Philosophical questions can be grouped into categories. These groupings allow philosophers to focus on a set of similar topics and interact with other thinkers who are interested in the same questions. The groupings also make philosophy easier for students to approach. Students can learn the basic principles involved in one aspect of the field without being overwhelmed with the entire set of philosophical theories.
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In mathematics, it is known that 2 + 2 = 4, but there is also knowing how to add two numbers, and knowing a person (e.g., oneself), place (e.g., one’s hometown), thing (e.g., cars), or activity (e.g., addition). Some philosophers think there is an important distinction between “knowing that” (know a concept), “knowing how” (understand an operation), and “acquaintance-knowledge” (know by relation), with epistemology being primarily concerned with the first of these.
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Historically, the symbol dx was taken to represent an infinitesimally “small piece” of the independent variable x to be multiplied by the integrand and summed up in an infinite sense. While this notion is still heuristically useful, later mathematicians have deemed infinitesimal quantities to be untenable from the standpoint of the real number system. In introductory calculus, the expression dx is therefore not assigned an independent meaning.
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