Example of a consequent statement
A logical truth or mathematical truth is a well-formed formula of a formal language that is true under all interpretations of the components (other than logical constants) of that language. In some texts and contexts (e.g., logical calculus and mathematical logic), logical truths are known as logically valid formulas (having logical validity). In some texts and contexts, logical truths are known as logically valid formulas.
Two generally accepted characteristics of logical truths are that they are formal and necessary. That they are formal implies that any instantiation of a logical truth is also a logical truth. That they are necessary means that it is impossible for them to be false, i.e., in all counterfactual situations, logical truths remain logical truths. That they are necessary means that it is impossible for them to be false, i.e., in all counterfactual situations, logical truths remain logical truths. Logical truths are sometimes confused with logical truths. Logical truths are sometimes confused with logical truths.
Logical truths are sometimes confused with tautologies. Tautologies are the logical truths of propositional logic. While every tautology is a logical truth, not every logical truth is a tautology.
PHILOSOPHICAL ANTHROPOLOGYAXIOLOGYCIENCES AND SCIENTIFIC BRANCHESCONCEPTION OF THE WORLDCOSMOLOGYDISCIPLINES AND PHILOSOPHICAL BRANCHESPISTEMOLOGYSCHOOLSECULTUREETHICSPhilosophical EXPRESSIONPHIL. HISTORY AND CULTUREPHIL. OF MATHEMATICSFIL. OF NATUREPHIL. OF RELIGIONPHILOSOPHERS. OF SCIENCEPHILOS. OF PHILOSOPHYPHILOSOPHYOF LANGUAGEPHILOSOPHIES. OF LANGUAGEPHILOSOPHY OF THE ORIENTPOLITICAL PHILOSOPHY AND SOCIALISMSLOCUTIONS AND IDIOMSLOGICMETAPHYSICSWORKSPERIODS AND GROUPSPSYCHOLOGY AND PHIL. OF THE MINDRELIGIONESSECTSSPECIAL TERMS
The Latin prepositions a, ab (= a before vowel) and ad appear in numerous Latin locutions used in philosophical literature, mainly scholastic, in the Latin language, but also in other languages; some of these locutions, moreover – like
Absurd’ means, literally, “out of tune”, to which
What does converso mean
What links logic to cognitive science? In this project, ICC scientists use propositional logic to study how biases influence the learning of new concepts or categories, especially when each of these concepts is described with different formulas or acquires different possibilities of being symbolized. The work is carried out by researchers of the Logic and Computability Group and starts from understanding the Algorithmic Information Theory.
Within Computer Science, a little explored area in scientific dissemination is Logic and Computability. Although it is a theoretical area, it is key to understand the foundations on which a language or a formal representation system is structured. In particular, ICC researchers do valuable formalization work using, among other tools, propositional logic for cognitive science problems.
“The main question we ask ourselves has to do with human cognition, about what learning is and how we learn. We ask this question taking into account that cognitive sciences are multidisciplinary, not only involving computation but also neurobiology, psychology, neural networks and artificial intelligence”, says Sergio Abriola, ICC researcher and member of the Logic and Computability Group (GLyC).
In logic, validity is a property that arguments have when the premises imply the conclusion. If the conclusion is a logical consequence of the premises, the argument is said to be deductively valid. Some consider these two notions identical and use both terms interchangeably. Others, however, consider that there may be arguments that are not deductively valid, such as inductions. In any case, inductions are sometimes said to be good or bad, rather than valid or invalid.
In the semantic method, an argument scheme is said to be valid when it is impossible for the premises to be true and the conclusion false. To determine whether this is the case, one assumes the truth of the premises, and by applying the definitions of truth, one tries to deduce the truth of the conclusion. Or again, one assumes that the premises are true and the conclusion is false, and applying the definitions of truth, one tries to deduce a contradiction (reductio ad absurdum).