The Nature of Propositions
There is much philosophical discussion about the nature of “truth-bearers” – the kinds of things that can be true or false. Various writers have suggested such things as propositions, statements, assertions, utterances, sentence-types, sentence-tokens, beliefs, opinions, theories, doctrines, facts, etc. However, I prefer to consider truth (and other epistemological questions) in terms of “atomic propositions” – those with only a few concepts, one of which is a particular relationship involving the others. (This happens to be called “Logical Atomism”, although I modify the classical formulation somewhat.(1))
Because of the significance of my preference for atomic propositions to the discussion of truth that follows, I want to spend some time exploring the nature of propositions, and documenting why I consider “atomic propositions” to be the only meaningful bearers of “truth”.
Proposition – “5. Logic. a. A statement in which the subject is affirmed or denied by the predicate. b. Something that is expressed in a statement, as opposed to the way it is expressed. c. A statement containing only logical constants and having a fixed truth-value.”(2)
As you can see from this excerpt from the dictionary, the philosophical meaning of the word “proposition” is somewhat special. A sentence in English is usually intended to say something about Reality. But there can be more than one way in English to say the same thing. In philosophy, and especially epistemology, the word “proposition” is used to refer to the sense or meaning of a sentence or statement irrespective of the words, sentence form, or even language or symbology employed. Consider the following list of sentences for example. Here’s the cover of Dr. Seuss’ children’s book “The Cat in the Hat”.
With this picture in mind, consider these two sets of sentences –
| The hat is on the cat. | Take the hat off the cat. |
| The cat is wearing a hat. | Where is the cat in the hat? |
| The hat is being worn by the cat. | Is the hat on the cat? |
| The cat is the one wearing the hat. | I hate a cat in a hat. |
| The cat is what the hat is on. | I love the cat’s hat. |
| The cat is in a hat. | Put the hat on the cat. |
In each case, the words and the sentence structure are different. In the sentences on the left, a particular assertion is being explicitly stated. In the sentences on the right, the same relationship between the cat and the hat is being hidden within other forms of sentence. But in all cases, the underlying sense or meaning of the relationship between the cat and the hat is the same. Each of these statements asserts or assumes that there is some thing denoted by the collection-concept “cat”, some thing denoted by a collection-concept “hat”, and a certain particular relationship between the two denoted by the collection-concept “in” or “is on” or “wearing”, etc.
Now consider this list of statements:
Saturn is the sixth planet from the Sun. [English]
Saturn je est planeta od slunce. [Czech]
Saturne est la sixieme planete la plus loigne du soleil. [French]
Saturn er den sjette planeten fra solen. [Norwegian]
[Hebrew]
Again, the words and the symbols are different, but the sense or meaning is the same – regardless of the language employed, the symbols or particular wording involved, or even the sentence structure. Each of these statements says that there is some thing denoted by the description-concept “Saturn”, some thing denoted by the collection-concept “sixth planet from the Sun”, and a certain particular relationship between the two denoted by the collection-concept “is”.
Propositions express relationships between concepts. In the twelve sentences about a cat and a hat, the proposition involved is the same, even when the sentence structure is a command to make the proposition true, or a question as to whether the proposition is true. In the “cat in the hat” proposition, there are three concepts involved (the “cat”, the “hat”, and the relationship of “in” or “is on”, etc.), and the proposition expresses a particular relationship between those concepts. So called “atomic” propositions involve just a single relationship concept, and the entity concepts to which the relationship applies. That is what makes them “atomic” propositions. In the “Saturn” proposition, there are also just three – “sixth planet from the sun” is a descriptive indicator for a single collection-concept. The simplest kind of atomic proposition involves just three concepts – it expresses the thought that one concept stands in a particular conceptual relation to another concept. More specifically, it expresses the thought that the existents subsumed within the first concept stand in some particular relationship to the similarity characteristics that bound of the second concept.
You cannot utter or think of a sentence or a statement without expressing some relationship between concepts. And the contents of that relationship is just an atomic proposition. More complex propositions are composed of some number of atomic propositions. The proposition “Alice hopes that Bob comes between five and six o’clock” contains two atomic propositions – p = “Bob comes between five and six o’clock”, and q = “Alice hopes that p“. The words “that”, “or”, “and”, and similar connectives are a clear indication that an additional atomic proposition is involved.
There are a number of advantages in dealing with atomic propositions instead of the more complex entries on that list of suggested “truth bearers”.
The truth of the proposition that Saturn is the sixth planet from the Sun depends only on the physics of the solar system, and not in any obvious way on human convention. By contrast, what these five sentences say does depend partly on human convention. Had English speakers chosen to adopt the word “Saturn” as the name of a different particular planet, the first sentence would have expressed something false. By choosing propositions rather than sentences as the bearers of truth-values, this relativity to human conventions does not apply to truth, a point that many philosophers would consider to be a virtue in a theory of truth. Propositions are abstract entities; they do not exist in space and time. They are sometimes said to be “Timeless’, ‘eternal’, or ‘omnitemporal’ entities. Terminology aside, the essential point is that propositions are not concrete (or material) objects. Nor, for that matter, are they mental entities; they are not “Thoughts”, they are what thoughts express.
“Truth” -The Internet Encyclopedia of Philosophy(3)
I do not mean anything mysterious by “proposition.” I use this word as a general term for the things people assent to, reject, find doubtful, accept/or the sake of argument, attempt to verify, deduce things from, and so on. (Some of the phrases on this list take more than one sort of object. One may, for example, reject not only propositions but bribes. I hope no one is going to be difficult about this.) We have plenty of “specialized” words for propositions in the language of everyday life, just as we have plenty of specialized words for human beings. On various occasions, we call propositions “doctrines,” “theses,” “theories,” “premises,” “conclusions,” “theorems,” “views,” “positions,” “conjectures,” “hypotheses,” “dogmas,” “beliefs,” and “heresies,” just as, on various occasions, we call human beings “women,” “babies,” “thieves,” “admirals,” “Trotskyites,” “Australians,” and “Catholics.”
It is thus uncontroversial that there are propositions. The only question that could arise is: What are propositions? Many philosophers apparently think that propositions are sentences, since they think that sentences are what is true or false, and it is evident that those things that are true or false are just the things that are the objects of the activities and states listed above. But I can make no sense of the suggestion that propositions are sentences, and I shall not discuss it further. It is true that I am willing on occasion to speak of sentences being true or false, but this is only shorthand. When I say that a given sentence is true, I mean that the proposition – a non-sentence – that that sentence expresses is true. (To say that an English sentence expresses a given proposition is to say, roughly, that the result of concatenating “the proposition that” and that sentence denotes that proposition.) Similarly, when I say that a name is honorable, I mean that the individual or family that bears that name is honorable. I can no more understand the suggestion that a sentence might be true otherwise than in virtue of its expressing a true proposition that I can understand the suggestion that a name might be honourable otherwise than in virtue of its being borne by an honorable individual or family.
Peter Van Inwagen, Ontology, Identity, and Modality(4)
Because it is the more generally favoured theory, and because of my own preference for its simplicity, the theory that atomic propositions – not sentences, not even complex propositions – are the bearers of truth-values will be adopted in this essay. When I talk of “truths”, I am referring to true atomic propositions. For the purposes of this essay I will consider that it is atomic propositions that can be, and are judged as, true or false.
Footnotes
(1) Proops, Ian, “Wittgenstein’s Logical Atomism”, The Stanford Encyclopedia of Philosophy (Spring 2006 Edition), Edward N. Zalta (ed.),
http://plato.stanford.edu/archives/spr2006/entries/wittgenstein-atomism/.
(2) Unless otherwise specified, all dictionary definitions are quoted from The American Heritage® Dictionary of the English Language, Third Edition copyright © 1992 by Houghton Mifflin Company. Electronic version licensed from INSO Corporation; further reproduction and distribution restricted in accordance with the Copyright Law of the United States. All rights reserved.
(3) Bradley Dowden and Norman Swartz, Truth, The Internet Encyclopedia of Philosophy, http://www.iep.utm.edu/t/truth.htm
(4) Van Inwagen, Peter, Ontology, Identity, and Modality: Essays in Metaphysics, Cambridge University Press, Cambridge, England. 2001.
ISBN 0-521-79548-6.