This is a very short course in logic for those who like to use the Socratic method in leading believers to see the falsity of theism. Even such a small course as this will prove helpful, for it is the very basis, the foundation of, logical discourse.
In your questioning of theists in order to lead them to the realization that theism has no basis in reality always remember, and when possible, utilize the three laws of logic, in establishing the truth or falsity of a thing.
What are the three laws of logic ? They are as follows.
(1) The Law of Identity, which states that something is itself, and not something else. The term being used corresponds and coincides with the thing being described.
(2) The Law of Non-contradiction. This law develops more fully the first law, in that it teaches that the thing being described in the first law cannot be both itself and not itself at the same time and in the same sense.
(3) The Law of the Excluded Middle. This final law says that a thing must be either true or false, it cannot be both. In other words, there is no middle ground. In other words, as an example, a woman cannot be a little pregnant.
Christians have tried to sneak in a fourth law, called the Law of Sufficient Cause. This is not one of the true laws of logic, there are only three, the three enumerated above. The purpose of this spurious fourth law is meant only to justify the existence of God as the sufficient cause of the universe.
So, there you have it. In using your Socratic questioning it would be only helpful to remember these three laws in establishing the truth or falsity of a thing.
It was merely an illustration of classification. Replace it with any other that suits you better—vetebrates and invertabrates, etc.
Allen, it's also a cliché.
I occasionally write articles read by people trained in the law. I either avoid clichés and certain other figures of speech or get responses I don't want.
You are quite right that it is important to choose examples aptly illustrating a point without introducing irrelevancies which distract unfocused or pedantic minds.
it is important to choose examples aptly illustrating a point without introducing irrelevancies which distract unfocused or pedantic minds.I can tell you worked on that :)
I disagree that we need to force classifications into a binary structure.
Non-binary classification can be handled by logic just fine.
The classification of species 1,2,3 in a genus G, for example:
species 1 → genus G
species 2 → genus G
species 3 → genus G
not (species 1 and species 2)
not (species 2 and species 3)
not (species 1 and species 3)
Perhaps you meant something else.
The point here is that classic logic only accounts for binary things, and most empirical observations aren't binary.
That's rather awkwardly worded.
Classical logic is two-valued—that is, a statement which has a truth-value is true or false. There have been a number of attempts to devise logics with three values, but quite often these attempts merely fail to assign a truth-value to certain classes of propositions—in other words the proponents of a third value are simply confused about the nature of truth-bearers within their systems. If statements without a truth value of true or false are removed, what usually remains is classical logic.
Perhaps the best known three-valued logic is Kleene's in which the values are true, false, and indeterminate. The problem with it is that there are no tautologies—that is, rules which remain true regardless of the truth-values assigned to the variables. Any formula with an indeterminate value for a variable is itself indeterminate.
The question is not whether 'empirical observations' are binary, but whether formal statements of them are true or false. Most people I think would prefer to call the statement
the distance from earth to its moon is 384,000 ± 21,000 km
a true statement than be satisfied with 'we cannot make a true or meaningful statement of the distance from the earth to the moon since the distance varies from time to time'.
Extensions or revisions of classical logic that have been successful do not involve the addition of truth values so much as trying to bring formalization to informal arguments outside the classical realm.
If statements without a truth value of true or false are removed, what usually remains is classical logic.
People devised more accurate ways to measure, or in the case of geometry they realized that the earth isn't a Euclidean plane.
The best laid plans....
Giving an honest answer to your question involves technical language not easily explained, but the general ideas are clear. It will be better to divide the answer into two parts.
There have been devised quite a number of different logics either revising or extending classical logic: modal, tense, deontic, epistemic, preference, imperative, and erotetic logics all extend classical logic in some way while many-valued, intuitionist, quantum and free logics revise it.
In addition to all these a systematic analysis of logic using category theory has been developed over the last half century. It reveals new properties of the underlying structure of logic and provides a clear definition and axiomatization of classical logic.
The two values of classical logic—true and false—are related to the roles of unique terminal and initial objects in a category and therefore have an essential character difficult to remove.