logic

nature and application of logic

Logic and illogic

This post follows several on logic such as here. Contrary opposites are mutually distinguished terms. One cannot exist without the other. If one is taken away, the other is also. Examples of contraries are up and down, in and out, before and after. More than two possibilities might also be distinguished, such as negative, positive, …

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Set theory and logic and their dual

(1) Set theory and logic, (2) number and algebra, and (3) space and time are three foundational topics that each have duals. Let us begin with the standard approaches to these three topics, and then define duals to each of them. To some extent, the original and the dual may be used together. (1) Set …

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Combining equations

Given two equations with the same variable, how can they be combined? If the equations are consistent, they may be solved as simultaneous equations. But what if the equations are inconsistent? There are two ways to combine them in that case, one is OR, the other is AND. Consider the equations x = a and …

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Contraries as duals

Contrariety is a property of pairs of propositions, but it also applies to pairs of terms or concepts. “Two general terms are contraries if and only if, by virtue of their meaning alone, they apply to possible cases on opposite ends of a scale. Both terms cannot apply to the same possible case, but neither …

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Balancing contraries

Other posts on contraries include this. Contrary opposites entail one another. There is no north without south or tall without short, for example. Some things such as sex are contraries in some respects but not in all respects. Contrary opposites are symmetric. Contraries can be reversed or inverted, and they are still there. Since mirror …

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New fallacies

There are several online lists of fallacious arguments: Fallacies, Full alphabetic list of fallacies, Logical Fallacies Handlist, List of fallacies, List of Fallacious Arguments, and especially Master List of Logical Fallacies, A list of Latin names is here. Aristotle categorized rhetorical strategies under ethos, logos, and pathos. Ethos is an appeal to credibility or authority. …

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Contraries and contradictories

Propositions are contrary if they cannot both be true (though they both may be false). Propositions are contradictory when the truth of one implies the falsity of the other, and conversely. Two properties are contraries if their intersection is null and their union is a whole. A merism is a rhetorical combination of two contrary …

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Form and logic

I’ve written before about Laws of Form (the calculus of indications); see here and here. In the beginning is an undifferentiated state, an unmarked space. The first distinction is the first differentiation, the advent of a mark, a cross, a form. The unmarked state is the urgrund of the form, its origin and basis. The …

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Propositional logic calculation

George Boole is known for introducing a logical calculus for propositions in the mid-19th century. Although others before him such as Leibniz worked on logical calculi, Boole developed the first systematic one. Later C. S. Peirce and Gottlob Frege developed calculi that took into account the difference between universal and existential propositions. Since then many …

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Logic as arithmetic

George Boole wrote on “the laws of thought,” now known as Boolean Algebra, and started the discipline known as Symbolic Logic. A different George, George Spencer Brown, wrote on “the laws of form,” which presented an arithmetic system underlying logic. Below are two symbolic logics equivalent to Boolean algebra that resemble ordinary arithmetic in some …

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