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.

Tags: Laws, Logic, Method, Of, Socratic

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I should have mentioned that there are two places to find out how Leibniz thought about the principle of sufficient reason. One is his book, Theodicy, which has been translated into English and is available online and the other and perhaps more convenient source is the correspondence between Leibniz and Samuel Clarke. They both wrote in French, but translations are available and there is a nice modern edition in print, but not available online as far as I know.

Leibniz was critical of Newton's mechanics and the principle of sufficient reason comes into his views of motion. Clarke gave him an ingenious but muted objection to the sufficient reason principle. He suggested that in some cases the only possible reason would be the will of God. His example was the location of two objects A and B in the world as opposed to the possibility of their being exchanged in position. He could see no difference in anything due to such an exchange and thought the only reason for one positioning over another was God's will.

I was going to say, without knowing what's meant by the sufficient reason or explanation, it's not possible to make sense of all this. 

You're quite correct that the concept lacks the clarity we would demand in view of the experience of modern science, but still it is rather simple in essence. If there is only one possibility for a situation, then it is necessary, but if there are two or more possibilities, and one prevails, Leibniz thought there must be a reason.

The first question is: in a situation where there are several possibilities, but only one occurs, how do we know others are actually possible? Might not some 'hidden variable' account for their non-occurrence in reality?

Leibniz believed this is the best of all possible worlds, presumably on the grounds that the creator would not choose anything less than the best. Hence that need for the best must be justified in some way, there must be a reason it is the best.

If there is only one possibility for a situation, then it is necessary, but if there are two or more possibilities, and one prevails, Leibniz thought there must be a reason.

What's a "reason"?  Suppose you have a deterministic evolution, say of atoms in a gas zipping around and colliding with each other. 

You can predict the entire past and entire future from the configuration at each instant. 

So is the configuration at each instant the "reason", the necessary and sufficient cause, for the configurations at all the other instants? 

In that case, you would have a situation where A is the reason for B, AND B is the reason for A. 

Are the "reasons" allowed to be circular? 

That sort of thing. 

A deterministic perspective provides no room for multiple possibilities, but suppose it were possible at any given time to interject--make a free choice. Then the rationale is perhaps that choice, like our choices when we make them, requires reason or chance (it is arguable whether true random exists). If free will exists, such that the choice could not be determined by a prior state, then there must be an uncaused reason why one possibility was chosen over another. Without a Newtonian physics perspective, we could even apply this line of thinking to inanimate objects. For instance, if a leaf could fall to any place, why does it fall here? If there is the possibility of the leaf falling somewhere else, then that in some sense implies a choice, which implies, if not the monotheistic God, then at least a powerful, conscious mover.

Of course, the solution to all of this is to accept that the leaf could have only fallen in the exact place it has fallen, and that the illusion of choice was caused by being unaware of all the variables.

A deterministic perspective provides no room for multiple possibilities

Essentially this is Leibniz's principle of sufficient reason: wherever we see multiple possibilities, there is something (the sufficient reason) which determines the reality. 

wherever we see multiple possibilities, there is something (the sufficient reason) which determines the reality.

Isn't quantum randomness a counterexample to that?

Certainly. The randomness of radioactive decay is a good counterexample to the principle of sufficient reason. It also furnishes a counterexample to the identity of indiscernables, another Leibniz principle.

Quantum indeterminacy is such that it is impossible to predetermine the value of a particle, but it is also impossible for us to know whether an observed particle would have had any other possible value at a given time. Consider Dennett's cellular automata where it is impossible to determine the next state from the prior, but the next state follows definite rules; if you knew the rules, you could determine it, but it would be impossible to know the rules even if you knew all prior states after the origin. Admittedly, we also have no proof that there is only one possibility, but I think Dennett's system is a good analogy insofar that we can't know.

Quantum indeterminacy is such that it is impossible to predetermine the value of a particle, but it is also impossible for us to know whether an observed particle would have had any other possible value at a given time. Consider Dennett's cellular automata where it is impossible to determine the next state from the prior, but the next state follows definite rules; if you knew the rules, you could determine it,

In quantum mechanics there aren't hidden rules or hidden variables that rescue determinacy.  That's Bell's theorem

the illusion of choice was caused by being unaware of all the variables.

In 2011 there was a proof published that any extension of quantum mechanical theory, whether using hidden variables or otherwise, cannot provide a more accurate prediction of outcomes, assuming that observers can freely choose the measurement settings

I don't think any of this contradicts what I've been saying. There is no argument that scientists cannot predict QM particles with more accuracy, but whether QM particles are truly random in the sense that a certain particle could have, when observed, settled at a different value at a certain time. I don't see how you could disprove that without a time machine to take an exact same measurement again. To be sure, let's say that there are two properties to randomness:

1) Predictability

2) Freedom

What the Bell Theorem and the 2012 model proof tells us is that QM particles are truly unpredictable, and that there is nothing we could theoretically do to know more. But is this an argument for "metaphysical" indeterminism (for lack of better word)? Not at all. Scientists are not bothered by metaphysical indeterminism. Indeterminism in a scientific setting means that the value could not be determined. Philosophically, indeterminism must also mean a freedom of possibilities.

To illustrate, let's say that there is a particle p with two possible values [true, false]. At time t, p was measured with the value true. The Bell Theorem tells us that prior to time t, not only can we never know a definite value of p, but that p was truly indeterminate. What it does not necessarily tell us is that at time t, p could have been false.

The analogy I brought up earlier, the cellular automata, demonstrates that it is possible to use a complex mathematical rule to populate the surroundings of every dot, creating a pattern which is unpredictable (by drawing conclusions from all prior states) for any iteration. It does not mean that the pattern could have been anything else than what it is given that rule. Now I have admitted that we have no evidence of any such rule in QM. What the analogy shows us is the possibility of metaphysical determinism despite non-predictability.

(A little off-topic, but there is a tendency to greatly overestimate the effects of QM in the plainly observable universe. Indeterminacy does not prove we, or the leaf, have freedom of choice. If we could calculate fast enough all the variables (e.g. wind velocity and direction, gravity and center of gravity, leaf weight, atmospheric pressure, etc.), then it would be possible to predict the fall of a leaf, just as it is possible to predict the trajectory of a ball thrown with enough force to make these variables negligible. In either case, the QM variable is negligible.)

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