# Argument

(Redirected from Soundness)
Argument terminology used in logic
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In logic, an argument (Latin argumentum: "proof, evidence, token, subject, contents") is a connected series of statements or propositions, called premises, that are intended to provide support, justification or evidence for the truth of another statement, the conclusion.[1][2]

To assess an argument, one must see whether its premises support its conclusion, more specifically, one must see whether the argument is either deductively valid and sound or inductively strong and cogent.[3][4]

## Deductive

A deductive argument asserts that the truth of the conclusion is a logical consequence (C) of the premises (P). Deductive arguments are judged by the properties of validity and soundness.[5] An argument is valid if and only if the conclusion is a logical consequence of the premises. A sound argument is a valid argument with true premises.

### Validity

In order for an argument to be valid, it has to satisfy the following condition: if the premises are true, then the conclusion has to be true as well. In other words, an argument is logically valid only in the case where it is impossible for the premises to be true and the conclusion false at the same time. This means that the premises may be false, but if they weren’t, the conclusion would be true. For example:

P1: All birds can fly.
P2: Penguins are birds.
C: Therefore, penguins can fly.

However, we know for a fact that penguins cannot fly. This argument is valid because, assuming the premises are true, the conclusion must be true. However, the first premise is false. Not all birds can fly. Birds are scientifically defined as “a group of warm-blooded vertebrates constituting the class Aves, characterized by feathers, toothless beaked jaws, the laying of hard-shelled eggs, a high metabolic rate, a four-chambered heart, and a strong yet lightweight skeleton.”

Validity is completely determined by an argument’s structure, not its content. If some argument is valid, then every argument with the same structure is also valid.

P2: The earth is round.
C: Therefore, the earth is a basketball

The overall structure of this argument lies below.

P1: All X are Y.
P2: Z is Y.
C: Therefore, Z is X.

Any argument with this structure is not valid. While the conclusion may be sometimes true, the logic is fallacious.

Inversely, dismissing any otherwise-truthful proposition as false simply based on the invalidity of how it is argued is committing the fallacy fallacy. This is because there are cases where true conclusions can come out from false premises.

Invalid arguments involve several fallacies that do not satisfy the requirement that an argument must deduce a conclusion that is logically coherent. A common example is the non sequitur, where the conclusion is completely disconnected from the premises.

Not all fallacious arguments are invalid. In a circular argument, the conclusion actually is a premise, so the argument is trivially valid. It is completely uninformative, however, and doesn't really prove anything.

### Soundness

Soundness is related to validity and has the following requirements:

1. The argument is valid.
2. The argument has true premises.

The following argument is valid and sound.

P1: All Greeks are human.
P2: All humans are mortal.
C: Therefore, all Greeks are mortal.

The above example is based on a simple argument structure, but arguments can have many many premises, which can make debating the soundness of an argument extremely difficult in some cases.

Note that an argument can be valid without being sound. Take for example:

P1: If someone knows and employs logic and scientific reasoning, then they do not propagate woo.
P2: Deepak Chopra knows and employs logic and scientific reasoning.
C: Therefore, he does not propagate woo.

The inference from P1 and P2 to C is valid (affirming the antecedent) and thus the argument is valid. However, because P2 is false, the argument is not sound.

## Inductive

An inductive argument asserts that the truth of the conclusion is supported by the premises (P) with some degree of probability. As the premises of an inductive argument do not necessitate the truth of the conclusion, the criteria of validity and soundness cannot be used to evaluate an inductive argument. Inductive arguments are instead judged by the properties of strength and cogency.

### Strength

In order for an argument to be strong, it must satisfy the following condition: if the premises are true, then it is improbable that the conclusion can be false. It is not impossible for the conclusion to be false if the premises are true, but it is very likely to be true. That being said, the distinction between strong and weak arguments is a matter of degree rather than being all-or-nothing. For example, a strong argument would be:

P1: 90% of humans are right-handed.
P2: Socrates is a human.
C: Therefore, Socrates is probably right-handed.

C might not necessarily be true even if P1 and P2 are true, but the premises give us good reason to believe that the conclusion is true.

### Cogency

Cogency can be compared to soundness, in that an argument is cogent if all of its premises are true. As strength is a part of the definition of cogency, it is not possible for a weak argument to be cogent. However, it is possible for a strong argument to be uncogent.

## In debate or discourse

In everyday practice an argument may be structured into talking points, issues that are supposed to help support said argument. Talking points based on distorted or false reality are often used in propaganda venues and political debates in tandem with loaded language to sway the course of a debate towards a predetermined conclusion. Such tactics turn an argument into emotional manipulation (having an argument) as opposed to logical exercise (making an argument).[6]