There are still people who argue that the calculus does not solve the problem.
I would guess that they are wrong.
The real problem is that we construct abstract models of reality, and do our computations in those abstract models. The mistake is to assume that the model is reality. Zeno's paradox was due to a model that didn't fit well enough. It's a good illustration of why we need empirical evidence, and cannot just go by our theoretical deductions.
Zeno's paradox is due to a false premise: An Infinite sum cannot give a finite number. Calculus showed that this premise was false.
The laws of logic don't apply to reality. They apply to the human constructs that we use to model and describe reality. The logic can be done correctly, yet reach wrong conclusions, if it is used with respect to a model that does not fit well enough.
How would you define ''a model that does not fit well enough'' ? Would it not simply be a model that is missing some premises, or that some premises are false ? If this is the case then you are still well within the boundaries of logical thinking.
An argument that uses true premises and involves no fallacy will automatically give you a true conclusion, wether it concerns reality or abstract thought.
AbE I wrote it with the wrong ID and for some unknown reason I cannot edit it back.
AbE2 I don't want to be misunderstood here. I think I can accept that some abstract models do not apply when translated into reality. But this has nothing to do with logic, rather, it would be because of the difference between the nature of abstract thought and the nature of reality. (This is in fact what I am saying in my previous reply to CD)
Edited by AdminSlev, : No reason given.
Edited by AdminSlev, : No reason given.
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