On time and the A theory of McTaggart’s argument against Time, and why does it remains infinitely contradictory (an exercise in waste of time)

by Annaelle

This is much more confusing than I expected.
We want to show the contradiction in the A theory.

Step 1 :

Suppose a thing in the future, that has not happened yet.
it has futurity in the past and in the present.
So the thing’s futurity has presentness AND pastness.

And this is a contradiction. We’ll get to that later.

We try to qualify the futurity’s past and presentness and see that we cannot solve the contradiction.  The problem is that it just *pushes* along the contradiction without eliminating it.

We say that it has :

Past [n] futurity
Present [n] futurity

What we can do is that we can add any number of present in the [n] argument.

so, let’s say n=0

Past futurity
Present futurity

let’s say n = 1

Past [present] futurity
Present [present] futurity

What I want to do is to show that adding temporal qualifiers to temporal properties doesn’t solve anything even if we add enough of them.

And Now I have a discrete value that I can set to infinity

Past [n] futurity
Present [n] futurity
For n = infinity

Past [infinite present] futurity
Present [infinite present] futurity.

Boom, contradiction not solved.

Now I have solved for the future, so I will generalize for all cases.

Step 2 :

For any X that has temporal property under the A theory.

No matter what, X will always have future pastness.
No matter what, X will always have past future pastness.
No matter what, X will always have present future pastness.

That is, every event in time will be in the past in the future, if they aren’t in the past already, in which case they will remain in the past for the future.

(What I have done here, is expressed X that I don’t know what time it’s at in a way that the word «future» appears everywhere. You can try it, it works.)

For the B theory, this is no problem, because «having pastness» is not a real property, but rather a useful linguistic shorthand.

The A theory claims – it is a central claim of the A theory – that pastness, present-ness and futurity are real and mutually exclusive properties.

So this presents a challenge.

Normally, a thing can have mutually exclusive provided it does not have them at the same time.

The problem is precisely that for any finite set of temporal combinations, a contradiction arises.

Let’s try to go for infinity, then.

Case 0

a) X has past future pastness
b) X has present future pastness

Is this contradictory?

If X has past future pastness, it means that, in the past, X will have had pastness in the future of the past.
If X has present future pastness, it means that that there is a moment in the future of the past in which X coincides with X having presentness.

X’s pastness in the past has futurity.
X’s pastness in the present has futurity.
Let’s call X’s pastness X’
By a), X’s pastness has futurity in the past.
And by b) X’s pastness also has futurity in the present

So X’ has present futurity
And X’ has past futurity.

Let’s consider X”s futurity and call it X”

It has presentness and pastness.

This is the contradiction.

So we have to solve it.

a) X” has presentness.
b) X” has pastness

The one thing we can’t do is place X on a timeline and say «there it is» because this represents abandoning the A theory for the B theory. Although doing that would expose this mindfuck quickly and make everything simpler, it is simply not within the tools of the A theory (which must rely on time properties), this does not mean that there is anything wrong with time or philosophy or logic – this is purely a weakness of the A theory, to make a complicated mess out of something that a competing theory explains better.

This alone is a good case against the A theory, but it’s not decisive if there is no contradiction.

Let’s go to case 1.

a) X” has presentness.
b) X” has pastness

X” has presentness in the future of the past.
It also has pastness in the future of the past.

So X” has

present futurity
past futurity

And we have shown earlier in the beginning, that, when we have that, we have something like

Past [n] futurity
Present [n] futurity

In this case :

X” has Past [n] futurity
X” has Present [n] futurity

And I can set n to infinity.
Infinite contradiction

No matter what time X happens in.

What I have done now is shown that I can’t solve the contradiction simply by adding temporal qualifiers.
That it, I can’t solve the contradiction by formal brute force, so to speak.

So now, I’ll give my honest best attempt to solve it semantically.

The following may not be 100% decisive :

Let’s go back

X” has presentness in the future of the past.
It also has pastness in the future of the past.

Now, here is something special :

having presentness in the future of the past.
And having pastness in the future of the past.

Those are the temporal properties of X in the first place.

And we got to X” in the first place by trying to explore the common temporalities of X and putting them on the same tense and this creates more divergence.

By the same reasoning, we’ll get a X”” that has

X”” has presentness in the future of the past.
It also has pastness in the future of the past.

And this is not an accident. That is, every event in time will be in the past in the future, if they aren’t in the past already, in which case they will remain in the past for the future.

Which means that everything we’re doing is just piling on temporal qualifiers.

Which we have established don’t work.

So our work here is done.

The A theory is shit.

And the B theory avoids all that shit by putting events on a timeline and just saying «Stop fucking around, people, there it is».

This is why the B theory is superior, even thought it has legit trouble accommodating the notion of «change».

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