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- Thread starter Mr Davis 97
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Mark44

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I would say so, yes.I am studying propositional logic, and have studied how propositions can be combined with logical connectives and such, and truth tables can be used to analyze the resulted truth values, depending on the truth values of involved variables. However, when not talking in the theoretical, how do we know when propositions are actually true or false? For example, "The wall is blue." Is the truth value of this statement solely contingent on our definition of blue?

There are several axioms involving the = operator. The relevant one here is the reflexive property of equatlity. I.e., a number is equal to itself.Mr Davis 97 said:Also, what about mathematical statements? For example, what is the truth value of "1 = 1" dependent on? Do the truth values of statements in mathematics depend on the axioms of the system in question, such as maybe the axioms of arithmetic? How do we "prove" that 1 = 1?

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Stephen Tashi

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That illustrates the difference between mathematics and applying mathematics. As I recall, the mathematics of propositional logic simplyHowever, when not talking in the theoretical, how do we know when propositions are actually true or false?

There is nothing in mathematics that says "If you look at this real life situation, you must represent it in the following manner..." So mathematics does not tell you the "actual" truth values of things or even which things you must assign truth values to.

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Ssnow

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In general in a formal systems (or "theory") you start with a system of axioms that are evidently true, then by logic rules you deduce theorems and propositions from this set of axioms ... (as example you can think to relativity theory and his axiom of constancy of the velocity of the light,the theory predicts new results respect hold theories ...) so yes statements depends on the axioms ...Do the truth values of statements in mathematics depend on the axioms of the system in question, such as maybe the axioms of arithmetic?

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Stephen Tashi

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In the thread on the logic puzzle, as @haruspex pointed out:

There are self-referential statements that do not meet the criteria of being "propositions" because they cannot be assigned a single truth value. ( For example, in your other thread, suppose you had only 1 statement (instead of 100) and that statement said "1. Exactly 1 of these 1 statements is false". )Self-referential statements are not really allowed in a formal study of logic.

Do we apply propositional logic when we do mathematics ? Yes, in a informal sense, but not in the formal sense. Propositional logic itself is a field of mathematics. If we applied propositional logic to make statements about propositional logic, that would require making self-referential statements.

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