Thursday, April 29, 2010

Drink some high octane coffee, and read some St. Anselm, and your brain excretes a blog post against your will

The truth, past and future

Consider this passage (from Anselm) on the truth of statements:

Let him who can, think of a time when the following began to be true, or when it was not true, namely, that something was in the future to be: or let him think of a time when the following will cease to be true, namely, that something will have been in the past. But if neither of these two suppositions can be conceived, and if they cannot be true without truth, it is impossible even to think that truth have a beginning or an end. Moreover, if truth had a beginning, or if it will have an end, it was then true before truth began that there was no truth; and after truth will have ceased to be, it will be true that there will be no truth. But nothing can be true without truth; and there will be truth after truth will have ceased to be; which is utterly inconsistent. Whether, then, truth be said to have, or whether it be understood not to have, beginning or end, truth can be limited by no beginning or end.

This passage has two succinct and tightly formulated arguments, and it makes a very interesting point about truth. Let’s unpack it a bit:

It helps to use particular examples. That is what Anselm is asking us to do. So, who are we to refuse? Here are two.

Our first example: My continued life as of 12-24-2011. (Hey I’m an optimist, and take my simvastatin). Let’s render this ‘thing to be’ as a statement:

1. SB will be alive on 12-24-2011.

Suppose that statement is now true. The fact to which this statement refers, (my biological functioning at the given date) is looked at, and described from a future regarding perspective, that is; from the point of view of someone ‘observing’ from today toward that happy future.

Now a second example, an example of something ‘that will have been in the past’ using the same date:

From the ‘retrospective perspective (looking back from 2011)’:

2. SB was alive in 1970.

Anselm asks us to consider the first statement with this question in mind: Is it possible that the statement began to be true at some time? Is it possible that the statement “SB will be alive on 12-24-2011” started to be true at some time? To be clear, this is a question about the actual world we live in, not some parallel possible world. So, is it possible, in this world or universe that we actually live in, that the statement concerning my living in 2011 began to be true at some point in time, and was not true, but was either false, or neither true nor false , before that point in time?

Well, suppose it did begin to be true, let’s say, on my birthday or on 12-24-11 itself. Well, the day before that event, it would have been false (or neither true nor false) to say that I would be alive on 12-24-11. On and after my birthday (or 12-24-11), it would be true to say this. One might think here that we have successfully done what Anselm considers impossible. But there is a slippery ambiguity here that easily beguiles and confuses.

It is true that I, a human being, began to exist on my birthday, but it does not follow that a statement to that effect began to be true on that day. A statement describing my birth would have been true before that day simply by virtue of the fact that it correctly described what was then in the future. Similarly, my being alive on 12-24-11 makes it the case that the future looking statement number 1 to that effect is also now true.

Long before I existed, that statement was true, because it accurately described the future (a future that contained my birth, and a bit later, my living on 12-24-11). Once again, we must keep squarely in mind that the statement Anselm is having us consider is a statement that is “world indexed” that is a fancy way of saying that it refers us to this universe we live in, not some other possible universe. It refers to the actual universe, that super big immense thingamabob we are all in, and which does include me as an insignificant speck. By our assumption, statement 1 is now true, and has been true since the big bang even though for much of cosmic history, no one would have had a clue of its existence or any good reason to believe the statement was true, or would turn out true.

Think of a similar statement considering the universe as a whole; that the universe will end up as a cold haze of elementary particles. Right now, we are not in a position to tell if this is in fact what will happen. Yet, if it is going to happen, then any statement we make today that describes that unhappy state of affairs is now true. Things are no different with statement 1.

In short, there are two different readings of an “is it possible that X..?” question. One reading translates roughly to “is there a possible world where X is the case?” The other reading translates roughly to “is it possible in this world that X is the case?” Anselm is having us consider the latter sort of question with regard to the truth of statement number 1.

Much the same can be said for the question regarding the truth of statement number 2, but it is in a way easier for us to grasp, because number 2 refers to the past: Is it possible, in this world that statement #2 would at some future date cease to be true? Clearly, the answer is ‘no’. What’s done is done, set in stone, fixed, (feel free to evoke your own clichĂ©). One is reminded of a standard example with regard to divine omnipotence: Even God cannot make it the case that God never existed, and by extension, cannot make it the case that a statement saying that God existed in the past is false.

Anselm summarizes his position by saying that truth has no beginning or end. He then goes on to a second argument that switches focus. It has us focus on truth itself, not so much the truth of individual statements. If you were to imagine that truth itself came into being at some point in time, then it would be true to say that before that time truth did not exist. But, if it is true to say something, then truth exists. But this contradicts the initial assumption that truth did not exist at that time. So, that assumption must be false, and truth did not start to exist at any time in the past and in fact has always been.

All of this leads one into the briar patch of getting clear about what sorts of necessary truths are being discussed in cases like this. Considering ‘future truths’ we can ask; since all true statements about the future must necessarily be true in order to be true statements about the future, does it follow that all future truths are necessary truths?

There is a subtle and easy to miss ambiguity of scope in this question, it’s tryin’ to slip one by ya. It is a necessary truth that all future truths are truths (this is simply definitional). If they weren’t truths then...well...they wouldn’t be truths. No duh. And they obviously couldn’t then go on to be future truths.

But, it is not the case that all those states of affairs that are described by statements that describe future truths are themselves things that had to be, things that are themselves necessarily true. While it is necessarily true that a true statement describing me as alive in 2011 is true, it is not necessarily true that I will be alive in 2011 (darn!) I could have succumbed to my genetic predisposition to heart disease despite simvastatin, or I could be hit by a car, a meteor a train, or etc...

A last interesting briar patch related to these sorts of questions: Given that it is now true that I will drink two cups of espresso on 12-24-2011, do I really have any sort of choice in the matter? Am I freely choosing to do so? One can in fact ask this question about every single choice one makes in the future. Right now there is an immense set of true statements about your future actions. In fact, the set is exhaustive. True, you are not now familiar with most of these choices, and your decisions, yet, all those truths are ‘out there lurking’ and just waiting to come into actuality. So, are you ever really free at all?

The charm offensive continues: Mr. Official Iranian Salute Guy now blogs