Final answer:
Not all logical possibilities are necessarily mathematically possible and vice versa. Despite intuitive understandings, these domains are distinct, and scenarios in physics, like Einstein's theories, can showcase their differences.
Step-by-step explanation:
Is everything that is logically possible also mathematically possible, and vice versa? This question pertains to the realms of both logic and mathematics and explores their relationship. While many logical possibilities can be modeled mathematically, the two domains are not perfectly overlapping. For instance, in the context of language, we can intuitively understand grammatical rules that dictate the order of words in a sentence, such as 'How did that happen?' without having to test every permutation.
In mathematics, similar intuition applies to arithmetic and geometric truths that are not influenced by the skeptical hypotheses proposed by philosophers like Descartes, who questioned the certainty of knowledge. Despite the potential to dream or to be deceived, mathematical facts such as '1 + 1 = 2' or 'a square has four sides' hold true.
However, in physics, such as with Einstein's theories of relativity, what might seem logically plausible is not always mathematically consistent with the laws of physics. Measurement in different inertial frames, for example, must yield consistent results even if our intuition suggests otherwise. Therefore, while logic and mathematics often support each other, they do not always align perfectly in every scenario or discipline.