Re: Collatz conjecture question

On 3/24/2025 12:09 PM, Ross Finlayson wrote:

On 03/24/2025 08:59 AM, Jim Burns wrote:

https://en.wikipedia.org/wiki/Affirming_the_consequent
⎛
⎜ Affirming the consequent
⎜
⎜ In propositional logic, affirming the consequent
⎜ (also known as converse error, fallacy of the converse,
⎜ or confusion of necessity and sufficiency)
⎜ is a formal fallacy (or an invalid form of argument)
⎜ that is committed when,
⎜ in the context of an indicative conditional statement,
⎜ it is stated that because the consequent is true,
⎝ therefore the antecedent is true.

>
Doesn't that round-file material implication?

No.
Consider P Q P⇒Q
All possible circumstances:
 P Q P⇒Q
 T T  T
 f T  T
 T f  f
 f f  T
----
Material implication:
 P, P⇒Q true
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
  Q inferred
All still.possible circumstances:
 P Q P⇒Q
 T T  T
 ̷f ̷T  ̷T
 ̷T ̷f  ̷f
 ̷f ̷f  ̷T
Q can only be true.
Infer Q.
----
Affirming the Consequent
 P⇒Q, Q true
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
  P inferred
All still.possible circumstances:
 P Q P⇒Q
 T T  T
 f T  T
 ̷T ̷f  ̷f
 ̷f ̷f  ̷T
P might be true and might be false.
Don't infer P.

Or, you just pick when it's so?

The defining goal of
this entire project called "logic"
is to not.pick.
So, no.
But really, really, really "no".