Logical argument in the context of Implicit assumption

In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.

In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems.

Analogy is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share.

Logically, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction. It is also used where at least one of the premises, or the conclusion, is general rather than particular in nature. It has the general form A is to B as C is to D.

In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof, and/or by ordinary human reason.

Some epistemologists deny that any proposition can be self-evident. For most others, one's belief that oneself is conscious and possesses free will are offered as examples of self-evidence. However, one's belief that someone else is conscious or has free will are not epistemically self-evident.

Self-deception or self-delusion is a process of denying or rationalizing away the relevance, significance, or importance of opposing evidence and logical argument. Self-deception involves convincing oneself of a truth (or lack of truth) so that one does not reveal any self-knowledge of the deception.

The Quinque viæ (Latin for "Five Ways") (sometimes called the "five proofs") are five logical arguments for the existence of God summarized by the 13th-century Catholic philosopher and theologian Thomas Aquinas in his book Summa Theologica. They are:

1. the argument from "first mover";
2. the argument from universal causation;
3. the argument from contingency;
4. the argument from degree;
5. the argument from final cause or ends ("teleological argument").

Aquinas expands the first of these – God as the "unmoved mover" – in his Summa Contra Gentiles.

The philosophical aspects of the abortion debate are logical arguments that can be made either in support of or in opposition to abortion. The philosophical arguments in the abortion debate are deontological or rights-based. The view that all or almost all abortion should be illegal generally rests on the claims that (1) the existence and moral right to life of human beings (human organisms) begins at or near conception-fertilization; that (2) induced abortion is the deliberate and unjust killing of the embryo in violation of its right to life; and that (3) the law should prohibit unjust violations of the right to life. The view that abortion should in most or all circumstances be legal generally rests on the claims that (1) women have a right to control what happens in and to their own bodies; that (2) abortion is a just exercise of this right; and that (3) the law should not criminalize just exercises of the right to control one's own body and its life-support functions.

Although both sides are likely to see the rights-based considerations as paramount, some popular arguments appeal to consequentialist or utilitarian considerations. For example, anti-abortion groups sometimes cite alleged medical and psychological risks of abortion, such as the existence of post-abortion syndrome or the abortion–breast cancer hypothesis. On the other side, abortion-rights groups say that criminalizing abortion will lead to the deaths of many women through "back-alley abortions", that unwanted children have a negative social impact, or conversely cite the legalized abortion and crime effect, and that reproductive rights are necessary to achieve the full and equal participation of women in society and the workforce. Consequentialist arguments on both sides tend to be vigorously disputed, although they are not widely discussed in the philosophical literature.

Unwritten rules, also called unspoken rules, are behavioral constraints imposed in organizations or societies that are not typically voiced or written down. They usually exist in unspoken and unwritten format because they form a part of the logical argument or course of action implied by tacit assumptions. Examples involving unspoken rules include unwritten and unofficial organizational hierarchies, organizational culture, and acceptable behavioral norms governing interactions between organizational members. These rules typically align with the behaviors of the local majority group and seem normal to them, but can be obscure, invisible, and exclusionary to minority groups.

A stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context. When the term already exists, this definition may, but does not necessarily, contradict the dictionary (lexical) definition of the term. Because of this, a stipulative definition cannot be "correct" or "incorrect" within its stipulated context; it can only differ from other definitions, but it can be useful for its intended purpose.

For example, in the riddle of induction by Nelson Goodman, "grue" was stipulated to be "a property of an object that makes it appear green if observed before some future time t, and blue if observed afterward". "Grue" has no meaning in standard English; therefore, Goodman created the new term and gave it a stipulative definition.