Principle of Mathematical Induction-I

You might think that scientists begin with hypotheses such as "all swans are white" and then go about looking for evidence to support them. Karl Popper disagreed. He suggested that scientists begin with bold hypotheses that can be falsified by evidence. But rather than looking for supporting evidence, Popper argued scientists go out of their way to refute their hypotheses testing them to destruction. They go out searching for black swans, not more white swans. Science is all about falsification not confirmation. It's a series of conjectures and refutations. Marxists argued that there was a scientific analysis of history, everything that happened was determined by class struggle and a worker's revolution was inevitable. When workers failed to revolt rather than taking this as a refutation of their view Marxists suggested workers were simply victims of false consciousness unable to see the situation as it indeed was. Popper fulminated against this way of dealing with counter-evidence claiming it immunized Marxist's hypotheses which were originally testable turning them into irrefutable pseudoscience. There was no imaginable observation that could prove the Marxists were wrong. If the workers revolted that shows the Marxists were right. If they didn't revolt, that also shows they were right. It was a win-win.?

INDUCTION AND CONTINUITY

The world exhibits underlying order and continuity.?Our knowledge of this seems partially a priori?and the product of discovery by trial and error. For instance, there is evidence to suggest that infants expect objects to fall and know in advance that objects increasing in size are getting closer.

PRIMACY OF INDUCTION??

Predictability is the assumption underlying inductive reasoning, whereby we generalize from a set of particular instances.?If deduction is reasoning from the general to the specific; then induction is arriving at the general from the specific. It is disjoint with this reversal. The logic is broken. Induction may be inextricable from how we encounter a more or less uniform world, but we must concede that inductive reasoning is psychological rather than strictly logical. Why??

To understand this concept, One should follow a logical and mathematical approach.

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