I've been thinking about tautologies all day long. Don't ask me why; they're not in any paper I'm currently working on (that I know of). So finally, on the train home from work, I started scrabbling a bit in my notebook. When I actually got home and checked what a tautology is, I had to make some adjustments in my thinking. Here's what I came up with:
First, let's get the (semi)-formal definition out of the away: in propositional logic a tautology is a propositional formula that is true under any possible valuation (also called a truth assignment or an interpretation) of its propositional variables (Wikipedia). Straight forward enough.
Example: the not so meaningful proposition "A or not-A" is a tautology (oddly enough, in propositional logic, truth, as it is manifested in a tautology, is meaningless as it adds nothing new to our knowledge of the world, as Wittgenstein pointed out; it is the contingent truth that may hold the more interesting daily 'truths').
OK. But if we translate it to the natural language, for, shall we say "it will either rain or it will not rain" things get complicated. According to the law of the excluded middle there are only two options: rain or no rain. However, I propose, that for the 'only' part of the sentence to work (and thus create a tautology) one has to have some sort of "knowledge of the world" (whether it is about rain, the possibility of rain or even, perhaps, the application of logical laws on the subject matter itself). If this is so, then a natural language tautology is not pure a-priori but requires some sort of empirical elements.
There are three possible and mutually exclusive conclusions I can draw:
1. The proposition I gave as an example is not a tautology because of the supposedly empirical element (it requires verification and contains the possibility of it being not true).
2. The proposition is a tautology. Natural language tautologies, unlike formal language tautologies, do contain an empirical grain.
3. There was an error in my deduction/thought process and there is no empirical grain in the proposition.
Considering how tired I am right now, I'm leaning towards option 3.
This post's song, not unlike previous posts, has some pun intended. Regardless of my sorry, layman doubling here though, it is a good song by a good band.
Athlete - Best Not to Think About It {MP3} (from Beyond the Neighbourhood)
Band picture from their artist's profile on Last.fm.
Bill Callahan
13 years ago