# If the world is always everything that is the case then is the world always the case?

If the world is always everything that is the case then is it always the case?

Can this be demonstrated with logical notation, quite easily?

i.e. like the beginning of the Tractatus in temporal logic

The world is everything that is the case. What is the case (a fact) is the existence of states of affairs. A logical picture of facts is a thought. A thought is a proposition with a sense.

• What do you mean by "is the case," do you mean "is the case" as some sort of predicate or do you mean "is the case" as in it has a True truth value? "The world is always the case" seems like a really ambiguous statement given the little amount that you've written. Also "always" is a logical operator in temporal logic; are you asking about temporal logic? Jan 20 '17 at 12:00
• In set theoretic notation you seem to define W:={x | IsTheCase(x)} and ask if IsTheCase(W) obtains. The short answer is no, it doesn't. This is similar to IsASet in set theory and you need an axiom to make sure that such definitions produce sets. Yours in particular uses unrestricted comprehension, and leads to contradictions with the "set of all sets", so it is not accepted. The problem is that your definition is self-referential, and it is unclear if what it defines is included into its own scope. Jan 21 '17 at 22:08
• you do know that late wittgenstein utterly repudiated early wittgenstein, no?
– user20153
Jan 21 '17 at 23:00
• define "it" in "is it always the case", please.
– user20153
Jan 21 '17 at 23:03
• @MATHEMETICIAN, just came upon this and thought you would appreciate Ayer's assesment that, "it's not quite clear what Witgenstein's atomic elementary statements were meant to be" Feb 21 '17 at 21:14

The statement "If the world is everything always, then the world is always" can be written in temporal logic as:

Let i = "The world is everything"

Let e = "The world exists"

Let H be the temporal operator "It has always been the case that"

Let G be the temporal operator "It will always be the case that"

(Hi ^ Gi ) -> (He ^ Ge)

If what you mean by "is the case" is giving i and e True truth values, then yes, the implication has a value of True.

## Analyze

Let’s have a look at the first component:

If

This is a means of saying whether or not something is. In case something is, then that’s the answer we’re looking for. The piece of information following the 'if' is what we’ll be comparing with the piece of information following that piece of information.

Onto the following:

The world is always everything that is the case

This says that the world always is everything that is the case—meaning that all the time that ever will exist, the world is everything that is the case.

Here’s another component:

Then

In this case, this describes that we’re comparing the first piece of information with the second due to the 'if'.

And the piece following the 'then':

Is it always the case?

This asks if the world always is the case.