Is Logic Time-Dependent?

Question

Greetings:

In philosophy, are there certain aspects found in Symbolic Logic that would be considered "time-dependent"? In other words, I know that in Symbolic Logic, the truthfulness of a statement is analysized through symbols...which describe relationships between objects or events.

For example, If object A is parallel to object B then object B is also parallel to object A [symmetry].

But is there any sense of Time, in Symbolic Logic? Since, Symbolic Logic seems to deal more with relationships and form....

I know this seems like a confusing question, and I hope I explained it, but if there is any one with knowledge of Symbolic logic and philosophy, I hope you can answer my question and clarify my question.

Thanks again..

Answer 1

Peel the onion.  The symbols and very concepts assigned to the concept of logic are defined by a culture in a time and place.

Answer 2

I don't know why you presume this world is time dependent or that time even exist? And even further why you think Logic is logical. If you were not on earth how would you keep time? Really time is a reflection of the rotation, wouldn't time differ if you say lived on a different planet? Even then you would be relating time on that planet to the one on earth. Even further in your example, modern geometry states there are no parallel lines, at some point they will meet. So with those apples in the basket, your logic is only time dependent if you are time dependent or logical, and ultimately you are both and you are neither.

Answer 3

Yes, they are called 'tenses' - especially when we talk about propositions.

For instance, the proposition that 'P' has a fixed truth value at   one time, but at a later time, called it time 2, the truth-value of 'P' may alter to '~P'.

___________

Aristotle noted the following problem, which is relevant to both time and logic, or more specifically, with propositions.

Consider the proposition right now: 'Tommorow there will be a sea battle'. We know that by the law of bivalence, every proposition is either true or false, and that propositions say of something how it is. So, the proposition that 'tommorow there will be a sea battle' is either true or false - right now - as this is implied by the law of bivalence. Formally, we get:

(tommorow there will be a sea battle) v ~(tommorow there will be a sea battle) is true)))

There is a bit of problem here, though. IF it is true right now - today - that tommorow there either will or will not be a sea battle, and we know that via the law of noncontradiction, that only one of the disjuncts (there will be a sea battle tomm.) or (there will not be a sea battle tomm.) can be true at one time, then one of the disjunctive-propositions must be true.

IF either (there will be a sea battle tomm.) must be true, or (there will not be a sea battle tomm.) must be true, then that implies metaphysical fatalism - as one of the disjunts *must* obtain.

Aristotle thought that this couldn't be the case: the logic of propositions seems to entail fatalism, but this cannot be so...Thus, Aristotle thought that propositions whose content is about the future are neither true nor false.

So - the proposition that 'either there will be a sea battle or there will not be a sea battle tommorow' is neither true nor false. Yet, to say that seems to deny the law of excluded middle and bivalence....a paradox indeed.

One solution is that the laws of logic do not apply until the actual states of affairs have obtain or failed to obtain. But it seems clear that this is incorrect; when someone says 'tommorow it will rain' and tommorow it indeed rain, we like to think that that person was right - they didn't just get lucky as to a propositions truth value.

One thing is for sure, though, and that is a proposition and it's negation cannot be true at one and the same time. This is partly based on a correspondence theory of truth where a proposition is true if and only if it corresponds to the facts. So, when you apprehend some fact, it is in your mind as a proposition - an apprehension of that fact - when the facts change, hopefully the apprehension of the fact will change as well (hence the proposition will change) *over-time.

Any way, I know this is not totally relevant to your question, but it is partially relevant. The question is very old and very good. (p.s. My example was borrowed from the book: 'Riddles of Existence: A Guided Tour of Metaphysics' by Theodor Sider and Earl Conee.

Answer 4

Symbolic logic deals with truth values. In so far as truth values are "time dependent," then it seems like "aspects" of logic is affected by time. A proposition uttered at different times is going to have different truth values. "It is raining outside," might be true today and not true tomorrow. I am not sure if this is what you are asking.

Regarding your example of parallels, I do not think this has much to do with symbolic logic. It is a tautology which arises from the definition of "parallel." Perhaps there are similar examples in regards to time (like maybe "If event A happened before event B, then event B happened after event A.") But this is really more consequences of our definition of the terms than rules of symbolic logic. If you are asking for some examples like that, I think it might be a dictionary, not a logic book, that would be the most help.