Why do we confine ourselves to static ‘thing’ logic when we are dealing formally with time, which is dynamic?

Question

All ‘temporal’ logic statements are expressed in solely static terms that can be compared to static reference phrases or related to the number line and evaluated with arithmetic.

For example, suppose you asked a computer and a human to determine in which order two events occurred, given the occurrence of the two events (you raised one hand and then the other):

1. The human would be able to answer immediately and directly, having an innate sense of time.

2. The computer would not be able to answer directly, but would have to first determine the clock time at which each of the two events occurred (place them on a linear, or space-domain, scale of time), then check that against which rule the local time runs upon (ascending or descending numbers) in order to infer the order in which the events occurred. In the case of ascending clock numbers, the lower numbered event would be the earlier one (and the other later). In the case of descending clock numbers, the higher numbered event would be the earlier one (and the other later).

Answer 1

I'm not sure I fully understand the question. In the first place, logic isn't particularly about "things" as opposed to say "relations" including relations in time like before/after. However, I think what the OP is getting at is that statements in formal logic often look "tenseless", i.e. like they are eternal, timeless statements.

I think OP is inferring from the fact that statements of first-order logic (the kind we learn in the intro logic class) are tenseless that therefore logic has no ability to represent time. That inference isn't right though.

Here are three ways in which time can be represented logically:

• First, in ordinary first-order logic, we can simply add time as a parameter to our predicates. So to say "x is an F at time t" we write: F(x,t) instead of just F(x).
• Second, we can extend first-order logic by adding modal operators. So let 'FUTURE(phi)' be an operator that takes the sentence phi and says that that sentence will be true in the future. We can now write "x will be F" as 'FUTURE(F(x))'. This approach to time and tense is widely studied I think in contemporary linguistics.
• Third, we can also represent time in logic by allowing truth values of our propositions to change. This is called dynamic logic and it can be used to represent the flow of information through a complex machine which changes through a series of different states. Unsurprisingly, dynamic logic is of interest to computer scientists and AI researchers.

Answer 2

I think the answer may be that the purpose of "formal" dealings with times is to explicitly remove the troublesome intuitive concepts which lead to great deals of disagreement regarding time. Consider that you say:

The human would be able to answer instantly and directly, having an innate sense of time.

You make this statement axiomatically. It's an assumption. You assume humans can do this. Many have assumed similar. The result tends to cause all sorts of issues. The famous issue of the grandfather paradox is one example. An attempt to apply human intuition to a rather nuanced problem typically results in all sorts of problems, hence why it is considered a paradox. A formal approach to time is typically used to break this up.

There are countless examples of where the human innate sense of time breaks down. Consider the famous Ship of Theseus.

The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their places, in so much that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.

The result of this was the classification of two extreme views on time, the endurable point of view which roughly models time as a series of frames like a movie, and the perdurable point of view which explores objects as things in "4 space," 3 dimensions plus time. We do not, in fact, confine ourselves to static thinking, unless we choose to limit ourselves to only using the endurable point of view.

The innate sense of time is also made far more complicated by scientific discoveries about how the mind work. It is becoming harder and harder to treat our perception as metaphysical hocus pocus; we are having to come to grips with the physical processes that appear to make the universe work. One key reality is that a surprisingly large amount of what we do can be modeled using local equilibrium thermodynamics, where the "relaxation rate" of small scale events is so much faster than the larger scale events we care about that we can handwave them away as error terms. Only a small portion of physics calls for non-equilibirum thermodynamics to achieve acceptably accurate predictive results. For systems where local equilibrium thermodynamics is sufficient, modeling time as a series of snapshots is actually a very effective approach. It is so effective, in fact, that in a surprisingly large number of cases people don't even realize they are making an assumption when they fall into the endurable point of view.

Of course, if you look at a large portion of the literature, the endurable approach is popular. Personally I believe that its because the questions that arise from the perdurable point of view are troublesome. In many cases, we want answers, so we turn to the more tractable endurable approach.

You will find a different focus in Eastern literature. Much of Eastern philosophy revolves around the Dao, which is much more reasonably modeled as a dynamic perdurable entity rather than an endurable series of frames. The Dao is ever changing, in their philosophies. As a result, they tend more towards perdurable ways of thinking. The result is that they require many concepts, such as Chi and the Dao, which seem strange to Westerners because they, with a typically endurable mindset, do not fully understand why the concepts are useful to the Eastern philosophers.