected with a proposition that is connected with reality or not. That seems to me to be a sufficient explanation for what is going on both with propositions such as “1+1=2” as well as “it is raining outside”.

 

[aquinothomas]

the proposition “every even number is the sum of two primes” is either true or false. but what makes it true (or false)? if numbers are simply thoughts or sentences or speech-acts or groups of natural objects, then how can a statement about an infinite number of such objects ever be true if the only available referents for the statement are finite in number?

Like I said earlier, logical being doesn’t necessarily need to refer to actually existing natural objects. Logical being is real being but not necessarily actual being. When we’re talking about an infinite number, we’re talking about a potentially infinite number of things. The set of real numbers refers to a potentiality of beings in rerum natura, not an actuality. But, that makes it no less real as a logical construct (logical being). So, a mathematical proposition can be true which utilizes an infinite set since the set refers to logical being, which is real. In that case, it can be said to correspond to reality. But, since it’s a logical construct, it is still in the mind.

but there are an all kinds of things-that-are-true like that in math - all kinds of references that we make to infinite quantities and sets with infinite numbers of members, and so on. but how can any of those claims be true (or false) if they fail of reference? i mean, if there aren’t an infinite number of things in the world, then i am not actually referring to anything when i talk about infinite sets, or “every number”, etc.; and if that’s true, then any claims i make about those things can’t be true or false, right or wrong. but that’s absurd…

It would be absurd if we were referring to actual beings, yes. But propositions about infinite sets are logical. The beings the mind makes reference to (in a purely logical sense) are no less real than actual beings, but they are entirely dependent on the created mind for existence. So, if it’s possible for an infinite number of actual beings to be combined in the manner that a mathematical proposition asserts, then the truth of the proposition can be verified. Keep in mind that the proposition (in the way that makes sense to me) is simply an articulation of the mind of ideas and judgments about those ideas. So, ultimately, truth still boils down to the correspondence of the mind to reality, potential or actual.

It’s the minds reference to potentiality and actuality that is the basis for modal logic, it seems to me. When we refer to something possible, we refer to something real but not actual. And, when we refer to something necessary, we refer to something that can be no other way, given our knowledge of reality. When we posit that which is impossible, we are referring to that which could not exist in rerum natura (e.g. - an infinite number of things). If something is impossible, in other words it corresponds in no way to reality, then by definition that is false.

statements of logic and math are generally considered to be necessarily true; but if they are true-only-when-thought-by-a-thinker, then they can’t be necessarily true…

If what I’m saying about the correspondence of mind to reality as a definition of truth holds, then statements about logic and math wouldn’t even exist without minds because there would be no minds to formulate the propositions. Concerns regarding their truth or falsehood would be irrelevant. Does it really make sense to talk about logic in a world with no minds?