petitio principii for the mathematically inclined

petitio principii

Petitio principii for the mathematically inclined? Awright!

This brief video infra, which is posted on YouTube by a supposed pedagogic site and which I reproduce here under fair use, is truly a remarkably simple, mathematical illustration, using the most basic arithmetic, of a circular argument and even serves to illustrate a diallelus. And all that in 75 seconds. Wow!

"One, two, four, seven and so one"? (@ 27")

Due to the lack of any equation, formula or algorithm, numerous series, sequences or "patterns", could be established after 1, 2, 4, 7. For example, the following three numbers could just as easily follow and "form a pattern": 13, 24 and 44.

• Add the two numbers before 4 and add them to 4. (1+2+4=7)
• Add the two numbers before 7 and add them to 7. (2+4+7=13)
• Add the two numbers before 13 and add them to 13. (4+7+13=24)
• Add the two numbers before 24 and add them to 24. (7+13+24=44)
• ...
  

Uh, and 12, 19 and 30 could no less easily follow and "form a pattern". When she has started and claims to be “continuing with the same pattern” (@ 45”), one easily sees another, different evolving pattern. She starts with 1 after which she continues by adding prime numbers (see second row, 1+2+3+...). Thus, instead of adding 4 to obtain 11 (7+4), one could continue by adding 5, 7, 11, 13, 19 et cetera.

• Add 2 (a prime number) to 2. (2+2=4)
• Add 3 (a prime number) to 4. (3+4=7)
• Add 5 (a prime number) to 7. (5+7=12)
• Add 7 (a prime number) to 12. (7+12=19)
• Add 11 (a prime number) to 19. (11+19=30)
• ...
  

Or how about this pattern, 4, 2 and 1, as "the next three numbers" (@ 21") by simply seeing a potential palindrome (1, 2, 4, 7, 4, 2, 1)? Or ...

QED

PS
The series in the video is not logically invalid per se; nonetheless, begging the question is a fallacious form of argument since it uses the point to be proven as part of the argument to be proved. ... Hmm, why does that remind me of creationist reasoning? Oh, well, wasn't it Russell who said: "Many people would sooner die than think? In fact, they do."
PPS
2B Cont.