# Are verb tenses actually irrelevant in logic?

In my Introduction to Logic course, we learned that verb tenses are irrelevant when symbolizing and deducing arguments. However, it seems to me that the verb tenses could sometimes choose whether or not a set of sentences is inconsistent.

For example:

Premise 1: Bill ate a hamburger.
Premise 2: Bill will not eat a hamburger.

If we ignored the verb tenses and symbolized this as B, ~B....then we would conclude that the 2 premises are contradictory....

However, if we do consider the verb tenses, they don't seem to be contradictory. Premise 1 indicates that Bill ate a hamburger in the past, and Premise 2 indicates that Bill will not eat a hamburger in the future.... These are perfectly consistent, are they not?

• In elementary logic time-related issues, and therefore tenses, are not explicitly included. This means that some reasoning where they matter can not be formalized in it. But you can sidestep this in your example by defining two separate propositions: ate-in-the-past, BP, and will-eat-in-the-future, BF. Then BP and ~BF are consistent. There is temporal logic that takes time into account more systematically, but it is non-elementary. Sep 2 '19 at 0:28
• @Conifold thank you very much!
– Lily
Sep 2 '19 at 14:29

They are "irrelevant" in the sense that standard first-order logic does not give us a way to systematically treat them, so in translation these more fine-grained distinctions are usually dropped in order to keep the symbolization simple.

For example, in natural language,

from

Bill has never eaten a hamburger

we should be able to infer

Bill didn't eat a hamburger yesterday

but this deduction is not possible in first-order logic based on the semantics of the verb tenses alone. We would need special predicates and additional axioms in order to carry out such inferences.

Likewise, in order to express the difference (and non-contradictoryness) between

Bill ate a hamburger

and

Bill will (not) eat a hamburger

we would have to encode the different verb tenses as two different predicates -- like eat-in-the-past and eat-in-the-future.

Such a symbolization is of course possible, and if you do it this way, there results no contradiction in negating the one of them. But such a more fine-grained symbolization that explicitly encodes tense is usually not done -- and this is what is presumably meant by your source by "verb tense is irrelevant for logic" -- because for the valid arguments that elementary logic can treat, tense does not play a role, since it is not systematically "recognized" by the logic anyway, so we might as well keep the language simple and, in the translation, drop the additional complication of tense that the logic doesn't "understand" anyway.
Whether we say 1. "If Bill is hungry, he eats a hamburger", 2. "Bill is hungry", 3. Therefore "Bill eats a hamburger" or 1. "If Bill is hungry, he will eat a hamburger, 2. "Bill is hungry", 3. Therefore "Bill will eat a hamburger", both inferences can be formalized by symbolizing the different tenses of "eat" as just "eat", and the inference will work in both cases, because the only thing that plays a role for the validity of the argument is modus ponens, and not whether the event expressed by the predication takes place now, in the past or in the future.
The arguments where the difference in time does matter, like the inference presented in my first example, can not be formally treated by standard logic anyway. And for all the inferences that are analyzable with standard logic, it makes no difference whether we talk about now or the past or the future. So for the sake of keeping the language simple and not have overly long predicates we can just translate all of them as "eat" and know as a background assumption that with this translation we mean now or the past or the future.

But that means that when we do want to express more fine-grained distinctions like truth of predications at different points of times, this needs to be done by an explicit (and not very elegant) treatment in the translation by symbolizing the different verb tenses as different predicates that are independent of each other, because FOL itself does not distinguish between different points in time by itself, it only knows predicates and any statement is considered to be evaluated at the same "time".

In order to treat tense and carry out inferences like the one above in a systematic way that more closely reflects how we do it in natural language, we need to enrich the logic and make use of systems like temporal logic or modal logic (or combinations thereof) -- these systems can treat predications under different tenses, but they are not what is usually referred to by ordinary "logic" (which would be standard classical propositional or first-order logic).

• Thank you so much! This is very helpful :)
– Lily
Sep 2 '19 at 14:14

Consider the example:

Premise 1: Bill ate a hamburger.
Premise 2: Bill will not eat a hamburger.

As the OP claims these two sentences are not contradictory. Dropping the information conveyed by the different tenses ignores something important about their meanings.

The authors of forallx suggest a different approach toward symbolizing sentences and their negations. One needs to treat negations more carefully: (page 26)

A sentence can be symbolized as ¬A if it can be paraphrased in English as ‘It is not the case that...’.

If we use that as a guide and consider Bill ate a hamburger to be A, then ¬A should be some sentence that we could paraphrase as It is not the case that Bill ate a hamburger. The second premise does not fit the expected paraphrasing of a negation of the first premise. As the OP notes, the first premise was about the past; the second premise was about the future.

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2019. http://forallx.openlogicproject.org/forallxyyc.pdf

• This just repeats the OP's observation that the two statements are not contradictory, but does not explain how this fits together with the often made claim verb tense is, in a sense, irrelevant in the translation from natural language to logic, which is what the OP actually asked about. Sep 2 '19 at 10:19
• @lemontree The OP's observation happens to be correct. The guide from forallx shows how one should interpret negation of a sentence in natural language. One keeps the tense and does not force a negation where there isn't one by dropping it. Sep 2 '19 at 12:48
• Well yes -- that's the result you get when you do keep the tense. But the question was why this is often not done. Sep 2 '19 at 12:50
• @lemontree The question is These are perfectly consistent, are they not? They are perfectly consistent unless one drops the tense and forces them to appear as negations of each other - which they are not. Sep 2 '19 at 12:52
• Yes, that's one sentence with a question mark in the body, but the main question is "Are verb tenses actually irrelevant in logic?" -- how to resolve the obvious conflict between what the OP observed and what they were told in their introductory logic class. Sep 2 '19 at 12:55