I don't think it is strictly true that Grothendieck didn't rely on examples. Here is a quote from a letter from Luc Illusie, who was a grad student under Grothendieck. Quote:
...“In his filing cabinets, located behind his desk, Grothendieck kept many handwritten notes, where he had studied specific examples: he sometimes told me that he was weak on surfaces, but as everybody knows, he was not so weak in local algebra, and he knew enough of curves, abelian varieties and algebraic groups to be able to test his ideas. Also, his familiarity (and constant intere
Semi related article (pdf link):
What Is the Enemy of My Enemy? Causes and Consequences of Imbalanced International Relations, 1816–2001
Abstract:
...This study explores logical and empirical implications of friendship and enmity in world politics by linking indirect international relations (e.g., “the enemy of my enemy,”“the enemy of my friend”) to direct relations (“my friend,”“my enemy”). The realist paradigm suggests that states ally against common enemies and thus states sharing common enemies should not fight each other. Nor are states expected to ally w
The Logic Matters blog has three posts on the topic "Does mathematics need a philosophy?"
The page What Has Experimental Philosophy Discovered about Expert Intuitions? on the Experimental Philosophy blog has been updated. It contains several links to papers on the area.
You may remember early in the Arabian revolutions in Libya, an American student took the summer off college to fight in the revolution.
Adding to this, there is an entire online community of these people at the Black Flag Cafe. Outsiders label them as "war tourists," but the majority of them are journalists, war photographers, businessmen, and humanitarians/activists. The website was founded by Robert Young Pelton (whose wikipedia page is worth reading). He wrote a great book, that is filled with practical information.
RE: how / why distinction.
John Whitmore's book Coaching for Performance goes into this. Snippit from the book:
...If commanding a person to do what they need to do does not produce the desired effect, what does? Let's try a question.
"Are you watching the ball?" How would we respond to that? Defensively, perhaps, and we would probably lie, just as we did at school when the teacher asked us if we were paying attention.
"Why aren't you watching the ball?" More defensiveness -- or perhaps a little analysis if you are that way inclined.
Tychomancy: Inferring Probability from Causal Structure by Michael Strevens (a philosophy professor at NYU). From the blurb:
...Maxwell's deduction of the probability distribution over the velocity of gas molecules—"one of the most important passages in physics" (Truesdell)—presents a riddle: a physical discovery of the first importance was made in a single inferential leap without any apparent recourse to empirical evidence.
Tychomancy proposes that Maxwell's derivation was not made a priori; rather, he inferred his distribution from non-probabili
Logic: The Drill by Nicholas J.J. Smith and John Cusbert.
Free 300 page PDF that contains a variety of solved exercises from propositional and predicate logic. Description from the authors:
One obvious use of this work is as a solutions manual for readers of Logic: The Laws of Truth—but it should also be of use to readers of other logic books. Students of logic need a large number of worked examples and exercise problems with solutions: the more the better. This volume should help to meet that need.
Related to this, there are a couple of professional philosophers around that are starting to take conspiracy theories seriously. Not just in the manner of critically analysing them, but also in the sense of how to actually make inferences about the existence of a conspiracy, how to contrast official theories and conspiracy theories, and how to reason with disinformation present.
One of these individuals is Matthew Dentith, who did his PhD In defence of conspiracy theories on these topics (and is in the process of writing a full book on the matter). The oth...
With respect to (2) classical rhetoric has the topics of invention.