What is an elementary proposition?

Question

In the Tractatus, Wittgenstein talks of 'elementary propositions'.

Rather than giving a definition, can you give me examples?

Answer 1

I think the later Wittgenstein would point out examples aren't possible because there are no such things as 'elementary propositions'. What I can do is attempt to construct what sorts of properties an example might have. I'll also give an analysis of a sentence as given by Russell.

Take for example the proposition: 'It is raining and 1 + 1 = 2'. The proposition is clearly a conjunction of two propositions: namely 'it is raining' and '1 + 1 = 2'. Therefore it's not an elementary proposition. We can analyze this sentence as being two propositions that I'll call P and Q. The question that arises is whether or not, for example, the proposition P is analyzable into "simpler" propositions.

The tenability of this project of analysis depends on their being a unanalyzable proposition. So it was postulated that there elementary propositions can exist. It is not entirely clear that 'it is raining' or '1 + 1 =2' are elementary propositions. Attempting to analyze '1 + 1 =2' would be difficult enough in itself (although a very interesting study and formed the basis for this line of thinking.)

Now Russell considered a rather odd sentence for analysis. It is not clear whether or not he reduced it to 'elementary propositions' (if there even such a thing which is doubtful) but it should give you an idea of what Wittgenstein had in mind. Much of my discussion will come from Russell's paper On Denoting with a link in the sources. The sentence he considered was as follows:

'The Present King of France is bald.'

If we treat this with one predicate: namely the predicate "is bald" which I'll write as B(k) which means 'k is bald' where k names the Present King of France. (I'm treating predicates as functions because this is the notation used in the On Denoting piece and it was a convention started by Frege. This isn't a terribly common convention now although I've seen it used in mathematics occasionally.)

Now the problem is that there is no "Present King of France" so the statement lacks a referent: 'k' is not an object. One temptation would be to say it's not a proposition at all; it is meaningless and it cannot have truth value. Russell believed that it was meaningful and does have a truth value. What Russell did was treated "The Present King of France" as a predicate. So we'll let introduce another predicate: K(x) which will mean "x is The Present King of France". What this gives us is as follows:

There exists an x such that K(x) and B(x).

We've now analyzed the sentence into (assumably) elementary propositions. Russell can now say that the proposition is meaningful but false since there is no entity that is "The Present King of France".

Whether or not this interpretation of the sentence is the "correct" one is debatable and it has been critiqued by a number of philosophers including Strawson. But it does illustrate, roughly, what Wittgenstein had in mind with analysis.

Answer 2

Success would never be as gratifying without the possibility of failure. If you know when you set out on a venture that it is bound to work out well, where's the challenge? I feel I need to be careful how much I tell you, even though I have nothing but good news to share. Still, though, if you hear it and believe it, where will be your motivation? And, how will you live without the dramatic tension of uncertainty? Don't be too eager to dispel all doubt. A little mystery may yet give rise to a lot of magic.

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Answer 3

Gary Glitter outside a school.

Answer 4

The basic fundamental of a proposal