Non sequitur (Latin for "it does not follow"), in formal logic, is an argument in which its conclusion does not follow from its premises.[1] In a non sequitur, the conclusion could be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion. All invalid arguments are special cases of non sequitur. The term has special applicability in law, having a formal legal definition. Many types of known non sequitur argument forms have been classified into many different types of logical fallacies.
Post hoc ergo propter hoc (Latin: "after this, therefore because of this") is a logical fallacy (of the questionable cause variety) that states "Since event Y followed event X, event Y must have been caused by event X." It is often shortened to simply post hoc. It is subtly different from the fallacy cum hoc ergo propter hoc ("with this, therefore because of this") (correlation does not imply causation), in which two things or events occur simultaneously or the chronological ordering is insignificant or unknown. Post hoc is a particularly tempting error because temporal sequence appears to be integral to causality. The fallacy lies in coming to a conclusion based solely on the order of events, rather than taking into account other factors that might rule out the connection.
modus tollens[1][2][3][4] (or modus tollendo tollens and also denying the consequent)[5] (Latin for "the way that denies by denying")[6] is a valid argument form and a rule of inference.
The inference rule modus tollens, also known as the law of contrapositive, validates the inference from 
implies 
and the contradictory of , to the contradictory of .
implies and the contradictory of , to the contradictory of .
In propositional logic, modus ponendo ponens (Latin for "the way that affirms by affirming"; often abbreviated to MP or modus ponens[1][2][3][4]) or implication elimination is a valid, simple argument form and rule of inference.[5] It can be summarized as "P implies Q; P is asserted to be true, so therefore Q must be true." The history of modus ponens goes back to antiquity.[6]
While modus ponens is one of the most commonly used concepts in logic it must not be mistaken for a
logical law; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the "rule of definition" and the "rule of substitution".[7] Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an ever-lengthening string of symbols; for this reason modus ponens is sometimes called the rule of detachment.[8] Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones",[9]and Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q [the consequent] . . . an inference is the dropping of a true premise; it is the dissolution of an implication".[10]
A justification for the "trust in inference is the belief that if the two former assertions [the antecedents] are not in error, the final assertion [the consequent] is not in error".[11] In other words: if one statement or propositionimplies a second one, and the first statement or proposition is true, then the second one is also true. If P implies Q and P is true, then Q is true.[12] An example is:
- If it is raining, I will meet you at the theater.
- It is raining.
- Therefore, I will meet you at the theater.
Modus ponens can be stated formally as:
where the rule is that whenever an instance of "P → Q" and "P" appear by themselves on lines of a logical proof, Q can validly be placed on a subsequent line; furthermore, the premise P and the implication "dissolves", their only trace being the symbol Q that is retained for use later e.g. in a more complex deduction.
It is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms such as affirming the consequent, denying the antecedent, and evidence of absence. Constructive dilemma is the disjunctive version of modus ponens. Hypothetical syllogism is closely related to modus ponens and sometimes thought of as "double modus ponens."
Ignoratio elenchi, also known as irrelevant conclusion,[1] is the informal fallacy of presenting an argument that may or may not be logically valid, but fails nonetheless to address the issue in question.
Ignoratio elenchi falls into the broad class of relevance fallacies.[2] It is one of the fallacies identified by Aristotle in his Organon. In a broader sense he asserted that all fallacies are a form of ignoratio elenchi.[3][4]
Ignoratio Elenchi, according to Aristotle, is a fallacy which arises from “ignorance of the nature of refutation.” In order to refute an assertion, Aristotle says we must prove it's contradictory; the proof, consequently, of a proposition which stood in any other relation than that to the original, would be an ignoratio elenchi… Since Aristotle, the scope of the fallacy has been extended to include all cases of proving the wrong point… “I am required to prove a certain conclusion; I prove, not that, but one which is likely to be mistaken for it; in that lies the fallacy… For instance, instead of proving that ‘this person has committed an atrocious fraud,’ you prove that ‘this fraud he is accused of is atrocious;’” … The nature of the fallacy, then, consists in substituting for a certain issue another which is more or less closely related to it, and arguing the substituted issue. The fallacy does not take into account whether the arguments do or do not really support the substituted issue, it only calls attention to the fact that they do not constitute a proof of the original one… It is a particularly prevalent and subtle fallacy and it assumes a great variety of forms. But whenever it occurs and whatever form it takes, it is brought about by an assumption that leads the person guilty of it to substitute for a definite subject of inquiry another which is in close relation with it.[5]—Arthur Ernest Davies, "Fallacies" in A Text-Book of Logic
Post hoc ergo propter hoc (Latin: "after this, therefore because of this") is a logical fallacy (of the questionable cause variety) that states "Since event Y followed event X, event Y must have been caused by event X." It is often shortened to simply post hoc. It is subtly different from the fallacy cum hoc ergo propter hoc ("with this, therefore because of this") (correlation does not imply causation), in which two things or events occur simultaneously or the chronological ordering is insignificant or unknown. Post hoc is a particularly tempting error because temporal sequence appears to be integral to causality. The fallacy lies in coming to a conclusion based solely on the order of events, rather than taking into account other factors that might rule out the connection.
The regression (or regressive) fallacy is an informal fallacy. It ascribes cause where none exists. The flaw is failing to account for natural fluctuations. It is frequently a special kind of the post hoc fallacy.Things like golf scores, the earth's temperature, and chronic back pain fluctuate naturally and usually regress towards the mean. The logical flaw is to make predictions that expect exceptional results to continue as if they were average (see Representativeness heuristic). People are most likely to take action when variance is at its peak. Then after results become more normal they believe that their action was the cause of the change when in fact it was not causal.
This use of the word "regression" was coined by Sir Francis Galton in a study from 1885 called "Regression Toward Mediocrity in Hereditary Stature". He showed that the height of children from very short or very tall parents would move towards the average. In fact, in any situation where two variables are less than perfectly correlated, an exceptional score on one variable may not be matched by an equally exceptional score on the other variable. The imperfect correlation between parents and children (height is not entirely heritable) means that the distribution of heights of their children will be centered somewhere between the average of the parents and the average of the population as whole. Thus, any single child can be more extreme than the parents, but the odds are against it.
Confirmation bias (also called confirmatory bias or myside bias) is the tendency of people to favor information that confirms their beliefs or hypotheses.[Note 1][1] People display this bias when they gather or remember information selectively, or when they interpret it in a biased way. The effect is stronger for emotionally charged issues and for deeply entrenched beliefs. People also tend to interpret ambiguous evidence as supporting their existing position. Biased search, interpretation and memory have been invoked to explainattitude polarization (when a disagreement becomes more extreme even though the different parties are exposed to the same evidence), belief perseverance (when beliefs persist after the evidence for them is shown to be false), the irrational primacy effect (a greater reliance on information encountered early in a series) and illusory correlation (when people falsely perceive an association between two events or situations).