nature and application of logic
The traditional Aristotelian square of opposition is like that of first-order logic apart from existential import: Or in words: Outer negation is the contradictory, i.e., affirm/deny, and inner negation is the contrary, i.e., all/none. For quantifiers (or other operators) there is a duality square: Outer negation is negation of the whole quantifier; inner negation is …
What is moral exists without a necessary opposite. Moral truth, goodness, and beauty are defined as those that exist on their own, without the necessity of a contrary (inner) or contradictory (outer) opposite. God is moral because God exists without a necessary opposite. Whatever is of God is also moral. Whatever contradicts God or something …
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, …
(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 …
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 …
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 …
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 …
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. …
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 …
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 …
