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A deductive argument is said to be valid or invalid. If one assumes the premises to be true (ignoring their actual truth values), would the conclusion follow with certainty? If yes, the argument is valid. Otherwise, it is invalid. In determining validity, the structure of the argument is essential to the determination, not the actual truth values. For example, consider the argument that because bats can fly (premise=true), and all flying creatures are birds (premise=false), therefore bats are birds (conclusion=false). If we assume the premises are true, the conclusion follows necessarily, and thus it is a valid argument. If a deductive argument is valid and its premises are all true, then it is also referred to as sound. Otherwise, it is unsound, as "bats are birds".
If all the premises of a valid deductive argument are true, then its conclusion must be true. In other words, it is impossible for the conclusion to be false if all the premises are true. Inductive arguments An inductive argument, on the other hand, asserts that the truth of the conclusion is supported to some degree of probability by the premises. For example, given that the U.S. military budget is the largest in the world (premise=true), then it is probable that it will remain so for the next 10 years (conclusion=true). Arguments that involve predictions are inductive, as the future is uncertain.

An inductive argument is said to be strong or weak. If the premises of an inductive argument are assumed true, is it probable the conclusion is also true? If so, the argument is strong. Otherwise, it is weak. A strong argument is said to be cogent if it has all true premises. Otherwise, the argument is uncogent. The military budget argument example above is a strong, cogent argument. Deductive Main article: Deductive argument A deductive argument is one that, if valid, has a conclusion that is entailed by its premises. In other words, the truth of the conclusion is a logical consequence of the premises—if the premises are true, then the conclusion must be true. It would be self-contradictory to assert the premises and deny the conclusion, because the negation of the conclusion is contradictory to the truth of the premises. Validity Main article: Validity (logic) Deductive arguments may be either valid or invalid. If an argument is valid, it is a valid deduction, and if its premises are true, the conclusion must be true: a valid argument cannot have true premises and a false conclusion. An argument is formally valid if and only if the denial of the conclusion is incompatible with accepting all the premises. The validity of an argument depends, however, not on the actual truth or falsity of its premises and conclusion, but solely on whether or not the argument has a valid logical form. The validity of an argument is not a guarantee of the truth of its conclusion. Under a given interpretation, a valid argument may have false premises that render it inconclusive: the conclusion of a valid argument with one or more false premises may be either true or false. Logic seeks to discover the valid forms, the forms that make arguments valid. A form of argument is valid if and only if the conclusion is true under all interpretations of that argument in which the premises are true. Since the validity of an argument depends solely on its form, an argument can be shown to be invalid by showing that its form is invalid. This can be done by giving a counter example of the same form of argument with premises that are true under a given interpretation, but a conclusion that is false under that interpretation. In informal logic this is called a counter argument. The form of argument can be shown by the use of symbols. For each argument form, there is a corresponding statement form, called a corresponding conditional, and an argument form is valid if and only if its corresponding conditional is a logical truth. A statement form which is logically true is also said to be a valid statement form. A statement form is a logical truth if it is true under all interpretations. A statement form can be shown to be a logical truth by either (a) showing that it is a tautology or (b) by means of a proof procedure. The corresponding conditional of a valid argument is a necessary truth (true in all possible worlds) and so the conclusion necessarily follows from the premises, or follows of logical necessity. The conclusion of a valid argument is not necessarily true, it depends on whether the premises are true. If the conclusion, itself, just so happens to be a necessary truth, it is so without regard to the premises. Some examples: All Greeks are human and all humans are mortal; therefore, all Greeks are mortal. : Valid argument; if the premises are true the conclusion must be true. Some Greeks are logicians and some logicians are tiresome; therefore, some Greeks are tiresome. Invalid argument: the tiresome logicians might all be Romans (for example). Either we are all doomed or we are all saved; we are not all saved; therefore, we are all doomed. Valid argument; the premises entail the conclusion. (This does not mean the conclusion has to be true; it is only true if the premises are true, which they may not be!) Some men are hawkers. Some hawkers are rich. Therefore, some men are rich. Invalid argument. This can be easier seen by giving a counter-example with the same argument form: Some people are herbivores. Some herbivores are zebras. Therefore, some people are zebras. Invalid argument, as it is possible that the premises be true and the conclusion false. In the above second to last case (Some men are hawkers...), the counter-example follows the same logical form as the previous argument, (Premise 1: "Some X are Y." Premise 2: "Some Y are Z." Conclusion: "Some X are Z.") in order to demonstrate that whatever hawkers may be, they may or may not be rich, in consideration of the premises as such. (See also: Existential import). The forms of argument that render deductions valid are well-established, however some invalid arguments can also be persuasive depending on their construction (inductive arguments, for example). (See also: Formal fallacy and Informal fallacy). Soundness Main article: Soundness A sound argument is a valid argument whose conclusion follows from its premise(s), and the premise(s) of which is/are true. Inductive Main article: Inductive reasoning Non-deductive logic is reasoning using arguments in which the premises support the conclusion but do not entail it. Forms of non-deductive logic include the statistical syllogism, which argues from generalizations true for the most part, and induction, a form of reasoning that makes generalizations based on individual instances. An inductive argument is said to be cogent if and only if the truth of the argument's premises would render the truth of the conclusion probable (i.e., the argument is strong), and the argument's premises are, in fact, true. Cogency can be considered inductive logic's analogue to deductive logic's "soundness". Despite its name, mathematical induction is not a form of inductive reasoning. The lack of deductive validity is known as the problem of induction. Defeasible arguments and argumentation schemes Main article: Argumentation scheme In modern argumentation theories, arguments are regarded as defeasible passages from premises to a conclusion. Defeasibility means that when additional information (new evidence or contrary arguments) is provided, the premises may be no longer lead to the conclusion (non-monotonic reasoning). This type of reasoning is referred to as defeasible reasoning. For instance we consider the famous Tweety example: Tweety is a bird. Birds generally fly. Therefore, Tweety (probably) flies. This argument is reasonable and the premises support the conclusion unless additional information indicating that the case is an exception comes in. If Tweety is a penguin, the inference is no longer justified by the premise. Defeasible arguments are based on generalizations that hold only in the majority of cases, but are subject to exceptions and defaults. In order to represent and assess defeasible reasoning, it is necessary to combine the logical rules (governing the acceptance of a conclusion based on the acceptance of its premises) with rules of material inference, governing how a premise can support a given conclusion (whether it is reasonable or not to draw a specific conclusion from a specific description of a state of affairs). Argumentation schemes have been developed to describe and assess the acceptability or the fallaciousness of defeasible arguments. Argumentation schemes are stereotypical patterns of inference, combining semantic-ontological relations with types of reasoning and logical axioms and representing the abstract structure of the most common types of natural arguments.[11] A typical example is the argument from expert opinion, shown below, which has two premises and a conclusion.[12] Argument from expert opinion Major Premise: Source E is an expert in subject domain S containing proposition A. Minor Premise: E asserts that proposition A is true (false). Conclusion: A is true (false). Each scheme may be associated with a set of critical questions, namely criteria for assessing dialectically the reasonableness and acceptability of an argument. The matching critical questions are the standard ways of casting the argument into doubt. By analogy Argument by analogy may be thought of as argument from the particular to particular. An argument by analogy may use a particular truth in a premise to argue towards a similar particular truth in the conclusion. For example, if A. Plato was mortal, and B. Socrates was like Plato in other respects, then asserting that C. Socrates was mortal is an example of argument by analogy because the reasoning employed in it proceeds from a particular truth in a premise (Plato was mortal) to a similar particular truth in the conclusion, namely that Socrates was mortal. Other kinds Other kinds of arguments may have different or additional standards of validity or justification. For example, Charles Taylor writes that so-called transcendental arguments are made up of a "chain of indispensability claims" that attempt to show why something is necessarily true based on its connection to our experience,[13] while Nikolas Kompridis has suggested that there are two types of "fallible" arguments: one based on truth claims, and the other based on the time-responsive disclosure of possibility (see world disclosure).[14] The late French philosopher Michel Foucault is said to have been a prominent advocate of this latter form of philosophical argument.[15] In informal logic This section needs additional citations for verification. (April 2020) (Learn how and when to remove this template message) Argument is an informal calculus, relating an effort to be performed or sum to be spent, to possible future gain, either economic or moral. In informal logic, according to one view, an argument is a connection between an individual action through which a generally accepted good is obtained. For example: You should marry Jane (individual action, individual decision) because she has the same temper as you. (generally accepted wisdom that marriage is good

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