If Scott Walker is made of cheese, then Wisconsin is in the Midwest.
Or, better yet:
If Scott Walker is made of fresh curds, Wisconsin state workers have 5 weeks of paid vacation (like Sweden).
Oddly enough, if either of these two conditional statements is formalized in the typical way, they both will be considered true. Or, to be more precise, they will both be considered valid. The "paradox" here is that, intuitively, neither argument appears true or valid in any way at all. So why are they formalized in this way?
The key is a move away from content and toward structure that is typical of much Euroamerican thought starting at the end of the 19th century. In logic, this move is reflected in a separation of "validity" from "soundness." A "valid" argument is one that has the proper structure, whereas a "sound" one contains true premises. Whatever (potentially nefarious) motivations might underlie this separation, it certainly has proved useful, since it was essential to the development of computers. If your fridge has a microprocessor in it, this reasoning about Scott Walker would like perfectly fine to it. And this is why fridges do not run the world (yet).
But to get back to the formalization, what is it? A conditional is often formalized as a "material implication." Here's a simple version:
p ⇒ q
This is read, "if p, then q." In our example, "p" and "q" stand for the sentences that are the "antecedent" (p = If Scott Walker is made of fresh curds) and the "consequent" (q = Wisconsin state workers have 5 weeks of paid vacation).
The next step is to understand that this type of conditional can be reduced to a simpler logical operation, namely, a conjunction ("and"). So:
p ⇒ q ≡ ¬(p∧¬q)
We can read this as: "the statement, 'if p then q', is logically equivalent to the statement, 'it is not the case that p and not-q.'
This way of rendering the conditional makes a certain amount of sense. Take an obvious example: "if Obama was born in Hawaii, then he is a US citizen." Here, the intuition is that this is equivalent to saying, "It is not the case that Obama was born in Hawaii and yet he is not a US citizen."
While intuitive to a certain extent, this way of reducing a material implication to a simpler operation, the conjunction "and" (∧), completely ignores any relation between p and q. When we look at the possible values for this formalization, the problem becomes obvious:
| p | q | ¬q | (p∧¬q) | ¬(p∧¬q) | p ⇒ q |
| T | T | F | F | T | T |
| T | F | T | T | F | F |
| F | T | F | F | T | T |
| F | F | T | F | T | T |
This truth table shows that the conditional is false only when the antecedent is true (Obama was born in Hawaii) but the consequent is false (It is not the case that he is a US citizen). The problem, however, is especially the third and fourth lines: as long as the antecedent (p) is false, the conditional will always be true. Thus, we say, "If Scott Walker is made of fresh curds, Wisconsin state workers have 5 weeks of paid vacation (like Sweden)." And this conditional is always true because Scott Walker is not made of fresh curds (at least, not entirely).
Now, despite the political success of arguments that begin with a false antecedent ("If Saddam had WMDs, then ..."), most of the time we recognize that arguments of this kind make no sense (We just say, "But Saddam did not have WMDs!"). Yet in formal terms, a conditional with a false antecedent always remains valid, despite our intuition. And the reason it remains valid is that structure has been divorced from content, such that there is no relation between the antecedent (p) and consequent (q) that allows us to reason from one to the other. Instead, the relation between the two is a mere conjunction, which amounts to simply putting one next to the other without any relation between them. If we understood that the conditional required such a relation, then the minute the antecedent (p) was false, we would say, "Wait a minute! Your argument only makes sense if this first statement is true!"
Buddhist thinkers starting with Dharmakīrti recognized this problem, and for them the use of a mere conjunction amounts to a "mere co-occurrence" (sahabhāvamātra) of the antecedent and consequent. Dharmakīrti rejects mere co-occurrence as adequate to understanding the way we reason, and he thus developed the notion of a "natural relation" (svabhāvapratibandha) that attempts to describe more intuitively the way that we use reason.
More on that some other time....
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