They are perfectly valid rules of reasoning, of course. Wikipedia cites Aristotle: :
- The law of identity: “that every thing is the same with itself and different from another”: A is A and not ~A.
- The Law of Non-contradiction: that “one cannot say of something that it is and that it is not in the same respect and at the same time”
- Law of Excluded Middle: “But on the other hand there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate.”
And of course they work just fine for binary, true-or-false, statements, which is why Boolean logic is so powerful.
But I suggest they are not Laws of Thought.
As far as I can see (and I’m neither a philosopher nor a logician) they don’t work at all well for probabilistic statements:
- A thing can be both possibly A but also possibly not-A.
- A thing can be possibly something, and possibly not something, in the same respect and in the same time.
- And most importantly, a proposition can be possibly true AND its negation can be also possibly true.
Jacob Cohen in his great paper, The Earth is Round (p<.05) writes:
The following syllogism is sensible and also the formally correct modus tollens:
- If a person is a Martian, then he is not a member of Congress
- This person is a member of Congress
- Therefore, he is not a Martian.
Sounds reasonable, no? This nes syllogism is not sensible because the major premise is wrong, but the reasoning is as before and still a formally correct modus tollens:
- If a person is an American, then he is not a member of Congress. (WRONG!)
- This person is a member of Congress
- Therefore, he is not an American.
If the major premise is made sensible by making it probabilistic, not absolute, the syllogism becomes formally incorrect and leads to a conclusion that is not sensible:
- If a person is an American, then he is probably not a member of Congress (TRUE, RIGHT?)
- This person is a member of Congress.
- Therefore, he is probably not an American.
All this doesn’t mean that the so-called Laws of Thought are false, but that they aren’t Laws of Thought, because, I submit, thinking is fundamentally probabilistic, and probably (heh), specifically, Bayesian. The so-called Laws of Thought are a special case of human reasoning applicable when we are dealing with certainties.as we can be, if we define our axioms ab initio, and per arguendo. But in day-to-day reasoning, nothing is certain, and we behave like scientists (at best) or like politicians (at worst) making the best fitting models we can to the data available, and conducting on-line error-minimising optimisation processes in coming to provisional (if we are lucky) decisions or least-risky decisions (if we have to act earlier before we have access to all the data we’d ideally like).
And I suspect that this is why Barry et al at Uncommon Descent have such a Thing about the three classical Laws of Thought. ID, as she is spoke, is not scientific, although sometimes mathematical, and frequently theological. Which is not to say ID couldn’t be scientific – it could. But to be so, its practitioners would have to understand the probabilistic nature of scientific reasoning, and the provisional nature of its conclusions, and for all the ID words that have been written about probability, ID proponents do not, in my experience, fundamentally understand what probabilities are probabilities of, and what information is required to calculate them (even though they define probabilities as bits of information).
I suggest they need to get outside the binary “Laws of Thought”, and start to understand probabilistic Thinking. Which will also lead to a greater understanding of Intelligence, and thus of Design, but does require dropping the notion that any proposition must be either True or False.