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In logic and philosophy, arguments that are indirect are called "Reductio ad absurdum" in Latin. Now the question is, what exactly is the argument that is direct, called in Latin?

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  • Strictly speaking, reductio ad absurdum doesn't refer to any sort of indirect proof, but specifically to a proof by contradiction. (Unless that's what "indirect" means in philosophy?)
    – Draconis
    Jul 19, 2023 at 16:48
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    I'm not sure this is even the best place for this question. This might be better on the philosophy stack, since it's asking about a specific philosophy term. Thoughts, @Draconis?
    – cmw
    Jul 19, 2023 at 17:09
  • @cmw I was on the fence, but I think it fits better here because we have a long history of answering questions about Latin terminology in various fields (medicine, law, etc).
    – Draconis
    Jul 19, 2023 at 17:29
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    Can you define what you mean by direct and indirect proof and why reductio ad absurdum is right term for indirect argument?
    – cmw
    Jul 20, 2023 at 0:50
  • @cmw If I were to write about modern mathematics (including mathematical logic) in Latin, I wouldn't use reductio ad absurdum for indirect proof. Instead, I'd go with demonstratio recta/obliqua. I have no clue whether these are attested. In the context of mathematics the answer might be different than in philosophy.
    – Joonas Ilmavirta
    Jul 20, 2023 at 19:55

2 Answers 2

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Even with a background in mathematical logic, I have never heard of an "indirect proof", so this answer may not be what you are looking for, but reductio ad rationem and reductio ad sensum are two attested Latin locutions in academic contexts (especially in Italian, it seems).

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    Can you expand on this at all? Why are those terms used for "direct arguments"? How can you be confident in suggesting them if you're not sure what indirect and direct arguments are? Or are you only unsure of the indirect proof? Is there a difference between proof and argument?
    – cmw
    Jul 20, 2023 at 0:49
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Both demonstratio directa and demonstratio ostentiva are attested translations:

Demonstratio directa dicitur, quae ex principiis, vel propositionibus prius demonstratis id, quod in quaestione erat, demonstrat. [...] Demonstratio indirecta dicitur, in qua aliquid eorum, quae concessa sunt, aut omnino manifesta, evertitur, reducendo contradicentem vel ad absurdum, vel ad impossibile. (Reichelt 1704)

A proof is said to be direct when it proves what was in question from principles or propositions previously demonstrated. [...] A proof is said to be indirect when it refutes one of the things that have been conceded or are altogether manifest, by reducing the opposite to absurdity or impossibility. (Reichelt 1704)

and

primum demonstrationis genus dicitur demonstratio directa, sive ostensiva; alterum demonstratio indirecta, et reductio ad absurdum. (Baldinotti 1855)

The first kind of proof is called direct or ostensive; the other is called indirect or reductio ad absurdum. (Baldinotti 1855)

(Don't take my translations too seriously, I did them very quickly.)

Your definition of an "indirect proof" is also found in the modern logic literature:

Argumentation Logic separates proofs into direct and indirect, the former being without the use of reductio ad absurdum. (Kakas et al. 2014)

References

  • Julius Reichelt, Elementale Mathematicum (1704).
  • Caesar Baldinotti, De recta humanae mentis institutione (1855).
  • Antonis C. Kakas, Francesca Toni and Paolo Mancarella, Argumentation Logic, Frontiers in Artificial Intelligence and Applications (2014) 345-356.

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