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These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from p to q is deductively valid then the claim "if p then q" is a logical truth. [16] Formal logic needs to translate natural language arguments into a formal language, like first-order logic, to assess whether they are valid.
Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence. [1]
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", [1] while they are rational according to the broader requirement that they are based on reason and knowledge.
Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. [1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion.
Reason is the capacity of consciously applying logic by drawing valid conclusions from new or existing information, with the aim of seeking the truth. [1] It is associated with such characteristically human activities as philosophy, religion, science, language, mathematics, and art, and is normally considered to be a distinguishing ability possessed by humans.
In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. [1]
Philosophy of logic is the area of philosophy that studies the scope and nature of logic.It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application.
The law of identity: 'Whatever is, is.' [2]. For all a: a = a. Regarding this law, Aristotle wrote: First then this at least is obviously true, that the word "be" or "not be" has a definite meaning, so that not everything will be "so and not so".