Category Archives: logic

Mathematical Aphorisms. Part 6.

It seems underemphasized that the parsimony of ZFC in the way of ‘types’ (having only one sort called sets) has the following practical and notational virtue: you can get by with a single type of the quantifier , and a … Continue reading

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Reading Bolzano. Part 0.

This serial will provide, in many and short installments, created every now and then, provide a new translation into English of, and commentary on, the German original of Bernard Bolzano’s 1837 classic book ‘Wissenschaftslehre’. I omit the front-matter and table … Continue reading

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Vignettes. Part 11.

There is a body of results in higher category theory which this expository blog post will present you a toy version of. Not to bias this post too much, and not to slight said body of results (they actually are … Continue reading

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Vignettes. Part 10.

In one of his very useful writings, Robert Harper writes the following thoughtful sentence: But the upshot of Gödel’s Theorem is that as soon as we fix the concept of formal proof, it is immediate that it is not an … Continue reading

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Vignettes. Part 8.

The following is an illustration of a very widely known, yet not widely-enough-known basic connection between things. Explanations will not be given. They can easily be found, given internet access. This connection gives a structure and systematic explanation for some … Continue reading

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Mathematical Aphorisms. Part 2.

One should intentionally take an intensional view on the things one cares about.

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Vignettes. Part 6.

If one cares for categories, one should intentionally take an intensional view on them:  axioms matter. In particular, associativity is an axiom. But it is excusable that one sometimes forgets that associativity is axiomatic: so many categories are concretizable (and then, … Continue reading

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