He just mixed up "mathematical induction" and "induction".
...which are not the same thing. They're qualitatively different, in part because of the inductive leap, and it is that "leapy" form of induction that Popper discusses. In paradoxical contrast, mathematical induction has deductive strength because it's still based on the deductive steps that underpin mathematics. It has nothing -- zero -- to do with the attempts at empiricism, falsifiability, and induction he tried to employ to falsify the first two hypotheses in his proof.
In mathematical induction there is no inductive leap because we can define relations on a set that we say hold for all members of the set -- the "completeness" that you're describing in Spanish. Then for some proposition involving that relation we can perhaps show that it holds for two members of the set because of the relation. And if we show that, we can induce that into the set as a whole via the relation since the relation is defined completely. Showing that if a proposition holds for a specific case it holds for the set is inductive because it starts with what is shown to hold for two or more elements of the set and reasons to the general case of all members of the set. But it does so in mathematics deductively, because the relation is a contrived premise in a categorical syllogism, not an observation bound by uncertainty. It is more properly deduction because the mathematician has defined a universal relation over the set. Deductive proofs work by extracting what must be true in some case from what is known to be true in all such cases. In mathematics we know it to be true because we simply defined it that way.
Turning back to Buddha's proof, if we take as a premise that the "videotape" of evidence in either case of the uncreated universe is proffered as complete evidence of such (regardless of my ability to empirically review it), then I can perhaps extract the consequent lemma that any two discrete, adjacent minutes of that tape must then be claimed to constitute a full, continuous, sequential record of those two minutes. Now I sit down and empirically verify that the first minute of videotape completely and accurately shows the state of the universe. By the mathematical style of induction and the proffered lemma I can say that the second minute, which I have not reviewed, must be identically probative and continue from the first. And by further induction, the third minute is satisfactory, and so forth. Such a "proof" would work with any length videotape, even infinitely long. But obviously such patterns of proof work only when such relations arise, which happens only in the axiomatic world of mathematics.
No, mathematical induction does not fix Buddha's broken argument, his broken philosophy, nor his flip-flopping on whether he means induction or deduction. It has nothing to do with Popper's induction, nor with any branch of positivism. Further, the statement that all proofs in mathematics are based on inductive logic is false on its face. We use mathematics to introduce beginning students to deductive patterns of reasoning. We use the natural sciences to introduce them to inductive logic. Inductive reasoning is the reasoning of drawing conclusions from evidence, usually from observation. Since Buddha claims he performs statistical analysis, I would expect him to know this intimately. Inductive reasoning, in order to be useful, requires a measure of uncertainty in the evidence and in the empirical controls. Statistics is the branch of mathematics that provides that measurement.
But I wouldn't distrust Buddha having some sort of academic achievement. After all there are hundreds of bad colleges and universities out there...
Agreed, which is why I qualified my doubt as pertaining to accredited schools of engineering. No accredited school of engineering in the U.S. will accept for graduate study a student who has not first received a bachelor's degree from an accredited engineering school. This is because such schools in the U.S. teach all engineers a core of basic engineering subjects at the bachelor's level regardless of their chosen specialization, and require that core at the graduate level. Being a professional degree, engineering has a responsibility to convey a certain minimum competence in everything the word means. A bachelor's degree in applied mathematics would not qualify him to study engineering at the graduate level in an accredited U.S. university.
Yes, if he did practice control-systems engineering, with or without a degree and license, then he did use empirical methods to verify designs, and he did use inductive reasoning to conclude from that evidence that a design probably works. That doesn't qualify one as a philosopher. And as we have seen, Buddha cannot demonstrate any degree of competence in philosophical reasoning. He's mostly just dropping names and regurgitating irrelevant history.
Those things he probably learnt decades ago are forgotten and working as buzzwords, while he read Popper five months ago so Popper is now in fashion and he must keep talking all the time about him -before he also forgets it-.
I take a dimmer view. I don't believe much of Buddha's claims to education. But in his favor, I've argued that they are irrelevant to his claims to be able to prove the existence of God. And he hasn't explicitly placed them at the foundation of his argument. So if I'm going to stay true to that argument then I musn't try to make them that foundation. His academic credentials are off-topic when he mentions them, therefore they must also be off-topic when I mention them, even to challenge them.
What I glean from this, however, is a general tenor of dishonesty which removes any benefit I might have given when doubting Buddha's preparation to formulate and defend his proof on the world stage. Insofar as his proof is based on claims to superior understanding, I fall back on the shadiness of his academic claims to undermine that basis. I don't think he's arguing in good faith, and so that's going to inform my approach to his arguments from now on.
