Home Forums Math & Science Formal Logic

last updated by C.S Gitthens 4 weeks ago
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    • #4526
      C.S Gitthens
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      A topic that is geared towards utilizing mathematical logic, logical consequence, truth-functions, and a multitude of things in the field.

    • #4527
      C.S Gitthens
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      220

      Some people have different definitions or beliefs about the nature of logic, but I would just say that logic is the study of logical consequence. In short truth-preservation by virtue of its form. Basically in sum, that means that logic should preserve the truth throughout the premises to the conclusion necessarily. Ofc, this only applies to deductive arguments and not inductive arguments since inductive arguments rely on the probability that the conclusion follows from the premises. In formal logic, for example, we have this neat idea called “truth-functions” just like the arithmetic functions you have on a calculator also called “operators”, we have these operators too in logic, and the neat thing is that the operator depends on the truth of its components for its whole truth value. The operators in formal logic are defined via truth functions, they are called valuation functions. To demonstrate this let’s make a little compound statement by using the “material-conditional operator” also said in ordinary English as “if, then” so “If \(A\), then \(P\)” can be symbolized as “\(A \Rightarrow P\)”. If we assume that “\(A\)” is true, then “\(P\)” also must be true, (because if “\(P\)” is not true, while leaving “\(A\)” true, then we have an invalid argument) this can be symbolized as “\(\left \{ T, T \right \}\rightarrow \left \{ T \right \}\)” and also if “\(A\)” is false then “\(P\)” can still be true “\(\left \{ F, T \right \}\rightarrow \left \{ T \right \}\)”. these semantic notions are neatly packed within “truth tables”.

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