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As in the title can you give a succint explanation that goes beyond definitions?

Edit: Here is what I understand of these so far.

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    1) an argument may have more than ore premises. – Mauro ALLEGRANZA Sep 9 '16 at 17:36
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    Yes; a syll is a three-sentences argument: two premises and one conclusion. – Mauro ALLEGRANZA Sep 9 '16 at 17:46
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    I wouldn't necessarily treat these as overly technical terms. A premise is a claim that must hold true for an argument to work. Think of it like a foundation. A premise is often defined as an "assumption," and while some premises are assumptions, some are also argued for in their own right. The number of premises isn't necessarily two. A proposition, a statement, and an assertion are the same thing, depending on context. Are you dealing with philosophy of language? – Student Sep 9 '16 at 17:49
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    One kind of proposition well-know in logic is the categorical proposition that is the core of Aristotelian logic : "Every Human is Mortal", "Some Cats are Black". Their "logical form" is respectively: "Mortality belongs to all Men" where Mortality and Humanity are terms. – Mauro ALLEGRANZA Sep 9 '16 at 18:04
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    For a clear introduction, you can see Ch.1 of Peter Smith, An Introduction to Formal Logic (2003). – Mauro ALLEGRANZA Sep 9 '16 at 19:41
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A sentence is a statement or an assertion telling you the facts of the matter; its not asking you to evaluate whether it is true or not.

Socrates is Greek

A sentence is a proposition when it is asking you to evaluate whether it is true or not; in English this is shown by a sentence in the form of a question

Is Socrates Greek?

In formal logic question marks aren't used; one has to understand this from the context; I could write this out as

IsGreek(Socrates)

This makes it obvious what the connection is to the above sentence; there are two parts to this sentence and the first part 'IsGreek' is called the predicate, and the second part 'Socrates' is called the subject.

This is a style of refering to propositions that one sees in verbose programming languages; but equally I could write it out more enigmatically as:

G(Socrates)

which by merely looking at it without any explanation tells you very little...could you guess that G(x) stands for "Is x Greek?"

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