Ockham on induction

I have made a start on book III-3 of Ockham's Summa Logicae by translating some of the chapters on induction. The part 3 of the third part is received little attention from philosophers, and as far as I know has never been translated. The chapters I have looked at come across as terribly weak, unlike the powerful and insightful work of the first two parts.

Ockham says that induction "is a progression from singulars to the universal", which is pretty much the modern understanding of the term. He gives the example "this [man] runs, and that one, and so on, therefore every man runs". What does the 'and so on' mean? If it means 'every other man apart from this one and that one', then the argument amounts to 'Man a and man b and every other man apart from a and b run, therefore every man runs', which is trivial, though admittedly valid. Or does he mean that the 'and so on' is a placeholder for a longer proposition which enumerates every man there is, and so does not include the word 'every', but concludes with the word 'every'? But that would not work, because the enumeration would have to conclude 'and there are no more men'. Mathematical induction, of course, is different from any of these. As I understand it, it is an inference from the properties of the successor of every number, to the properties of all numbers of a particular type (the naturals). Thus the antecedent and the consequent of mathematical induction both contain the word 'every'. I may be wrong, I'm sure my mathematically minded commenters will leap in to correct me if so.

Logic and scientific reasoning

This is a follow-on from my earlier post about whether Aristotle's account of scientific reasoning truly captures what scientific reasoning is. He describes two forms: propter quid where we reason from cause to effect, and quia, where we reason from effect to cause.

Propter quid
Being an A is the cause of anything being a B
This X is an A
This X is a B

Quia
Being an A is the only cause of anything being a B
This X is a B
This X is an A

Neither of these captures the process of geniune scientific reasoning or discovery. In propter quid, the major premiss cannot be known unless the causal connection 'A causes B' has already been established. Since proof of the causal connection is the end-product of scientific reasoning and methodology, rather than the beginning, Aristotle's syllogism captures nothing useful. The same objection applies to the quia form, with the additional objection that the 'only' qualification cannot be established with any certainty at all. Scientific reasoning involves constructing a model of reality that explains the observed effects. It is difficult to establish that such a model is the only one. Ptolemy's model of the solar system (where the earth is at the centre) explained the observations available to ancient scientists. Copernicus' model (sun at the centre, circular orbits) explains the same observations, but in a different way. Kepler's model (sun at the centre, elliptical orbits) is different again. Further changes and refinements to this model continued into the twentieth century. It is difficult to prove that any model is the only explanation of the observed effects.

And in any case, how could such a simple syllogism as Aristotle's capture the essence of what is essentially a complex reasoning process that could take many forms?

See also Thomas Reid on the utility of logic.

"The art of syllogism produced numberless disputes, and numberless sects who
fought against each other with much animosity, without gaining or losing ground,
but did nothing considerable for the benefit of human life. The art of
induction, first delineated by Lord Bacon, produced numberless laboratories and
observatories, in which nature has been put to the question by thousands of
experiments, and forced to confess many of her secrets that before were hid from
mortals: and, by these, arts have been improved, and human knowledge wonderfully
increased.

"In reasoning by syllogism from general principles, we descend to
a conclusion virtually contained in them. The process of induction is more
arduous, being an ascent from particular premises to a general conclusion. The
evidence of such general conclusions is probable only, not demonstrative: but
when the induction is sufficiently copious and carried on according to the rules
of art, it forces conviction no less than demonstration itself does."

On whether 'induction' is any improvement on Aristotelian 'deduction', more later.