On page 443, section 1.1 Expanding to Contradiction, in José Ferreirós' A Road To Modern Logic - An Interpretation, the following is written:

Philosophical conceptions of logic have been complex and varied; here we are only interested in the tradition of ‘formal logic’, and formal logic meant the theory of the syllogisms—above all the Aristotelian syllogisms but also the so-called hypothetical and disjunctive syllogisms.

Prior to reading the above quote, and this Wikipedia article linking to it, I had only read formal logic as referring to the larger, formalized study of logic (see this Britannica article for an example). This leads me to think there has been a shift in the use of the term, its use originating as a name for all syllogisitic logics, before being appropriated as a the name for the discipline of studying, creating and using formalized logics.

So, my two questions are mostly about etymology and usage, which does place this question scarily close to belonging in EL&U; however, I deem this question a bit too technical to be a good fit for that site, in that it requires an educated parsing of the logics discussed in relevant texts in order to know how and why the categorizes were composed. That's the etymology part, which is history (linguistic history, but history nonetheless). The usage part is less justifiable, but I am asking about a not so extensive account of the current usage from a historical perspective; as in, how is it different from the past and why.

So, to be completely clear, here are my questions:

  1. What did formal logic mean before?
  2. What does it mean now, and why has this changed?
  • $\begingroup$ My guess is that both many years ago and now, the phrase "formal logic" does not have a sufficiently standard meaning to conclude much along the lines of what you are asking about. Moreover, the fact that Ferreirós seems to be using a slightly different formulation isn't much evidence of a change, and besides, he might simply be saying how he intends to use the phrase (in a way that could have been edited to be more explicit). That said, I found myself wondering about the distinctions between axiomatic logic and symbolic logic and mathematical logic (last two are definitely distinct). $\endgroup$ Apr 12, 2022 at 16:16
  • $\begingroup$ The author says: "The road to modern logic began, some time around 1850, with a huge thematic expansion." Thus, he means that, prior to 1850 (i.e. prior to Boole (1847)) formal logic refers to the "traditional" Aristotle logic. $\endgroup$ Apr 13, 2022 at 8:11
  • $\begingroup$ After Boole, the discovery of how to "apply" mathematical methods and symbols to the study of formal logic gave rise to the modern mathematical logic. $\endgroup$ Apr 13, 2022 at 8:13
  • $\begingroup$ See also The Algebra of Logic Tradition and Leibniz’s Influence on 19th Century Logic. $\endgroup$ Apr 13, 2022 at 8:15
  • $\begingroup$ The "measure" of the change occurred is represented by Russell's quote (1903): "The subject of symbolic logic is formed by three parts: the calculus of propositions, the calculus of classes, and the calculus of relations." This is simply the structure of modern ML textbooks. $\endgroup$ Apr 13, 2022 at 8:30


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