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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.
Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. Euclid's Elements has been referred to as the most successful [a] [b] and influential [c] textbook ever written.
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.
Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments. Reasoning is the activity of drawing inferences. Arguments are the outward expression of inferences. [6] An argument is a set of premises together with a conclusion.
Example of an early argument map, from Richard Whately's Elements of Logic (1852 edition). Argumentation theory is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning.
Critical thinking is the process of analyzing available facts, evidence, observations, and arguments to make sound conclusions or informed choices. It involves recognizing underlying assumptions, providing justifications for ideas and actions, evaluating these justifications through comparisons with varying perspectives, and assessing their rationality and potential consequences. [1]
The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct (or valid) and incorrect (or fallacious) inferences.
A flaw in reasoning that occurs in natural language arguments due to ambiguity, irrelevance, or other factors outside the formal structure of the argument. injection A function that maps distinct elements of its domain to distinct elements of its codomain, also known as an injective function or one-to-one function. injective