Q&A: Axioms in Logic
Axioms in Logic
Question
Are there axioms in logic?
If so—why am I bound by everything that follows from them? The same question applies to God as well.
If not—could you please explain why it is necessary? Why should the fact that, in our way of thinking, we arrived at a “logical” conclusion mean that it must be the absolute truth?
Answer
There are axioms in logic, but they are not axioms like those in any other axiomatic system. In logic, the axioms are necessary in and of themselves. You have no option not to assume them.
The request to justify logic is self-defeating. For whatever justifications I offer, you could ask for a justification of those as well. So where would we stop? We stop at those assumptions that are most self-evident to us, and that from our perspective do not require external justification—that is, grounding them in something clearer than they are. They are the clearest things to us.
I didn’t understand your question regarding God.
Discussion on Answer
These arguments have been discussed here ad nauseam. So I’ll just refer you to the article: https://mikyab.net/%d7%9b%d7%aa%d7%91%d7%99%d7%9d/%d7%9e%d7%90%d7%9e%d7%a8%d7%99%d7%9d/%d7%a2%d7%9c-%d7%aa%d7%95%d7%a8%d7%aa-%d7%94%d7%a7%d7%95%d7%95%d7%a0%d7%98%d7%99%d7%9d-%d7%95%d7%98%d7%a2%d7%a0%d7%95%d7%aa-%d7%90%d7%9e%d7%95%d7%a0%d7%95%d7%aa-%d7%a1%d7%aa%d7%99%d7%a8%d7%aa%d7%99
There’s much more on the site, and you can search for it.
In your answer you use phrases like: “You have no option not to assume them,” and “They are the clearest things to us.” Seemingly, that is true only for us as human beings, but perhaps there is a different logic that, for example, God adopts, and for Him that is the clearest and correct one.
If that is true, it undermines the validity of the logic familiar to us.