According to Aristote:
Time is the measure of change.
The law of non-contradiction says that a thing cannot have and lack the same property in the same respect at the same time.
The law of non-contradiction seems to be the fundamental basis of logic. Yet it presupposes the concept of time, which in turn presupposes that of change. Thus, it seems, for Aristotle, the concept of change is more fundamental than logic itself. That doesn’t seem very plausible to me.
But perhaps there is a different way to understand the “at the same time” qualifier in (2). Sometimes, we give a rule with something we call an exception, but it’s not really an exception. For instance, we could say: “It is an offense to lie to an officer of the law, except unintentionally.” Of course, there is no such thing as an unintentional lie, but it is useful to emphasize that unintentional falsehoods are not forbidden by the rule.
Now, Aristotle is, as far as I know, a presentist. On presentism, the only properties a thing has are its present properties, and it lacks precisely those properties it doesn’t presently have. So it’s not really possible for an object to have and lack the same property, since the having and lacking would have to be both present, and hence at the same time. But it is useful to emphasize that having the same property at one time and lacking it another is not forbidden by the law of non-contradiction, and hence the logically unnecessary qualifier “at the same time”. Strictly speaking, I think “in the same respect” isn’t needed, either.
6 comments:
Pruss: Could the concept of change be as fundamental as the rules of logic?
A couple of steps that occur to me:
1) Surely the meanings of words and the conceptual framework on which our sentences make sense are as fundamental to making true statements as are the rules of logic (applying the rules of logic to meaningless strings of letters does not yield truths).
2) The conceptual framework on which our words and sentences make sense appears to fundamentally and irrevocably rely on temporal concepts (verbs have tenses, and so any statement of existence or of the occurrence of anything will either entail that it is presently the case or that it is not the case at all... note that even the "is" in that sentence is in the present tense).
3) I'm not sure we should let Aristotle lead us to think that time is the measure of change. I think Aristotle is a wonderful guide for many fundamental things (for example, I think sufficient interest in him could resolve the entire so-called "problems of consciousness/mind"). But, I'm persuaded by Newton's concept of "mere duration", and the distinction between that and the physical measures of time's passing (the latter of which are indeed dependent on change). Perhaps the best reconciliation would be to say something like "The measure of time is the measure of change", which even Newton might find agreeable.
So, while I'm not sure that change needs to be regarded as fundamental as the rules of logic, I think tense and time are clearly so; and, if change is fundamental to time itself, then change too would be as fundamental as the rules of logic. But, I think that latter part needs Newton's distinction.
On eternalism, the time element seems necessary to me. You mention that Aristotle is a presentist, which is fine. But suppose that eternalism is true. Suppose that eternalism implies perdurantism. If the time element weren't necessary to the law of non-contradiction, then it might follow that it's not a contradiction to affirm that I'm both 2 feet tall (at 2 years old) and 6 feet tall (at 36 years old). The affirmation that I'm 2 feet tall just translates to my being not 6 feet tall, which translates to the affirmation that I'm both 6 feet tall and not 6 feet tall. The perdurantist will just say that part of my space/time worm is 2 feet tall (at an earlier time), and another (at a later time) part is 6 feet tall. The reason why the perdurantist doesn't contradict herself is because of the two tenseless qualifiers for the two parts. That seems to imply that temporal properties explain such a logical property. If x explains y, then x is more fundamental than y. Perhaps this is a round-about way of preferring presentism. If presentism is true, then any B-theory of time would have to be necessarily false. Otherwise, the fundamentality-relation would be contingently true. And if it were merely contingently true, then, given the truth of presentism, any B-theory of time would not be necessarily false. And if any B-theory of time wouldn't be necessarily false, then there'd be possible worlds where time wouldn't be more fundamental than logic, even if presentism were true in the actual world. So, would you say that time is only more fundamental than logic if eternalism is true?
Kairos
I'll use your height analogy...
The B-theorist places her hand on top of her head to measure her height while the A-theorist uses a measuring tape to gauge her height.
The real insight is not to "become" bewitched by the difference...
I'm not sure I follow. I brought up the height-analogy to highlight the difference between the fundamentality-relation of logic and time relative to eternalism and presentism. Whether the eternalist places her hand on her head to determine her height or not, the time t1 during which she places her hand on her head (to measure her height at t1) will be indexed to a temporal part on her space/time worm (if eternalism implies perdurantism). If, at t1, she is 2 years old, let's say she'll be 2 feet tall. At t2, let's say she's 5 feet, 5 inches tall. Thus, at t2, when she places her hand on her head, she's 5 feet, 5 inches tall. But if we get rid of the indexicals to the temporal parts of her space/time worm, we seem to have lost the metaphysical resources to avoid a contradictory set of properties exemplified by her worm: namely, the worm being both 2 feet tall 'and' 5 feet, 5 inches tall. The introduction of temporal parts explains why the set of properties is 'not' a contradiction: the properties are properties of different temporal parts of the same worm. Thus, on eternalism, time is more fundamental than logic. I could be wrong, but I was just teasing this out to see how that implication could be avoided. To make logic more fundamental than time, then (given this reasoning), eternalism needs to be necessarily false, it seems to me.
Kairos
With no other gauge the presentist girl places her hand on top of her head in order to determine her height.
She exclaims to her audience..."Look how tall I am!"
The girl has a quantified and non-quantified height property at the same time.
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