Editing Syllogism (section)

==Modern history==

The Aristotelian syllogism dominated Western philosophical thought for many centuries. Syllogism itself is about drawing valid conclusions from assumptions ([[axiom]]s), rather than about verifying the assumptions. However, people over time focused on the logic aspect, forgetting the importance of verifying the assumptions.

In the 17th century, [[Francis Bacon]] emphasized that experimental verification of axioms must be carried out rigorously, and cannot take syllogism itself as the best way to draw conclusions in nature.<ref name="instauration">[[Francis Bacon|Bacon, Francis]]. [1620] 2001. ''[https://web.archive.org/web/20190413000330/http://www.constitution.org/bacon/instauration.htm The Great Instauration]''. – via ''Constitution Society''. Archived from the [http://www.constitution.org/bacon/instauration.htm original] on 13 April 2019.</ref> Bacon proposed a more inductive approach to the observation of nature, which involves experimentation, and leads to discovering and building on axioms to create a more general conclusion.<ref name="instauration" /> Yet, a full method of drawing conclusions in nature is not the scope of logic or syllogism, and the inductive method was covered in Aristotle's subsequent treatise, the ''[[Posterior Analytics]]''.

In the 19th century, modifications to syllogism were incorporated to deal with [[Disjunctive syllogism|disjunctive]] ("A or B") and [[Conditional syllogism|conditional]] ("if A then B") statements. [[Immanuel Kant]] famously claimed, in ''Logic'' (1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know. (This work is not necessarily representative of Kant's mature philosophy, which is often regarded as an innovation to logic itself.) Kant's opinion stood unchallenged in the West until 1879, when [[Gottlob Frege]] published his ''[[Begriffsschrift]]'' (''Concept Script''). This introduced a calculus, a method of representing categorical statements (and statements that are not provided for in syllogism as well) by the use of quantifiers and variables.

A noteworthy exception is the logic developed in [[Bernard Bolzano]]'s work ''[[Bernard Bolzano#Wissenschaftslehre (Theory of Science)|Wissenschaftslehre]]'' (''Theory of Science'', 1837), the principles of which were applied as a direct critique of Kant, in the posthumously published work ''New Anti-Kant'' (1850). The work of Bolzano had been largely overlooked until the late 20th century, among other reasons, because of the intellectual environment at the time in [[Bohemia]], which was then part of the [[Austrian Empire]]. In the last 20 years, Bolzano's work has resurfaced and become subject of both translation and contemporary study.

This led to the rapid development of [[sentential logic]] and first-order [[predicate logic]], subsuming syllogistic reasoning, which was, therefore, after 2000 years, suddenly considered obsolete by many.{{original research inline|date=January 2013}} The Aristotelian system is explicated in modern fora of academia primarily in introductory material and historical study.

One notable exception to this modern relegation is the continued application of Aristotelian logic by officials of the [[Congregation for the Doctrine of the Faith]], and the Apostolic Tribunal of the [[Roman Rota]], which still requires that any arguments crafted by Advocates be presented in syllogistic format.
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What follows is at best *very* obscure and desultory. I'll have a go at rewriting it when I can.
You can simply put list of rules for validity&nbsp;— as in Russian wp -->

===Boole's acceptance of Aristotle===
[[George Boole]]'s unwavering acceptance of Aristotle's logic is emphasized by the historian of logic [[John Corcoran (logician)|John Corcoran]] in an accessible introduction to ''[[Laws of Thought]]''.<ref>[[George Boole|Boole, George]]. [1854] 2003. ''[[The Laws of Thought]]'', with an introduction by J. Corcoran. Buffalo: [[Prometheus Books]].</ref><ref>van Evra, James. 2004. "'The Laws of Thought' by George Boole" (review). ''[[Philosophy in Review]]'' 24:167–69.</ref> Corcoran also wrote a point-by-point comparison of ''[[Prior Analytics]]'' and ''[[The Laws of Thought|Laws of Thought]]''.<ref name=":1">[[John Corcoran (logician)|Corcoran, John]]. 2003. "Aristotle's 'Prior Analytics' and Boole's 'Laws of Thought'." ''History and Philosophy of Logic'' 24:261–88.</ref> According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were "to go under, over, and beyond" Aristotle's logic by:<ref name=":1" />

# providing it with mathematical foundations involving equations;
# extending the class of problems it could treat, as solving equations was added to assessing [[Validity (logic)|validity]]; and
# expanding the range of applications it could handle, such as expanding propositions of only two terms to those having arbitrarily many.

More specifically, Boole agreed with what [[Aristotle]] said; Boole's 'disagreements', if they might be called that, concern what Aristotle did not say. First, in the realm of foundations, Boole reduced Aristotle's four propositional forms to one form, the form of equations, which by itself was a revolutionary idea. Second, in the realm of logic's problems, Boole's addition of equation solving to logic—another revolutionary idea—involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving. Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle."