imdef @imdef@qoto.org

This is an interesting attempt to give the field of #MachineLearning a foundation.
https://royalsocietypublishing.org/doi/full/10.1098/rsta.2017.0237

#Cochrane makes statement
https://www.cochrane.org/de/node/81904

I should have been more precise. The two formal expressions

(2|x ^ 3|x) -> 6|x
(2|x -> 6|x) v (3|x -> 6|x)

are equivalent. However, it is less clear cut with their ordinary language translations:

"If x is divisible by 2 and x is divisible by 3, then x is divisible by 6."
"If x is divisible by 2, then x is divisible by 6, or if x is divisible by 3, then x is divisible by 6."
#logic #implication #conditional

Should have been more precise. The two formal expressions

(2|x ^ 3|x) -> 6|x
(2|x -> 6|x) v (3|x -> 6|x)

are equivalent. However, it is less clear cut with their ordinary language translations:

"If x is divisible by 2 and x is divisible by 3, then x is divisible by 6."
"If x is divisible by 2, then x is divisible by 6, or if x is divisible by 3, then x is divisible by 6."
#logic #implication

Example 2: write a|x for "x is divisible by a" or "a divides x". Then
(2|x ^ 3|x) -> 6|x
(2|x -> 6|x) v (3|x -> 6|x)

In both cases, the first form is natural and obvious and the second is something you'd normally never write. But, if pressed, maybe you'd bite the bullet and agree it's an equivalent form. I'm still undecided but I enjoyed the paper.
#logic #implication #conditional (3/3)

Because of the thoughts like the above, I found the following paper quite interesting:
https://www.tandfonline.com/doi/abs/10.1080/11663081.2014.911540

Vidal points out that (P ^ Q) -> R is equivalent to (P -> R) v (Q -> R). Both these forms can be seen to be equivalent to ~P v ~Q v R. Specific instances of this equivalence can be awkward/counterintuitive:

Example 1:
("x is a rhombus" ^ "x is a rectangle") -> "x is a square"
("x is a rhombus" -> "x is a square") v ("x is a rectangle" -> "x is a square")

(3/n)

I was never sure what to make of this, because I have yet to read a discussion of why material implication is a better model of mathematicians' "if P, then Q" than other alternatives. For example, why not understand "if P, then Q" in mathematics as "necessarily, if P, then Q" and take it to correspond to [](P -> Q), where [] is an operator of modal logic? I'm sure people already thought of this, I just haven't seen the pros and cons of this alternative (and other alternatives) compared to the pros and cons of the material implication. E.g., what about the implication in relevance logic? (2/n)

Material implication P -> Q is equivalent to ~P v Q. It is generally agreed that the "if P, then Q" construction in ordinary language is not always the same as material implication. However, when you study mathematics, you're trained to think that, in mathematics, "if P, then Q" really is material implication. Here is an in many ways careful explanation: (1/n)
https://gowers.wordpress.com/2011/09/28/basic-logic-connectives-implies/

#logic #implication #conditional

Bill Clinton is not associated with politics in any way? #ChatGPT (2/2)

#ChatGPT is being a very good sport playing "one of these things is not like the other" with pretty hopeless examples of four things. However, it is taking some amusing liberties with facts and logic. (1/2)

Explanation of the greenhouse effect by @skdh@nerdculture.de. Several plot twists so must watch to the end. https://www.youtube.com/watch?v=oqu5DjzOBF8

One of the better commentaries
https://www.vox.com/future-perfect/2023/2/22/23609499/masks-covid-coronavirus-cochrane-review-pandemic-science-studies-infection

The actual paper
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.222001

"Method for solving notorious calculus problems speeds particle physics computations"
https://www.science.org/content/article/method-solving-notorious-calculus-problems-speeds-particle-physics-computations

Write up of the 2023 article:
https://www.cidrap.umn.edu/covid-19/covid-while-world-sanitized-surfaces-group-tried-warn-early-about-airborne-spread