Shahar, they are not necessary at all in any metaphysical sense. For almost every law of logic you can think of, someone has thought of a consistent and even useful logical system that does not include it. That includes the law of the excluded middle, which many people, including the Rabbi, claim is “self-evident.”

In my view, the justification for the laws you know is instrumental, similar to the justification for the laws of arithmetic. In many contexts, in many situations, what you infer with their help corresponds to reality, and therefore there is every reason to use them until you run into a situation in which they no longer work. In such a case, you simply use a different system.

What does it mean for something to have the definition X and not-X?
And what about something a bit softer, like a triangle that is a circle?

By the way, you’re welcome to read this too:

האם אמונה בסתירות לוגיות היא אפשרית?[1]

Tam,
1) So I conclude from what you’re saying that if I say a sentence that I really want to believe but according to classical logic it is meaningless—then there is another system of logical laws that would fit it?
If so, then even if I am limited to these laws, as long as they are not necessities of reality but only my own limitation, why should I think that God is limited by them too? I’ll simply say that He is not characterized by logical contradictions because He has His own system of laws. In that case, what is the point of any investigation of Him on my part, for example regarding the question of foreknowledge and free choice? After all, in any case the answer will always ultimately be that we are simply too small to understand (as you yourself said, this does not compel any metaphysical dimension).
2) When you say “use them until they no longer work,” do you mean that they fail to describe the reality I see (empirically), about which I have no doubt?

Sh, I understand that the statements you mentioned are meaningless, and I also know the article. I’m just wondering how necessary and self-evident these laws really are. In that article the Rabbi emphasizes that he starts from the assumption that God can be characterized by logical contradictions, and on that basis he builds his argument there (since at the end of the day there is an a priori contradiction, and it is resolved thanks to the assumption I mentioned).
However, from what I understand from the Rabbi, he does not really assume that God is characterized by logical contradictions, and that is essentially what I’m asking here.

Shahar,

1) Logic does not deal with “meaning.” Think of it as a system of rules that defines rules and relations between them. The rules are defined abstractly, and so are the relations between them. It’s like mathematics. In high school we learned to work with polynomials, multiply them and add them, without really needing to know what the X there actually is. The idea is similar in logic. There is a simplified system of rules and relations between them, and you don’t need to plug an actual “sentence” in Hebrew into it.

As for whether God is “limited” by the laws of logic—you said that you can say something about the logic that describes God’s behavior. That is true. But is that really how God’s logic works? There is a difference between hypotheses and a view that there is reason to take seriously. That is true both regarding God’s logic and regarding any other attribute of His.

2) For example.

Sh,
The first paragraph I wrote to Shahar. You asked interesting questions (with an answer), but one should not mix up meaning with logic.

In any case, just to help us move on from this point: if I have 10 apples and I bought 4 more, now I have 14 apples. If the time on your clock (with hands) was 10 at night and 4 hours passed, the time is now 2 at night, not 14. I have no problem adopting different systems of addition in the appropriate contexts. It turns out that a similar approach is useful in logic too. For you and me, it is not useful to talk about shapes by means of a logic in which one can speak about a “triangle that is a circle.” That confuses us more than it helps us. So we won’t do that.

How would you distinguish between a “hypothesis” and a “view that should be taken seriously” regarding the system of laws under which God operates?

From what I understood from the Rabbi, there is only one relevant system of laws, and it is “self-evident,” and it applies not only to us but to God as well. If I’m making sure I understand your view correctly, are you claiming that there actually are many systems that can be relevant, and there is no necessity specifically for that binary system such as the “principle of the excluded middle”?

Shahar,
Regarding the first part: I don’t have a principled answer to that question that would fit every hypothesis or every view that should be taken seriously. I can explain why in my opinion the proposal you raised regarding God’s logic is a hypothesis there is no reason to take seriously. Would that be enough?

Regarding the second part: I claim that the logic that is “self-evident” to the Rabbi is not self-evident to many people in many contexts. It is not some kind of metaphysical necessity. In certain situations, there can be other logics that will lead to better results in the following sense: what we infer through them will correspond to reality better.

(Tam, if I understand correctly, then you should know that you’ve taken an old and already-used screen name here.)

Someone who has never dealt with logic and thinking can think and say nonsense and believe that these are correct things.

And in general, logic does not hold in nature. Quantum reality is anti-logical in its essence.

I think the Rabbi actually has dealt with logic, and he disagrees with you (about the second part, not the first).

What mainly surprised me in this discussion is that there really are many different logical systems.
If anyone knows how to point me to sources that aren’t too complicated to read about this, I’d be very grateful 🙂

Cleaning Services, I don’t know who that is, but it’s not me. What is that screen name known for?

The Last Decisor, quantum reality is anti-logical? How? I’m not an expert in physics, but on the face of it that sounds incorrect.

Shahar, unfortunately, I don’t know of simple sources. I started with a logic course for mathematicians, and from there over time I learned various specific things along the way.

Anyone who thinks quantum mechanics conforms to logic has not understood it.

In logic, things can be true or false. In reality, things are in a probabilistic state.

In logic, a thing and its opposite cannot both be the case. In quantum mechanics, a thing is both here and not here as long as no measurement has been performed.

And many other principles that certainly seemed correct to us collapse and turn out to be wrong