User:LGreg/sandbox/Approaches to Knowledge (LG seminar 2020/21)/Seminar 18/Truth/Logical Truth

Definition and context
Logic is the study of the reasoning that leads to the acceptance of conclusions on the basis of premises. Logical truth is a core part of the study of logic, and a general interpretation of what it is involves the idea that a logical truth is such that it cannot be false. Logical truths are necessarily a priori truths, true if you replace certain meanings of individual words in the proposition (counterfactual circumstances), and must remain true in all replacement instances of its form. It is important to note that logical truths are analytic statements and are not used to propose informations about matters of fact. Logical truth is thus synonymous with one meaning of the word tautology, whereby tautology means that the statement (or proposition) is true under any interpretation of the words.

Implications
One of the most important applications of truth values in the study of logic is when they consequently apply to mathematics too. Hence the notion of a truth value not only has enormous semantic consequences but also scientific. Thus in considering logical truth, considering the term formalization becomes extremely necessary too. In propositional logic, formalization is the process of translating spoken language (e.g.: English) into the logical language (e.g.: Predicate). Here, the role of truth functional connectives must be carefully considered to apply the right transformation to the initial statement and ensure it's truth value is not mis-represented. In branches of logic such as proof theory, formalization and being able to render truth values into logic become extremely valuable.

This leads also to the consideration of analytic–synthetic distinction. Here, we are considering only analytic propositions in the consideration of applications of philosophical logic in mathematics. However, synthetic propositions, propositions which are true depending on how their meaning relates to the world, also contain elements of truth that must be considered. These distinctions were primarily put through by the philosopher Immanuel Kant in the late 18th century.