The evaluation of the correctness of arguments is the core of this blog post.

We will focus on justifications as premises are to be evaluated with the scientific method. However, the quality of premises must be considered. Only *true* premises can guarantee the truth of the conclusion, so the reasons must be impeccable. Therefore, *acceptable* premises can provide for the acceptance of the conclusion. Additionally, all premises must be *consistent* to form the conclusion.

Deductive inference (validity) is then used to come to the conclusion. An inference is *valid*, if all premises are true and the conclusion must be true (where the *must* refers to the relation between premisses and conclusion not the conclusion itself). Consequently, a valid inference cannot have a false conclusion from true premises.

A central feature of valid premises is that if the conclusion is false, then one of the premises must be false. However, if all premises are true, but the conclusion is still false, the inference must be invalid.

**Formal validity** is based on the structure of the assertion, not the meaning. [latex](X \in A \lor X \in B) \land \neg X \in B \implies X \in A[/latex].

**Material validity** is based on the relation between the concepts. E.g. a square has four sides of equal length.

*Conditional Claims*

A **sufficient** condition A for B [latex]A\implies B[/latex]. Logically, B must be true if A occurs, but could be true due to different condition C. B is a **necessary** condition for A [latex]\neg B\implies \neg A[/latex]. A is true at most if B is true, however, there could be a C that is also necessary for A to be true.

Inferential schemes for conditional claims If [latex]A[/latex] then [latex]B[/latex] are *Modus Ponens* [latex]A\implies B[/latex] and *Modus Tollens* [latex]\neg B \implies \neg A[/latex]. Invalid schemes include *denying the antecedent* [latex]\net A\implies \neg B[/latex] and* affirming the consequent* [latex]B\implies A[/latex] are a **formal fallacy** in reasoning (*non-sequitur*).

In the **fallacy of equivocation **the same expression is used in different ways in the premises than in the conclusion.

In the **naturalistic fallacy** a normative claim is deduced from a descriptive claim.

Non-deductive inferences claim to be correct (but not valid). An inference is correct iff its premises together provide a good reason for accepting its conclusion. However, a central characteristics of correct non-deductive inferences is that the conclusion can be false, even if the premises are true. The conclusion is supported with different degrees and can be strengthened or weakened with additional premises. Non-formal fallacies may occur if the reasons are too weak to support the conclusion.

**Inductive inferences** are an important class of non-deductive inferences, where the premises are analysed with the help the theory of probability and statistics. *Enumerative induction* concludes from a sample property distribution the whole population property distribution. *Statistical syllogism* derives from a population that two properties have been observed in common and concludes that one implies the other. *Predictive induction* observes two properties in a sample and concludes that one implies the other. Usual fallacies include *too small samples*, *non-representative samples*, *relevant information not considered*, and *false deliberation regarding probability*.

*Argument by analogy*

A claim is justified by analogy to another claim. This argument is often fallacious, as *illustrative analogies* (do not justify conclusions), *irrelevant analogies*, *weak analogy*, and *not considering a relevant disanalogy*.

*Causal inferences*

A factor F is considered to be a causally relevent if for an event, two situations must differ in that the event only occurs in the situation in which F is present. Typicall fallacies include* inference from temporal sequence*, *inference from positive correlation*, and *inference the inverse causal relevance*.

*Inference to Best Explanation*

A hypothesis is justified because it is the best (closest) explanation for the obtaining of certain facts.

**Rules of reasoning**

Shifting the *burden of proof*, instead of justifying a controversial claim, is done by attacking the opponents position or demanding justification. Other ways of shifting are appeals to authority.

The *relevance* of reasoning demands that an argument is in favour of owns claim. Throwing in arguments that are not related to the claim break relevance.

The *accuracy* of reasoning is undermined by a “straw man”-fallacy, where an exaggeration or change of claims of the opponent is introduced to make it more susceptible to criticism. More generally, a different claim is attributed to opponent to attack them.

The *freedom of speech* needs to be preserved by allowing criticism and justification of arguments. Fallacies include *argument ad baculum* (if you believe A than you believe B), *argument ad misercordiam* (have pity because X), and *argument ad hominem *(attacking the person, rather than the argument).

*Implicit premises* must be stated if they complete the argument. Fallacies include attributing false implicit premises to opponents and not accepting implicit premises in one owns arguments.

*Shared premises* have to be accepted to reach a reasonable agreement about a controversial claim. Fallacies include retreating from shared premises or attributing claims to be shared premises.

Accepting results of previous argumentation is necessary. Otherwise fallacies such as *argument ad ignorantiam* (taking absence of evidence as evidence of absence) or equating the defence of a claim with its acceptance.