3

Did any intellectual luminary ever articulate any major disagreement with Aristotle's logic prior to the inception of modern mathematical "classical" logic?

Which rational thinkers, such as scholastic theologians, philosophers, scientists, mathematicians etc. prior to 1850 formally articulated any substantial disagreement with Aristotle's theory of logic, as it is implicitly contained in and expressed by his syllogistic?

On the subject of logical implication and validity, I see Fregean logic to be in formal contradiction to Aristotle's syllogistic. As I understand it, all of mathematical "classical", i.e. two-valued, logic, including modal logic, subsequently adopted, through Russell's so-called "material" implication, the Fregean paradigm and, therefore, seems itself in formal contradiction with Aristotle.

However, prior to the inception of Frege's formal logic, I'm not aware that any intellectual luminary in the past ever articulated any substantial critique, and even less refutation, of Aristotle's logic. Am I correct?

Here are just a few of the potential candidates: Thomas Aquinas, Copernicus, Galileo, Descartes, Bacon, Newton, Leibniz, Locke, Spinoza, Berkeley, Hume, Kant, Hegel, but also the scholastic like Anselm of Canterbury, Peter Abelard, Duns Scotus or William of Ockham.

E...
  • 6,436
  • 4
  • 20
  • 39
Speakpigeon
  • 5,522
  • 1
  • 10
  • 22
  • 1
    Renaissance humanists (e.g. [Petrus Ramus](https://plato.stanford.edu/entries/ramus/)), Francis Bacon, Descartes. – Mauro ALLEGRANZA Jan 31 '19 at 08:59
  • 3
    "On the subject of logical implication and validity, I see Fregean logic to be in formal contradiction to Aristotle's syllogistic" **NO**; in modern terms (Fregean) A's syllogistic is **valid**. It is [*Monadic predicate logic*](https://en.wikipedia.org/wiki/Monadic_predicate_calculus). – Mauro ALLEGRANZA Jan 31 '19 at 09:00
  • 2
    The basic definition of "formal validity" was already present in [Aristotle's logic](https://plato.stanford.edu/entries/aristotle-logic/#SubLogSyl). – Mauro ALLEGRANZA Jan 31 '19 at 09:02
  • To [Leibniz](https://plato.stanford.edu/entries/leibniz-logic-influence/) it is due the **only** substantial new approach to formal logic after Middles Ages and prior to Boole and Frege. – Mauro ALLEGRANZA Jan 31 '19 at 09:04
  • 2
    By "formal contradiction" do you mean the [existential import](https://philosophy.stackexchange.com/a/55972/9148)? That was Brentano's doing. Other than that, Fregean logic of monadic predicates reproduces the syllogistic figures. As for semantics of consequence, Aristotle is too vague, see e.g. [King's review of lively medieval debates](http://individual.utoronto.ca/pking/articles/Consequence_as_Inference.pdf) that included conceptual containment, modal and linguistic interpretations, as well as "asyllogistic inferences", later endorsed by Leibniz and Wallis, among others. – Conifold Jan 31 '19 at 09:23
  • @MauroALLEGRANZA I agree that this extract should be taken as expressing Aristotle's notion of logical validity. However, there is unfortunately room for interpretation. Since the formulation of validity given by the SEP here is formally different from the quote of Aristotle's text, we don't have to accept it as reflecting Aristotle's meaning. – Speakpigeon Jan 31 '19 at 11:05
  • 1
    @Conifold Modern mathematical "classical" logic was calibrated to fit with all logical truths of the logical tradition, including syllogisms. It does so by using the material implication as a first approximation of the logical implication in the conventional, Aristotelian sense. It is a 1st order approximation. That in itself is no guarantee that it doesn't contradict Aristotle. Whether it is good enough for all practical purposes, I wouldn't know. I guess somebody probably would if it wasn't. – Speakpigeon Jan 31 '19 at 11:12
  • 2
    A good understanding of history of logic needs at least some knowledge of the sources; there are many good books. An introduction may be through SEP's entries : [Ancient Logic](https://plato.stanford.edu/entries/logic-ancient/), [Medieval Logic](https://plato.stanford.edu/search/searcher.py?query=medieval+logic), [Leibniz](https://plato.stanford.edu/entries/leibniz-logic-influence/), [The Algebra of Logic Tradition](https://plato.stanford.edu/entries/algebra-logic-tradition/), [The Emergence of First-Order Logic](https://plato.stanford.edu/entries/logic-firstorder-emergence/) with many links. – Mauro ALLEGRANZA Jan 31 '19 at 11:26
  • Do you mean contradict *informally*? Syllogistic is not expressive enough, I think, to register nuances that we might find in Aristotle's informal explanations (such as truth gaps for future contingents, etc.). And it is not clear that there is a contradiction, Russell also viewed the material conditional as only a technical device. [Lewis's strict conditional](https://en.wikipedia.org/wiki/Strict_conditional) and [Orlov's relevance conditional](https://en.wikipedia.org/wiki/Relevance_logic) are modern second approximations, and have counterparts in medieval interpretations. – Conifold Jan 31 '19 at 19:18
  • @Conifold I would expect a formal contradiction, but not directly with anything explicitly discussed in the Prior Analytics, but with our intuitive solution to syllogisms not yet considered, somewhat like the modal syllogisms I recently submitted for scrutiny here, where I see them as valid while current modal logic see them as invalid, so that there is a formal contradiction as to validity. – Speakpigeon Jan 31 '19 at 19:53
  • I wrote an explanation for that one in the chat yesterday - with the background assumption you are using modal logic endorses your inference. But what you seem to be getting at is the semantics of logical consequence, and Tarskian/Kripkean version of it did come under criticism recently, e.g. from Etchemendy, see Shapiro's nice review in [Logical consequence: Models and modality](https://www.academia.edu/1576018/Logical_consequence_Models_and_modality). I think it would be difficult/controversial to track Aristotle's position though, many of these nuances only came up later. – Conifold Jan 31 '19 at 20:01
  • @Conifold So, is it the case that not one big name in 2,300 years articulated any substantial disagreement? I think Locke went as far as saying that Aristotle's syllogistic was not very useful since all syllogisms were just too obvious to require any formal expression, but saying this is an effective endorsement, not a critique, of the logic of Aristotle, and it's not a comment on Aristotle's implicit notion of validity. OK, first, I have a lot to read, I guess. Thanks again. – Speakpigeon Feb 01 '19 at 12:40
  • @Speakpigeon Depends on what you mean by disagreement. The fourth figure and existential import were debated, non-syllogistic inferences were introduced since the Stoics, semantic interpretations were also diverging. It is just that without connectives and with only monadic predicates the differences between classical, relevant, paraconsistent, intuitionist, etc., logics do not really come out much. – Conifold Feb 01 '19 at 19:02
  • @Conifold I take Aristotle's main contribution to be not the syllogisms themselves or the subject-predicate structure used to express logical relations, but the way he implicitly defined validity through the definition of the notion of syllogism. The shortness and concision of the definition is in itself very significant. Given that it was I think all new, it seems to me a remarkable performance. Given this, I would have expected someone to expand on this definition well before modern logic. Apparently, not much, if at all. I take this to be a de facto endorsement of the definition. – Speakpigeon Feb 01 '19 at 19:36
  • @Conifold Contrast this with the sort of explosion in mathematical theories, starting essentially with Boole and Frege. I think this is best explained if we think of mathematical logic as mathematics rather than logic. In any case, I would be interested to see any proper justification either that mathematical logic follows from Aristotle, or that it captures our intuitive notion of validity better than Aristotle did. For the moment, I haven't seen either of those two things. I found nothing uncomfortable in Aristotle. I have found little really comfortable in mathematical logic. – Speakpigeon Feb 01 '19 at 19:56
  • I have a very different perspective. "Follows of necessity", "no further term is required" can mean any number of different things, and is not particularly helpful. Sexstus Empiricus mentions three different notions of validity already in antiquity, and we see them re-emerge as soon as the Analytic is translated into Latin during the middle ages. Stoics already expanded the definition beyond Aristotle, and his dominance in scholastics had more to do with the circumstances of transmission (Stoic logic was harder to understand and little copied). – Conifold Feb 01 '19 at 21:13
  • 14-th century logicians and then Leibniz reintroduce propositional logic again, long before Boole. Even if we stick to the syllogistic, it expresses so little that diverging notions of validity mostly agree on that, so it can not be used to discriminate among them. So, for the purposes of syllogistic, it makes little difference what Aristotle's idea of validity was. Even if he expressed it less vaguely, it would have ended up the same. I agree that mathematical logic mostly serves the purposes of mathematics (and science), but, I am afraid, we find little guidance on intuition in Aristotle. – Conifold Feb 01 '19 at 21:29
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/89146/discussion-between-speakpigeon-and-conifold). – Speakpigeon Feb 02 '19 at 10:38
  • John Stuart Mill criticised some forms of syllogistic reasoning as being question begging, and argued that inductive logic was more important than deductive. From a modern perspective we might say that he was talking more about epistemology than logic, but at the time he would have been understood as advancing a different logic from Aristotle. – Bumble Mar 26 '19 at 19:13

0 Answers0