I am going to think out loud for a second here. And, my grasp of formal logic is basic and 20 years out of the class room. So, I guess what I’m saying is that this one might not be worth reading. But when has that ever stopped me?
I have heard the proposition that “if you increase taxes on a thing, you get less of it.” I am willing to accept that as true. However, in propositional logic, as I understand it, the contrapositive of a true statement is necessarily also true, but the negative of that statement is not necessarily true. Roughly speaking this would mean that the contrapositive of the statement, negating both aspects, would be true — for the proposition above, that would be something like, “if you are getting more of something, you have not increased taxes on it.” Meanwhile, the negative of the statement would be “if you decrease taxes on a thing, you get more of it.” That could be true, but it’s not a logical necessity.
Conservatives, it seems to me are taking the negative of the proposition as necessarily true. They apparently believe as an article of faith that if we decrease taxes on production, we will necessarily increase production. The main problem, probably more so than the logical fallacy involved, is that our economy is not a binary system with the tax rate as the only meaningful input. People have to have to be employed producing things and services of value; they have to have to retain a great deal of that value for their own purchasing needs; and they have to spend that value on something other than debt service.
Seems to me we have a system where people work more sporadically than they would like; where the value they generate by and large ends up in someone else’s pocket; and where the money they earn is used to service debt while their purchases are made through incurring more debt. Too much of the value generated is pooled in the hands of too few who don’t spend the money in ways that add sufficient value to the economy. Our economy is like a leaky steam engine wasting energy.
O.k, this post didn’t turn out any prettier than I anticipated. But, I’ll post it anyway, warts, logical gaps, and all.
Doug –
The form of a contrapositive is as follows:
Statement:
If A, then B.
Contrapositive:
If not B, then not A.
So the contrapositive of:
Would be:
In logic, a statement and its contrapositive are always both true or both false.
I agree with your description of a contrapositive, but I think your application is inaccurate. Your “not B” in this case should be “not getting less,” so that:
“If you are not getting less of a thing, then you have not increased taxes on it.”
Hmmm.
I think one difficulty is that the application of a contrapositive is more clear when ‘A’ and ‘B’ are simple true/false assertions, rather than descriptions of activities or conditions that may have multiple states or be affected by multiple factors.
That said, I agree that your formulation is at least as stringent as mine – but I’m less sure that this analysis is really meaningful in real-world terms – which I think supports your overall point!