Does all of spacetime exist? In Brian Greene’s 2004 book, The Fabric of the Cosmos, he quotes Einstein on the meaning of time, 

…the distinction between past, present and future is only an illusion, however persistent. 

Greene then says, 

The only thing that’s real is the whole of spacetime. 

Is this a valid scientific deduction? 
 A: The idea behind that quote is that you can't really separate space and time in General Relativity, which is the most complete scientific theory concerning the geometry of space and time. Instead, it works best to consider them as one integrated thing, called spacetime. 
To go into a little more detail, first consider galilean spacetime. Here you can think about taking a snapshot of three dimensional space at one instant of time. Moreover, the whole spacetime is just a collection of these snapshots, with one snapshot for each point in time. The conclusion is that the set of spacetime points in galilean spacetime decomposes naturally into "snapshots" of simultaneous points, where each snapshot looks identical to another.
This stands in contrast to General Relativity, where there is no natural way to decompose spacetime in a similar fashion. Instead of saying two spacetime points occured at the same time, the most you can say is that two spacetime points are not causally related (that is, an event happening at one could not affect an event happening at the other). This not-causally-related property is much weaker than simultaneity. So since spacetime in General Relativity does not have a rigid structure allowing it to be viewed as a collection of "snapshots", you must thing of it as one indivisible object.
I think that is the idea of what he is trying to say. As far as whether or not it is a valid scientific deduction, I would say the statement is too vague to be scientific. The idea of the statement was probably just to give you a feel for how relativists think of spacetime, because its kind of interesting.
A: Just to offer a counterpoint: 
That the law of physics are the same for all observers is what is meant by "relativity". 
Now for any given observer, the distinction between past, present and future is not an illusion.
And, there is no observer seeing spacetime from the outside, so no observer can say anything about the whole of spacetime.
So the two statements you cite are false for any observer. They are only true from some god's view here taken by the physicist. So, what are their logical status ?
I would say they are meaningless. General Relativity describes spacetime from the inside; it does not provide a vantage point of view on spacetime as a whole. 
