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Consequence is a (if not the) core subject matter of logic. Aristotle's study of the syllogism instigated the task of categorising arguments into the logically good and the logically bad; the task remains an essential element of the study of logic. In a logically good argument, the conclusion follows validly from the premises; thus, the study of consequence and the study of validity are the same.
A History of The Consequence Relations
Introduction
1.1. Necessity and Counterexamples
1.2. Formality and Structure
1.3. A Priori and Giving Reasons
Aristotle [384 BCE-322 BCE]
Stoics [300 BCE–200 CE]
Medievals [476 CE–1453 CE]
4.1. Conseguentiae Buridan and Pseudo-Scotus
4.2. Self-Reference and Insolubilia
4.3. Obligationes
Leibniz [1646–1716]
Kant [1724–1804]
Bolzano [1781–1848]
Boole [1815–1864]
Frege [1848–1925]
Russell [1872–1970]
Carnap [1891–1970]
Gentzen [1909–1945]
Tarski [1902–1983]
Gödel [1906–1978]
Modal Logics
Non-monotonic Options
The Substructural Landscape
Monism or Pluralism