# logic

nature and application of logic

## Introduction to logic

This post follows others about logic, such as here. Purpose The purpose of logic is to ensure that one’s discourse makes sense. The most important part of making sense is avoiding contradictions, which would both affirm and deny a proposition. Some propositions may be affirmed in part and denied in part; that is different. The […]

## N-ary distinctions

The ground of each distinction is an indistinct mass or state or condition, a kind of whole without parts or at least without parts that have been discerned. Every instance of the whole is at first, an instance of one mass or state or condition. A unary distinction is a discernment of something out of

## Squares of opposition

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

## Moral and ethical distinctions

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

## 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,

## 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. Set theory

## 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

## 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

## 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

## 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.