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A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per se. Validity refers to entire arguments. The same is true in propositional logic (statements can be true or false but not called valid or invalid).
A first-order formula is called logically valid if it is true in every structure for the language of the formula (i.e. for any assignment of values to the variables of the formula). To formally state, and then prove, the completeness theorem, it is necessary to also define a deductive system.
The "thesis statement" comes from the concept of a thesis (θέσῐς, thésis) as it was articulated by Aristotle in Topica. Aristotle's definition of a thesis is "a conception which is contrary to accepted opinion." He also notes that this contrary view must come from an informed position; not every contrary view is a thesis. [3]
An argument can be “valid” even if one or more of its premises are false. An argument is sound if it is valid and the premises are true. It is possible to have a deductive argument that is logically valid but is not sound. Fallacious arguments often take that form. The following is an example of an argument that is “valid”, but not ...
In order to evaluate these forms, statements are put into logical form. Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its subject matter. [1] Being a valid argument does not necessarily mean the conclusion will be true. It is valid because ...
Forms of logical reasoning can be distinguished based on how the premises support the conclusion. Deductive arguments offer the strongest possible support. Non-deductive arguments are weaker but are nonetheless correct forms of reasoning. [28] [29] The term "proof" is often used for deductive arguments or very strong non-deductive arguments. [30]
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Arguments that involve predictions are inductive since the future is uncertain. An inductive argument is said to be strong or weak. If the premises of an inductive argument are assumed true, is it probable the conclusion is also true? If yes, the argument is strong. If no, it is weak. A strong argument is said to be cogent if it has all true ...