Can’t this be assumed?
It seems obvious, but I don’t think it is actually a first principle that time exists. Some of this hinges on semantics and tacit implications built in to modern language, but let’s err on the side of being explicit. And it’s worth establishing this seemingly obvious fact of existence because apparently not everyone agrees with me about it. I was surprised myself to learn about some of the diversity of views on the subject one evening at a bar shortly before I was violently ejected from it for taking an adversarial (but, I thought, respectful) stance in support of the claim that time does exist against one of that bar’s favourite regulars.
Let’s first consider a Universe wherein time does not exist. We could imagine a basically stateless Universe where all its contents exist in an identical form across all “time”. In such a Universe, time essentially doesn’t exist since there is no sense in which any of its contents are dynamic. What would distinguish “earlier” from “later”? There is simply a single and eternal “now.”
Begging a question for simplicity that space exists, one way to visualize this notion is to consider a three dimensional graph where two axes are latitude and longitude, respectively, and the third axis is time. We could plot the movement of a person about the surface of the earth. Because in our experience time always goes forward, the graph is a function in time, and the plot will look like a meandering tunnel in the space of the graph. You can imagine it would look rather like an ant farm, or the squiggly path a worm might make in eating through an apple. Considering it this way, we’ve mapped that space-time path into only space, where we can see the position of the person over all time all at once. The Universe itself could be like that: static and unchanging like some relic that once was build and subsequently abandoned.
The dynamic Universe
Let’s see that that’s not the case. Recall that the cardinal truth is that I (or, from your perspective dear reader, you) exist. Descartes is most famous for pointing this out in a simple three-word formulation: “I think, therefore I am.”
Let’s analyse this, which is a little tricky. We define thinking to be the process of cognition, the act of processing information. In assuming that I think (something I notice I do frequently), I assume the existence of some kind of thought-space. Indeed, the Cartesian formulation itself is an example of one of the thoughts which inhabit the space. There are others too, like, for example, the thought I had which led me to write this sentence.
Notice the language here. I had a thought which led to a sentence. Information is processed. Information, then, has at least two states potentially associated with it: processed, and by implication, unprocessed. It cannot occupy both states, and the act of processing it changes the state. The distinguishing dimension which partitions those states for some collection of information is time. Thoughts (and anything else which can be said to exist) are dynamic across that dimension. They come and go, and I’m not thinking about all of them simultaneously. Time allows us to distinguish the difference.
Insight about Descartes’s formulation
Returning to Descartes, thinking can now be understood more exactly as a logical operator on information that transforms certain information into certain other information. New information is produced as a result of consuming existing information. That old information need not necessarily be destroyed in the process either. Indeed, part of the notion of thinking involves the notion of memory, since information is meaningless outside of some interpretive context. Memory of previous thoughts helps to inform the shape that a current act of thinking will take. All of this requires that time exist to be the dimension across which the state of that information changes through the processing act of thinking.
We get some insight about the conclusion of the formulation too. If it were the case that I always exist, and that what is meant by me is forever static and unchanging, then the statement is simply tautological. It could be enough simply to say “I am.” (Suddenly God’s answer when asked his name by Moses makes a little more sense.) But the Cartesian claim itself is interesting precisely because I didn’t always exist, and the fact that I do now is expressed as an interesting consequence of the fact that I observe myself to think. That self-awareness, born of the marriage of my abilities both to think and to remember previous thoughts, is what enables me to conclude that I am something real. The very language of the claim doesn’t make sense without time, and so it must exist.