The term proposition has a broad use in contemporary philosophy.
It is used to refer to
some or all of the following: the primary bearers of truth-value, the objects of belief and
other "propositional attitudes" (i.e., what is believed, doubted, etc.), the referents of that-
clauses, and the meanings of declarative sentences. Propositions are the sharable
objects of attitudes and the primary bearers of truth and falsity. This stipulation rules out
certain candidates for propositions, including thought- and utterance-tokens which are
not sharable, and concrete events or facts, which cannot be false. [1]
Propositions
One of the fundamental concerns in philosophy is that with truth. But what kind of things
are true?—what is truth a property of? The traditional answer is that it is propositions
which are true or false, where propositions are to be distinguished from sentences.
There are four main arguments for denying that it is sentences which are true or false
and for introducing the apparatus of propositions to stand as the bearers of truth.
Firstly, "sentence" is a grammatical concept and not all grammatically well-formed
sentences appear to express anything which is capable of being true or false: for
example, "All green ideas sleep furiously". This sentence is grammatically well-formed,
but clearly meaningless. Some sentences, we shall say, do not express any proposition
at all.
Secondly, some sentences are ambiguous. We normally explain this by saying that one
sentence (string of words) is capable of expressing more than one proposition: for
example, "Flying aeroplanes can be dangerous", which can mean either that being a
pilot can be a dangerous activity, or that aeroplanes can be dangerous when they are
flying about in the sky.
Thirdly, different sentences can have the same meaning. We would normally think of
translation from one language to another to be possible because sentences from
different languages can express the same proposition: for example, "It is raining", "Il
pleut" and "Es regnet".
Fourthly, we tend to think that there is some meaning in common between the
indicative, interrogative and imperative sentences in the table below, and this is
normally explained by differentiating their assertoric force from their propositional
content.
The sentences below are synonymous with the
sentences to the left
Indicative The cat is on It is the case that the cat is on the mat
the mat.
Interrogative Is the cat on Is it the case that the cat is on the mat
the mat?
Imperative Put the cat on Make it the case that the cat is on the mat
the mat!
Assertoric force Propositional content
It is only because we normally concentrate on indicative sentences that we often fail to
recognise that there is a difference between sentences and propositions. But clearly
interrogative and imperative sentences are in some way also about things in the world,
about cats and mats in this case, just as much as indicative sentences are. Propositions
are invoked in an attempt to explain this.
Intension and extension
The Ancient Greeks did not know that the evening star (which they called Hesperus)
and the morning star (which they called Phosphorous) were in fact one and the same
thing—namely, Venus. The propositions
Hesperus is the second planet from the Sun
Phosphorous is the second planet from the Sun
are both therefore made true by one and the same fact—Venus being the second planet
from the Sun; they both refer to exactly the same things. Are they therefore one and the
same proposition? Here it is useful to introduce the distinction between the intension
(or sense or connotation) and the extension (or reference or denotation) of a
proposition. Extensionally, we will say, the propositions are equivalent, for they are
about exactly the same things in the world. But intensionally they are distinct. They are
distinct intensionally because one could believe one without believing the other, if, like
the ancient Greeks, one did not know that Hesperus and Phosphorous were one and
the same thing. Two propositions may be extensionally equivalent but intensionally
distinct, but if two propositions are intensionally equivalent then they are also
extensionally equivalent. Propositions, then, are individuated by their intensions.
An important addendum to the distinction between intension and extension is the
distinction between intensional contexts (or referentially opaque contexts, or
oblique contexts) and extensional contexts (or referentially transparent contexts).
Normally, an expression in a proposition can be swapped for an expression with the
same extension without changing the truth value of the proposition. So for instance,
swapping "Hesperus" for "Phosphorus" in the sentence "Phosphorous is identical to
Venus" could not change the truth value of the proposition from true to false. Similarly,
normally one can infer the existence of the objects referred to by a true proposition:
"Phosphorous is identical to Venus" entails the existence of Venus. These "normal"
occurrences of propositions are known as extensional contexts.
In certain, special, circumstances however, these two features do not hold. These
circumstances are known as intensional contexts. In such contexts one can no longer
swap extensionally equivalent (co-referring) expressions in a proposition without
potentially changing its truth value (the technical term for this is intersubstitutivity
salva veritate); consider the following two propositions:
Lois Lane believes that Clark Kent works at the Daily Planet
Lois Lane believes that Superman works at the Daily Planet
The first is true and the second false, despite the fact that Clark Kent and Superman are
one and the same.
Neither, in intensional contexts, can one infer the existence of the entities mentioned
(the technical term for this is existential generalisation). It may be true that
Children believe in Father Christmas
But it does not follow that Father Christmas exists.
Arguments
An argument is a set of propositions, one of which is the conclusion and the others
premises, in which the premises taken together are intended as providing a reason for
accepting the truth of the conclusion (where reason here is intended in the sense of
rational justification). Not just any set of statements or sentences make for the presence
of an argument. Normally arguments can be distinguished by the presence of argument
indicating expressions: such expressions serve both to signal the presence of an
argument, and to distinguish the premises from the conclusion. For example:
[premises] therefore [conclusion]
[premises] so [conclusion]
[premises] thus [conclusion]
[premises] hence [conclusion]
[conclusion] since [premises]
[conclusion] follows from [premises]
[conclusion] for [premises]
A good argument has two features: the premises must be true, and they must provide
adequate support for the conclusion. It is this latter feature which is the subject matter of
logic. There are two standards by which the support given to the conclusion by the
premises might be evaluated. Firstly, the premises, if true, might render the conclusion
probable. These kinds of arguments are called inductive arguments. But secondly the
argument might purport to show that if the premises are true then the conclusion must
be true. These kinds of arguments are called deductive arguments, and they especially
are the subject matter of logic.
The standard of deductive correctness in an argument is validity. An argument is valid
if and only if it is impossible for the premises to be true and the conclusion false. An
argument is sound if it is valid and its premises are true. It is important to remember to
what the terminology applies: propositions are true or false; sets of propositions are
consistent or inconsistent; (deductive) arguments are valid or invalid, sound or
unsound. There is no such thing as a valid proposition, or a true argument.
Good deduction Good induction
The form of the argument is what is The subject matter is relevant to the
important. The subject matter is irrelevant. evaluation of the argument.
The combination of true premises and The combination of true premises and false
false conclusion is inconsistent. conclusion is consistent.
The truth of the premises makes the
The truth of the premises makes the
probability of the truth of the conclusion less
probability of the truth of the conclusion 1.
than or equal to 1.
Adding a premise can never turn a good
Adding a premise can turn a good inductive
(valid) deductive argument into a bad
argument into a bad inductive argument.
(invalid) one.
Truth
So far a great deal has been said about what kinds of things are true, and how
arguments which attempt to demonstrate the truth of a proposition might be evaluated.
But nothing has been said about what truth itself is supposed to be. That is for good
reason. The nature of truth is a vast and central issue in philosophy. It would be
impossible to do the topic justice here, and so very little will be said. Instead, we will
simply outline, in the barest detail, two of the most popular accounts of what is meant by
truth.
Correspondence theories of truth take truth to consist in the relation of a proposition
to the world—in particular to its correspondence to the facts. A proposition is true if the
facts really are as it says they are. "The cat is on the mat" is true if and only if the cat
really is on the mat. This sounds like such a blindingly obvious thing to say that it seems
scarcely worth mentioning. However, the notion has proved more difficult to spell out in
detail, and in particular the precise sense of "correspond" and "fact" intended have been
difficult to specify.
Coherence theories of truth, on the other hand, take the truth of a proposition to
consist in its relation to other propositions—in particular in its coherence with a set of
propositions. The plausibility of this account of truth is directly related to how implausible
one finds the idea of being able to compare propositions one by one to discrete bits of
reality, and ascertaining whether some as yet unspecified relation of correspondence
holds. Instead the coherentist about truth maintains that truth is an internal feature of
systems of propositions. The only mark of truth is whether a proposition coheres with
the other propositions in the system: if it does not one may reject the proposition as
false, or adjust the system by rejecting some of the other propositions in the system as
false. The problem with such an account is that it sounds much more like a strategy for
forming beliefs than a characterisation of truth. The coherentist ought to be able to
specify which propositions a proposition is meant to cohere with in order to be true. But
this has proved difficult.
