Thursday, 24 July 2014

Propositions, Facts & Sentences

Different Sentences = Same Proposition

The popular and general idea (at least in Anglo-American analytic philosophy) is that if no particular expression of a proposition is identical to that proposition, then the proposition must be distinguishable not only from a specific expression of it, but from all expressions of it. The argument is usually that a proposition is distinguishable from a particular expression of it. However, perhaps the truth is that it's the sum of all possible linguistic expressions of it. That is, when all possible expressions of the proposition are in, then there's nothing left out of the proposition. There's nothing else to say about it. And if there's nothing else to say about the ostensibly expression-independent proposition that hasn't been said by the sum of all its linguistic expressions, then perhaps there's no distinction between them at all.

It's argued that propositions don’t belong to a particular language or even to the set of all languages. I would say that they do belong to the set of all languages (or to language itself). Clearly we can't believe in abstract propositions simply because the French words for "I love apples" or "The day after tomorrow" are different from the English words already given.

Proposition realists ‘explain’ the existence of the fact that "co-referential" sentences may have different truth-values by referring to pre-existent or eternal propositions. However, the only things you can say about these propositions (or the differences they may express which aren't explicit in the sentences themselves) is with yet more sentences (with, perhaps, different truth-values).

Despite the fact that many different sentential expressions can express the same proposition, it's still nevertheless the case that we never actually come across a proposition as it is free from - or independent of - sentential expressions.

We can say that a proposition can indeed be variously expressed by many expressions. It also follows that an expression can also be variously expressed by other expressions. In that sense, E (expression) can take the place of P (proposition). Now we can say that an expression can be variously expressed by various expressions as well as the expression that we initially took to be the proposition. In that sense, the proposition is only an expression that has somehow been given a special status. It can be said that a proposition is the sum of all the possible - and actual - expressions which assert the same thing. However, in principle we could account for all the various expressions of a given statement. Any that go unaccounted for will still be expressions of some kind. In addition, I stress the proposition/expression above precisely because it's an expression (this time) that's been given a special status.

The key question is:

Can the content of a proposition be separated from the form of that expression?

What sort of existence and identity does a proposition have before it finds itself ‘in’ an expression? Do we ever have the content of a statement before the statement itself? 

It can be admitted that what constitutes a proposition (facts, truth-conditions, abstract objects, possible worlds.... take your pick) exist separately from all sentences; though not the proposition itself. Books can exist separately from libraries; though when they're brought together, they constitute a library (but were not themselves libraries before they were brought together).

Many mind-independent things may be necessary for propositions; though only these things plus sentences (or expressions) are sufficient for propositions. This is what makes the proposition-realist make a mistake. Many of the constituents of propositions may indeed be mind-independent (or even abstract) and therefore separate - and separable - from sentences. Many proposition-realists therefore conclude that truth, truth-conditions, propositions etc. are separable from sentences.

The other way to defend to existence of propositions is that the same sentence can state different propositions. Or the same sentence "can have the effect of claiming, stating, or asserting different things". That, in itself, can't be an argument for the existence of propositions. A spoon can be used to eat soap of burn crack. Does that mean that we have two different things rather than one thing used in two different ways?

Michael Dummett goes into detail as to why Frege believed that there's such a distinction between a proposition and its linguistic expression – or, in Frege’s case, between a sentence and the "Thought" which it expresses:

"[A thought is] not true for you and false for me, it’s not true at one time and false at another time." 

The idea being expressed here is that it may appear to be the case that a Thought is true for me, though false for you; or true now, though false tomorrow. Yet that's only because its linguistic expression leaves something out. If expressions were more precise and more explicit, such things wouldn't be left out.

This leads us to the conclusion that the Thought itself is precise and explicit.

It's strange that something that is ostensibly completely non-linguistic can be both precise and explicit at all. How can something abstract and non-linguistic be precise and explicit? What does it mean for an abstract Thought or proposition to be precise and explicit? Surely only linguistic expressions can carry the requisite information that will allow a thought to be precise and explicit. How can it be precise and explicit with its – or any – linguistic expression? What would constitute its precision and explicitness?

So despite Dummett’s defence of the existence of abstract propositions, he acknowledges the fact that the proposition/expression dichotomy may not amount to much.

The amounts to the evident point that even if abstract propositions exist, what we say about them (or when we express them) evidently needs to be done with sentences. Thus we must "attach" truth to sentences even if it's really propositions which are the actual "bearers of truth". If it's the case that a sentence expresses a proposition, then it'll still be the case that that proposition will require (or need) a linguistic expression. Thus truth, again, must also be attached to sentences; not just to propositions. (If we can really attach truth to abstract entities at all.) However, Dummett still insists in talking about the "interpretations" of propositions. As I said, the fact of multiple and variable interpretations doesn't lead him away from propositions, but towards them.

Facts aren't Bits of the World

Many people take facts to be bits of the world to which true propositions somehow correspond. Many would disagree with the suggestion that facts are not bits of the world or that they are linguistic or sentential in nature. After all, isn’t it the case the proposition "Gordon Brown is PM" is true because of the bit of the world that is Gordon Brown’s being Prime Minister (among other things)? But facts are not just particulars or bits of world. They're arrangements (as it were) of bits of the world and also what's said about these arrangements. Michael Loux puts this in the following more metaphysical less semantic kind of way. He says that

"we cannot completely and adequately identify that in the world which makes a true proposition true merely by listing the various particulars and attributes (properties, kinds, and relations) that populate the world". 

In that weren't the case, there would literally be an infinity of possible facts. For example, the fact that Paul Murphy is two foot away from that blackboard; the fact that two black shoes are next to two white shoes; Or even that one million planets do not have water on Tuesdays. Indeed it's even a fact that  there are nth amount of specs of dirt on my computer screen; though yesterday there were ten less.

Even this infinity of possible facts inn't the only argument because we can say that despite this possible infinity, they're still nevertheless facts. The factual aspect, however, is more to do with what's said about these bits of the world (whether planets, specs of dirt or blue shoes). In terms of the specs of dirt on my computer screen, we can say that these specs of dirt were indeed bits of the world before anything was said about them; though there were no facts about them until such facts were stated.

Someone may now say that particulars like Gordon Brown aren’t factual on their own. However, we've already referred to the property of his being Prime Minister. Some may say that included in facts are universals, properties and their connections. Particulars, universals and connections on their own don't make facts either. It all boils down to what we say about these particulars, their properties and relations. Or, more specifically, it boils down to the linguistic situation that before we offer up our fact we must state something like: "It is a fact that…" Or: "It is the case that..." This shows us that facts are to do with sentential or mental attitudes towards particulars and their attributes and relations, not just the latter on their own. Particulars, attributes and relations are just bits of the word on their own. They aren't facts, not even when they belong together as bits of the world.

Facts as True Propositions & True Propositions as Facts

The proposition (or how the proposition is stated) is exactly the same as the fact which is supposed to make it true. Thus we have a kind of tautology (or an actual tautology). Of course the proposition

"Gordon Brown is PM."

is true because of the fact that Gordon Brown is PM.

Or more precisely:

The proposition "Gordon Brown is PM" is true because of it is a fact that Gordon Brown is PM.

Many philosophers actually say that "a fact is a true proposition" (e.g. Dummett). Thus we have this example of circularity:

fact = a true proposition


true proposition = a fact

Thus a true proposition just is a fact or a fact just is a true proposition. But facts "are supposed to be entities correspondence to which makes true propositions true" (168). They're supposed to be bits of the world. Thus if facts are true propositions, then either true propositions are bits of the world or facts are - as propositions - not parts of the world. Indeed it's easier, on this view, to accept that facts aren't bits of the world than it is to accept that propositions are bits of the world – which no one accepts. If we correlate facts with true propositions, and true propositions with true sentences, then we can indeed accept that facts aren't (only) bits of the world. (However, in a sense, sentences can be taken to be bits of the world.)

It follows that many will want

"a purchase on the notion of a fact that is independent of our understanding of the concept of a true proposition". 

Put it this way:

Q) What is it to say that this or that is a fact?

A) Is it not just to say it is true?

That is, if facts can be true, then doesn’t that mean that they must be sentential or at least propositional? After all, how can the bit of the world that is Brown’s being PM be true? What is said about Brown can be true; though not only his being PM. That would be like saying that the cup in front of me "is true".


i) Thus, to say that it is a fact that (or: it is the case that) Brown is PM. 

ii) is to say neither more nor less than that it is true that he is.

Facts are supposed to be what make propositions true. They surely can't be true themselves. If not, the fact that is true is making a proposition or sentence true. This doubling-up effect can be countered by accepting from the beginning that facts are indeed propositional. Or, on this account, that facts are sentential. In that case, if true propositions and true facts are identical, let’s get rid of one of them. Let’s get rid of (true) facts. Now we have true propositions. I take these to be linguistic.

Thus let’s get rid of true propositions. This will leave us with true (or false) sentences or sentential statements. The problem with the linguistic nature of supposedly worldly facts can also be applied to the linguistic nature of abstract propositions. Facts were seen to be linguistic, thus we got rid of them. Abstract propositions also turned out to be linguistic and not abstract at all, thus we got rid of them too. Again, we are now left with true (and false) sentences or statements.

Loux, on the other hand, accepts abstract propositions; though he also accepts that we have a conflation or mix-up between true propositions and facts. He writes:

"... we can hardly claim to have provided an explanation of the truth of that proposition by introducing the fact that he is President. The two are one and the same thing!" 

We can’t say that the statement

"Brown is PM of the UK."

is true by saying

"It is a fact that Brown is PM of the UK."

because the true proposition and the true fact are "one and the same thing!" (168). We think that Brown’s being PM of the UK is a bit of the world; though all it's actually doing is mirroring a true proposition which we have firstly constructed. I would say that the sentence, "Brown is PM of the UK" comes first.

Facts, Propositions and their Linguistic Expressions

We can go so far as to say that we "can only identify a fact through a proposition". This would mean that there are no facts without the propositions which express them.

What if propositions themselves can only be expressed through sentences?

Thus if it's correct to say that facts need propositions to be expressed, then we can also say that propositions require sentences in order to be expressed. Perhaps we can even forgo non-linguistic propositions and settle only with sentences or statements.

Can we also forgo facts?

We can if we've already forgone abstract propositions because, as I’ve said, facts require propositions and propositions require sentences. Thus, without propositions, facts simply require sentences to express them. It is sentences that individuate and determine what are the facts. Facts are as artificial as propositions. Thus all we have left are sentences which individuate and determine the parts of the world we wish to talk about. Without sentences, then, there would be no facts; just as there wouldn't be propositions without their sentential expressions.

Another reason for rejecting propositions is this. We

"can only identify a fact through a proposition: the proposition that my car won’t start, which can be 'nominalised' into the phrase 'my car’s not starting”’.

The problem is that is saying that "my car won’t start" is the same as "my car’s not starting". It is virtually the same sentence. We can see, then, that it's the sentence itself which individuates and determines the fact.

What we have, then, is the far from impressive conclusion that the "proposition that p is true if and only if it corresponds to the fact that p' (100). Surely, then, p is identical to, well, p – especially since they have the same content and are expressed in the same (linguistic) way. This may not be vacuous or contradictory. Perhaps we express what truth is in a way that "has to be that way". (As with Tarski’s T sentences.)

The end result seems to be that 

"it still remains true that to identify the thing that makes a proposition true, we must offer a proposition". 

It's a proposition that makes a thing true. Even if that proposition is abstract, it still requires a linguistic expression. And the linguistic expression we use for the proposition is the same linguistic expression we use to express the fact (or truth-condition) which makes it true!

Despite all that, Roger Scruton, for example, argues (in a realist spirit) that the

"proposition that p might never have been formulated; but still the fact that p would exist".

If proposition p might never have been formulated, that must mean that Scruton believes that it's mind-independent. If it's mind-independent, then it's also abstract and non-spatiotemporal. But the fact that it expresses must also share this property of being abstract and non-spatiotemporal because Scruton says that if the proposition hadn't been formulated, "the fact that p would exist’". Aren’t facts bits of the world? Yes. But I've already said that they're linguistically individuated and determined. Scruton says that they can exist without their propositional expression. If propositional expressions are by nature linguistic in nature, and therefore so too are facts, then how can there be any facts which haven't been given a linguistic expression? There can be no relation between a proposition and a fact that makes it true if that proposition is linguistically expressed in a way that relates to the fact and makes it true.

Scruton then writes that in

"comparing our propositions with the facts, therefore, we are comparing them with something other than themselves". 

Of course there's something other than propositions or statements about this something. However, it is sentences that determine and individuate the shape (as it were) of this something in the world. Only then can we call them ‘facts’. I'm not saying that bits of the world are sentences. Only that sentences determine and individuate what it is we take to be a fact; otherwise we only have a nondescript part of the world which hasn't been individuated or even determined. Thus this non-individuated and non-determined part of the world can't be a fact. It can only be a fact through its determination and individuation by a proposition – therefore by a linguistic expression.

Scruton doesn't accept that propositions are linguistic expressions. Though he does seem to accept that propositions and facts may be identical. He says that

"we seem to have no other way of identifying facts, save through the propositions that they are supposed to anchor". 

I would suggest that the suspicion Scruton shows about any real distinction between facts and propositions can be carried over to a suspicion about any real distinction between propositions and their linguistic expressions. Thus it follows that if we can't have facts without propositions, then neither can we have facts without linguistic expressions.

Scruton asks this about propositions and facts:

"Why are we sure that we have two things, when both are identified in the same way?" 

Now I will ask:

Why are we sure that we have both propositions and their linguistic expressions when both are identified in the same way?

If we can't break off facts from propositions, perhaps we can't break off propositions from their linguistic expressions. Or, more radically, perhaps there are no propositions.

Does this mean that there are no facts?

No, there are facts; though they aren't mind-independent and they're always individuated and determined by linguistic expressions.

In fact we can't even say "by their linguistic expressions" because this would seem to suppose that they somehow exist before their linguistic expression (or their linguistic individuation and determination). Facts, like the numbers of the intuitionists, "spring into existence" when they're linguistically expressed or individuated and determined by linguistic expressions.


Why isn’t the proposition-realist at least a little suspicious of this tight fit between propositions and the sentences which express them?

The realist could say that he must express propositions in some way. And the only way available to him is through sentences. I can still ask:

Yes; though do these sentential expressions of propositions precisely capture or match the propositions which they're expressing?

If his answer is, yes, then I can again ask:

Isn’t this strange – this perfect fit (or match) between propositions and the sentences which express them?

Why is it the case that sentences (or all the sentences which express proposition) can (as it were) miss something out of the proposition they (try to) express? However, this possible ambiguity, vagueness or imprecision of our sentential expressions isn't often acknowledged by proposition-realists. More than that: considering the importance they give to propositions (in terms of truth, certainty and objectivity) these possibilities would be anathema to them and would defeat the object of abstract propositions. That object, historically, has been that propositions are the guarantors of truth, objectivity and certainty.

At the heart of Derrida’s early philosophy of language is the thesis that there's no proposition beyond or behind the sentence – beyond language. Language is the beginning and the end of propositions:

"It [writing] is also to be incapable of making meaning absolutely precede writing…" (‘Force and Signification’, page 10, Writing and Difference, 1967/1978)

According to Derrida, "writing" doesn't simply transcribe something that already exists – a proposition. Propositions can only exist as expressions – in the guise of language:

"To write is to know that what has not yet been produced within literality has no other dwelling place, does not await us as prescription… Meaning must await being said or written in order to inhabit itself..." (1967/78)

Derrida then quotes Merleu-Ponty:

"Communication in literature is not the simple appeal on the part of the writer to meanings which would be part of an a priori of the mind… 'My own words take me by surprise and teach me what I think,' he said elsewhere." 

Propositions have been deemed to be necessary entities that help us secure certainty and absolute correctness. If we tune ourselves into the proposition, then we'll get things right. They help secure us from empirical vicissitudes and uncertainty. They are the "centers" (Derrida, 1967/78) around which all contingent and empirical expressions gravitate (see Dummett).

This is the old Platonic worry.

There must be propositions otherwise we'll succumb to relativism, uncertainty and other such things.

Perhaps it would be nice to have various centers or "sites" of various descriptions. Only then could dispute be stopped.

Abstract propositions, like universals and forms, would supply us with a means to find the correct meanings of our sentences. They would give us something determinate and precise for our contingent statements or sentences to be about. Thus we could find the true and correct answers to numerous philosophical and non-philosophical problems.

Abstract propositions guaranteed truth, correctness and certainty.

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