A rule of inference is a conditional statement that gives a sufficient condi-
tion for a sentence in a derivation to be justified. Modus ponens is one very common such rule: it says that if φ and φ →ψ are already justified, then ψ is justified. This means that a line in a derivation containing the sentence ψ is justified, provided that both φ and φ →ψ (for some sentence φ) appear in the derivation before ψ. — Open Logic p.120
Modus ponens doesn't require that a conditional is not contradictory, nor that the "major" premise (which must be a conditional) is not contradictory, nor that the "minor" premise (which might or might not itself be a conditional) is not contradictory, nor that the premises together are not contradictory
— TonesInDeepFreeze
What is your cite for this definition? — Hanover
Where pray tell do you find a definition of MP that takes into consideration a self referential contradictory conditional and asserts it satisfies the definition of MP?
All definitions I have located say otherwise, as do all Google and AI engines.
Provide to me your cite — Hanover
Why don't you already know this? — Banno
Nothing says that we may not substitute A for φ and ~A for ψ. Hence, we may. Indeed, that's kinda the point.
But this is trivial stuff! Why don't you already know this? — Banno
Nothing says we can — Hanover
your definition of MP is not logically entailed — Hanover
We haven't left Hanover any space to back down without loosing face. — Banno
We might allow some space for them to learn. — Banno
Logic is generally handled very badly here — Banno
As Tones explained, it's not MP you have misunderstood, but substitution. MP is a rule of inference, saying that if you have φ and φ →ψ, then you also have ψ, where φ and ψ are whatever formulae or propositions or sentences you are discussing. That includes substituting the same formula for both, and the negation of φ for ψ.It makes as much sense to define MP as excluding instances where A and not A coexist. — Hanover
A thread of mine attempted amongst other things to discuss plausible cases in which modus ponens might not apply. It was lost in misunderstanding, which is a shame but perhaps not a surprise. — Banno
Meanwhile, a moderator comes into scold the expression of exasperation while not a word that it is at least seriously frowned upon to cite bot misinformation and confusion, despite that (at least last I happened to read) the forum has said in general that that is not acceptable. — TonesInDeepFreeze
An example of Modus Ponen failure is presented in the Wiki article as the Vann Mcgee case — Hanover
It turns out that his argument does not suppose that the conditionals mentioned are taken in the sense of the material conditional. He says that if the conditionals mentioned are taken in the sense of the material conditional then modus ponens is not impeached by his argument. — TonesInDeepFreeze
Not the sort of thing I had in mind. Nor, frankly, am I inclined to go into details here, where simple substitution is apparently contentious. More agreement is needed before we might proceed to such other disagreements. — Banno
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.