@itsdespues Thanks, friend! π€ I am still pinching myself that the #RoR is on the rankings list around Ludwig Wittgenstein's CLASSIC, "The Blue and Brown Books", which I was assigned to study in one of my philosophy classes ...
... π many π moons π ago π ...
... as an UNDERGRAD! π³
Peripheral #RoR news here... In the front matter of the RoR, I mention being invited to do a review by Monumenta Serica for a book that overlaps my areas of academic strength: Eastern thought and philosophical logic. π¨βπ« Well, it just recently dropped:
https://t.co/xMRsnFgqAl
With the launch π of the RoR π on Amazon ONE WEEK away, 'tis time for a reveal... π²π
The central rule of inference, modus ponens, is, we are told, "primitive", not derived. That is a convenient LIE. Indeed, MP's proof in natural deduction is obvious! Here it is:
1. P β Q
2. P β΄ Q
-------------------
3. ~P β¨ Q DC 1
4. Q DS 3,2
Simple as that: TWO STEPS! πͺ
(Re the justifications... π¨βπ«
DC = Disjunctive Conditional in the RoR, a typical traditional designation of which is Material Implication (MI)
DS = Disjunctive Syllogism)
In the attached image files, π you can witness ChatGPT go from still not being able to figure this proof π out (Response 1) to FINALLY detecting what is up, putting it together, and presenting the proof (Response 2)!
In light of this, much truer in the traditional context would be that material implication (disjunctive conditional in the RoR) be taken as "primitive", though that is not really true, either, given the presence of the subproof methods of conditional and indirect proof, which, mind you, are speciously affirmed by that aforementioned LIE that modus ponens is "primitive" because when system closure is precluded, incorporating external methods is acceptable.
Indeed, the rule of inference of material implication is traditionally taken to be derived, and, to wit, AI π€ will give you proofs in natural deduction for it using conditional/indirect subproofs (that is, ironically to have to say, if it gives you a proof at all π€ͺ).
Now, it is notable that a proof in natural deduction for modus ponens can also be done, albeit slightly less elegantly, with, in order: (the horseshoe form of) the contrapositive theorems, commutation, and modus tollens. Of course, those three patterns of inference are all derived, too. For example, the proof for the contrapositive theorems requires (two iterations of) the disjunctive conditional and commutation.
Point being, it would make more sense if it were demonstrated within natural deduction that all of them were part of a closed set of logically interconnected, mutually implied fundamental patterns of inference, but that takes a ton of work, which, moreover, the methods of conditional proof stubbornly stand in the way of (because those methods β along with the ability to (arbitrarily) declare a rule of inference "primitive" β seem to render such work unnecessary).
THAT... WORK... HAS... BEEN... DONE,... and it is presented in the RoR, and so that first-ever closed system of natural deduction that has been kept under lock and key π for over three years now is one week away from being unveiled!
βοΈπ€―π
We had a good discussion tonight about the Bible, Christian Nationalism, etc. About 5 people tuned in throughout the night. Join me tomorrow @Jamesrs2025 it was a pleasure speaking with you.
Empathy is good
But fraudsters and embezzlers have hijacked our empathy
$81k/yr per homeless person
$52k/yr per capita income
This is insanity and is clearly untenable.
I appreciated the discussion. After learning I was 25% Middle Eastern, a person on the space, who I quite liked and wouldnβt have minded befriending, unfollowed me. This was after engaging in what I thought were some decent conversations. Due to this, as much as I enjoy the conversation, I donβt think Iβm gonna be able to participate with that heavy of a negative bias simply because of my genetics. Which to be fair, their target audience and message is very clear and many were welcoming. I enjoy the pro white, based, respectful, and intellectual dialogue. But even though I enjoy it and appreciate it, due to my genetics i get the sense that to some at least, Iβm not respected or welcome. That being said, wish you all the best, and good luck in accomplishing your goals.