## Sunday, May 24, 2015

### Beginnings

An obvious definition of having a beginning is:

1. x has a beginning provided that x exists at some time but there is an earlier time at which x does not exist.
But this doesn't seem right. After all, it may well be that (a) the universe has a beginning (about 14 billion years ago) but (b) there is no time before the universe. In light of this, I've tended to say something like:
1. x has a beginning provided that x exists at some time at which it has finite age.

There is a somewhat recondite potential counterexample to (2). Suppose that the universe has an infinite past, and object x has a temporally gappy existence, such that last year x existed only for half a year (the other half is the gap), the year before x existed only for a quarter of a year, and you see where that's going. So x's current age is something like 1/2+1/4+1/8+... = 1 year. So x is one year old. By definition (2), x has a beginning. But it doesn't seem like x has a beginning.

But perhaps this case is not fatal to (2). Maybe we should agree that x has a beginning. For the relevant time sequence for saying whether something does or does not have a beginning is internal time. And x has a finite internal time past. If we say this, then we will also say that a person y that has a slowed-down past of the following sort also has a beginning: over the last year, y functioned (in all respects, mental and physical) at half of the speed of a normal person; the year before, at a quarter of the speed of a normal person; the year before, at an eighth. Thus, y experienced 1/2+1/4+1/8+... = 1 years of internal time. Yet y has always existed. While I might tolerate saying that x has a beginning, to say that y has a beginning is very awkward. (Maybe it's true, though? It's worth exploring. But for now I shall dismiss this.)

The above cases show that age in (2) must be reckoned in an external manner. To be more precise we should revise (2) to read:

1. x has a beginning provided that x exists at some time T and there is a number N of years (or other units) of time such that x did not exist more than N years (or other units) before T, where the times are reckoned externally.

Note that this is very much an extrinsic characterization of x's having a beginning. We could imagine two objects whose intrinsic careers are exactly alike, one of which has a beginning and the other does not. Take, for instance, our slowed down y from the last counterexample, and then a person who lives through y's past in one ordinary external year. The slowed down y has no beginning, but the other person does, even though their internal lives could be exactly alike. This seems unsatisfactory.

Also, intuitively, having a beginning is more about the order properties of time rather than metric properties of time. But (3) (as well as (2)) makes it be a feature of the metric properties of time.

I am not quite sure what to do with these thoughts. Maybe this: The notion of a beginning isn't actually all that natural a notion. Perhaps the natural notion in the vicinity is the notion of having a cause?

Heath White said...

How about: x has a beginning iff x has a first moment of its existence.

Alexander R Pruss said...

Suppose x exists at all times after noon today, but doesn't exist at noon. Then x has a beginning but no first moment.

Alexander R Pruss said...

I should say: by "has a beginning" I am trying to capture the intuitive content of "came into existence".

IanS said...

How about : x had a beginning if there was a time before which x never existed.
"Never" is meant to deal with things with a "gappy" existence. Note that this uses only the ordinal properties of time.

Alexander R Pruss said...

Then universe whose timeline is an open interval at the lower end has no beginning.

IanS said...

True, but is this a bug or a feature? Such a universe literally does "have no beginning". To say it "came into existence" you seem to need some external timeline that goes back further. This seems to support you last paragraph: "things" coming into existence makes sense, but time coming into existence is hard to grasp.

Alexander R Pruss said...

But that something came into existence doesn't seem to entail anything about what happened before it came into existence.

Mark Rogers said...

Dr. Pruss have you ever tried collecting a tardigrade?

Unknown said...

This seems to support you last paragraph: "things" coming into existence makes sense, but time coming into existence is hard to grasp.

If it's true that time is a measurement of change (and not the other way around), then you could collapse time coming into existence into things coming into existence.

IanS said...

John West: Agreed. I meant "particular things coming into existence in existing time."

Dr Pruss: That something came into existence doesn't seem to entail anything about what happened before it came into existence. It seems at least to imply that there was a before. This is my problem with time "coming into existence". Maybe I'm being fooled by language.

Heath White said...

Suppose x exists at all times after noon today, but doesn't exist at noon. Then x has a beginning but no first moment.

I'm not sure I can make sense of this suggestion. I think you could generate a Paradox of the Not-So-Grim Birther to show why.

Suppose that God is going to create the universe immediately after noon. He is going to let one of an infinite number of angels push the button that starts it up. The first angel's button starts it one second after noon. The second angel's button starts it a half second after noon. The third angel's button a quarter second. Etc. Which angel pushes the button?

Anonymous said...

Alex Pruss: I should say: by "has a beginning" I am trying to capture the intuitive content of "came into existence".

It seems to me that the intuitive content of "came into existence" is far more aligned with (1) than with (2). When you use the phrase "came into existence," the average person is likely to think of a period wherein that thing does not exist followed by a period wherein it does exist.

AKG said...

Hello Dr. Pruss
I've been pondering about the Leibnizian cosmological argument for a while, and I recently came up with an argument of why a quantum field(which atheist use against the argument) cannot be a necessary being and would be contingent.
The laws of quantum fields describe which arrangements of the fields are physically possible and which ones are not possible. If this is the case than that means than for a particular arrangement of a quantum field such as the one that gave rise to our universe (I'm not saying it is true, I'm just assuming it to show why if this were case it would not be necessary)there is a logical and mathematical possibility that it could have developed into a different arrangement of fields. If this is the case then that means that the current arrangement of the field that may have given rise to our universe could have been different and did not have to be the way they are. Since this is true, then it would fall under Leibniz's definition of a contingent being as it could have been different then the way that it is and did not have to be a specific way, even if it was eternal, and thus it would require ultimately a necessary explanation.
I'm not sure if this is valid as I don't know too much about quantum fields and I was wondering if you could help me see where I'm wrong in this thinking and how I could make it better,

Alexander R Pruss said...

There are two kinds of contingency in a being:
1. The being could have failed to exist.
2. The being could have had other intrinsic properties from the one it does.

In classical theism, God does not have either sort of contingency. If I understand your argument, you're saying that even if a quantum field does not have type 1 contingency, it has type 2 contingency. Is that right?

AKG said...

Yes sir that is right, but is the reasoning behind it accurate?

Alexander R Pruss said...

Yes, I think so.

AKG said...

Thank you for your comment sir, but I'm still a bit on the edge if what I said about the quantum field(the science) is accurate.