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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).

  • Intriguingly, you suggest the human "...would be able to answer instantly..." even though science has shown it is not possible for a human to react to a stimulus in less than 100ms (the period it takes someone with olympic grade reflexes to respond to a light turning on by pressing a button). In fact, there are many cases where humans are remarkably bad at using their innate sense of time. We have great trouble grappling with causality at high speeds. – Cort Ammon Mar 26 '16 at 22:15
  • Sorry, perhaps a better word is 'immediately.' Humans would not have to look up references, but would be able to respond immediately upon receiving the stimului. Not so computers, which need a series of other operations before the results can be inferred and output. Speed of response is not the meaningful metric, in this instance, but sophisticated logical operations. Computers have no sense of time, but must be informed about time through static, or 'spatial' representations. Temporal sense is inherent in living entities. – Charles Moeller Mar 26 '16 at 22:46
  • Actually, we design computers to respond immediately as well. However, they are typically high speed circuits, as opposed to general purpose circuitry. A particular formulation known as NL might be worth researching, for it explicitly targeted such response times. It may be worth pondering whether human sensations of time might have a similar gradiated approach. After all, we do wish people happy birthday, and we can organize them chronologically. – Cort Ammon Mar 26 '16 at 22:48
  • To which 'NL' do you refer? I may be highly interested. Do you have a reference, or the name (written out)? – Charles Moeller Mar 26 '16 at 23:48
  • Process philosophy deals with the dynamic aspect of time. Whitehead for example. Also Heidegger deals with 'being' as a dynamical thing. Henri Bergson is another. – Ameet Sharma Mar 27 '16 at 0:33
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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.
  • Those representations confirm my original statement – Charles Moeller Mar 27 '16 at 1:29
  • @CharlesMoeller Then I don't at all understand what your question is supposed to be. Can you clarify it? Can you give us a definition like " x is 'static' if and only if . . ." ? What makes you think humans are actually doing anything different at all here? The fact that you can't introspectively determine how your mind represents time doesn't mean that your mind doesn't represent it pretty much the way a computer does. (That's more or less the point of cognitive science.) – user5172 Mar 27 '16 at 1:48
  • A computer is a machine that is special-built to manage symbols. That is all a computer can actually do. Anything else a computer may look like it is doing is a human-designed routine and interpretation of symbol management. You may say that humans manage symbols too. Yes, humans manage symbols, but that is only one of the multitude of things humans can do, while it is the single and only function that is necessary and sufficient for computing. See Searle’s Chinese Room Argument: plato.stanford.edu/entries/chinese-room – Charles Moeller Mar 27 '16 at 2:55
  • Time is perceived and identified by the duration between occurrences. Time has the ability to accept any conditions and events, without regard to when they occur. There are no favored or forbidden moments or durations. The occurrence, duration, and sequence of events are determined solely by the actions and reactions of the objects that create them. Time is without intrinsic feature, except for the events and conditions it contains. Time is therefore assumed to be non-discrete and continuous. Simply put, time is the sequence of events. – Charles Moeller Mar 27 '16 at 3:03
  • I understand the chinese room argument, but I don't understand any of the claims about time in the comment that follow, nor do I see why we should think they are true. What would it be for time to "accept" a condition? Suppose I accept time is just a relation of sequences of events. Why would it follow that it is continuous rather than discrete? (I have no problem thinking of time as continuous, I just don't see how this follows) Suppose I accept that time is continuous, why would it follow it isn't representable symbolically, and hence computable? After all, we can compute continuous things. – user5172 Mar 27 '16 at 11:41
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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.

  • Thanks for your input. One problem with the endurable, or frame, model of time in process control computers is the vast number of frames that must be processed and result in no operation in a controller that must respond rapidly, but seldom. These cases are typical for safety-, or time-critical functions that almost never occur. Competition for those resources by other linear-sequential processes results in higher clock rates. Wasteful, I say. My OP aimed to show the limitations of static and linear-sequential (thing) logic operation and then to suggest that perhaps there is an alternative. – Charles Moeller Mar 27 '16 at 2:50
  • @CharlesMoeller I think people are open to an alternative, but the real question is "what?" You specifically call out the innate sense of time living creatures have, but what do we actually want to learn from this innate sense? From research, that innate sense is far from perfect. FAR from perfect. And the parts that are rather close to perfect are well modeled by the existing linear time approaches. It would help to identify the cases where we look to learn from living creatures. For example, we seem to be remarkably good at interacting with chaotic systems like inverted pendulums... – Cort Ammon Mar 27 '16 at 18:26
  • ... for the quality of the sensory and motor control we have. Computers can sense much faster, and move much more precisely, and yet dealing with these chaotic systems is recognized as a challenge for them. – Cort Ammon Mar 27 '16 at 18:26
  • As for efficiency, and avoiding waste, I agree there is a valued goal there, and I think the industry agrees. For example, if you look at the world of multithreaded programming, we used to rely entirely on exclusion to generate a program flow that could have been single threaded (linear time). That was found to be inefficient. Modern atomic operations are designed to permit scenarios that cannot be described in a linear single threaded way. You have to approach time as a lattice to capture the exact behavior of atomic operations. Atomic operations, interrupts, vector clocks... – Cort Ammon Mar 27 '16 at 18:31
  • ... these are constructs that have been invented because people recognized the limits of a linear approach to time. At the same time, every one of them has a toe hold in linear time, even if it's just a mathematical limit, because we have found linear time to be mindbogglingly effective at describing things. – Cort Ammon Mar 27 '16 at 18:32

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