> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/300-logic/terms/consequence.md).

# Consequence

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 <https://www.sciencedirect.com/science/article/pii/B9780444529374500010>

1. Introduction

   1.1. Necessity and Counterexamples

   1.2. Formality and Structure

   1.3. A Priori and Giving Reasons
2. Aristotle \[384 BCE-322 BCE]
3. Stoics \[300 BCE–200 CE]
4. Medievals \[476 CE–1453 CE]

   4.1. Conseguentiae Buridan and Pseudo-Scotus

   4.2. Self-Reference and Insolubilia

   4.3. Obligationes
5. Leibniz \[1646–1716]
6. Kant \[1724–1804]
7. Bolzano \[1781–1848]
8. Boole \[1815–1864]
9. Frege \[1848–1925]
10. Russell \[1872–1970]
11. Carnap \[1891–1970]
12. Gentzen \[1909–1945]
13. Tarski \[1902–1983]
14. Gödel \[1906–1978]
15. Modal Logics
16. Non-monotonic Options
17. The Substructural Landscape
18. Monism or Pluralism