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On Wikipedia it is given that

In logic and philosophy, an argument is a series of statements (in a natural language), called the premises or premisses (both spellings are acceptable), intended to determine the degree of truth of another statement, the conclusion.

Here nowhere is implied that it also contains the conclusion, so, Does an argument contain conclusion? If yes, then how many conclusive statements? What is the general structure of an argument?

Navneet
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  • In math, an argument is a parameter that must be provided in order for a function to result in something meaningful. I think you might be looking for a different term, but I have no idea what it may be. – Andrew Chin Dec 16 '20 at 02:57
  • Do you mean how to write a proof? This question already exists here. – Toby Mak Dec 16 '20 at 03:25
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    You are quibbling over implementation details. – DanielV Dec 16 '20 at 03:28
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    The problem is that proofs in mathematics do not follow the same structure as those in logic or philosophy. If you could provide us with a specific example of what you would like to prove, we can better help you. – Toby Mak Dec 16 '20 at 12:27
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    See What is an argument?: "a collection of premises and [usually one] conclusion. The premises provide the evidence that supports the conclusion." A Deductive argument (or: Deduction) is "a pair $⟨Γ,ϕ⟩$, where $Γ$ is a set of sentences, the premises, and $ϕ$ is a single sentence, the conclusion" and "the evidence supporting the conclusion" are logical rules of inference. – Mauro ALLEGRANZA Dec 16 '20 at 14:43

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The terminology is not used entirely uniformly.

If one considers "argument" as synonymous to "inference", i.e. as a claim that may be valid or invalid, then:

An argument is a tuple $\langle \Gamma, \phi \rangle$ where

  • $\Gamma$ is a set of sentences, the premises,
  • $\phi$ is a single sentence, the conclusion.

So an argument has exactly one conclusion and an arbitrary number of premises.

In principle a set can be empty, and all definitions will work in the same way for the borderline case where there are no premises, but in this case one may not want to call it "argument", but rather simply a (valid or invalid) sentence.

If one considers "argument" as a series of reasoning steps, i.e. as a proof, rather than just a pair of premises and conclusion, then:

An argument is a sequence of sentences $(\phi_1, \ldots, \phi_n)$, where

  • each reasoning step $\phi_i$ is either a premise or the result of applying an inference rule on an appropriate number of previous steps $\phi_j, j < i$,
  • $\phi_n$ is the conclusion.

Note that axioms/lemmata/world knowledge can be viewed as special kinds of inference rules that require no previous steps.

In any event, an argument contains a conclusion, and premsies if applicable.

Natalie Clarius
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