Zain's Guide to Overthinking Everything

 Laws of Logic Logic relies on fundamental principles known as the three classical laws of thought: the law of identity, the law of excluded middle, and the law of non-contradiction. Together, these laws lay the groundwork for reasoning and logical analysis such that philosophy, mathematics, and everyday conversation could not stand without them. In this blog post, we will delve into these three rules that govern rational discourse.   1. Law of Identity: The law of identity states that every object is necessarily identical to itself. For example, if we have a statement A, then A is true if and only if A is true. It can be represented as "A = A".   2. Law of Excluded Middle: The law of excluded middle states that for any proposition A, either A is true, or its negation is true as there is necessarily no middle ground or third option. In simpler terms, a proposition is either true or false, and there is no other possibility. This principle can be expressed as "A ∨ ¬A...

  Mathematical a priori Statements       A triangle having three sides and angles equaling 180 degrees is an analytic a priori since the predicate of 3 sides and 180 degrees are in the word triangle. The equation, 2+2=4, would be a synthetic a priori because the concept of four is not present in two.       In the case of a triangle having three sides and angles equaling 180 degrees, the concept of a triangle already contains within it the idea of having three sides and angles adding up to 180 degrees. All three-sided polygon has 180 degrees and all triangles are three-sided polygons by definition. Therefore, the truth of this statement is considered analytic a priori, as it is true by definition and can be known independently of experience unless it can be proven otherwise.        On the other hand, in the case of 2+2=4, the concept of four is not contained within the concept of two. Rather, the truth of this statemen...