David Abel

Fun Idea Survey

For a few weeks in 2021, I collected a list of ideas, puzzles, questions, and research papers that I find fascinating. I may plan to pick this back up every so often. Here is the running list so far, cataloguing (1) the wiki article if it exists, (2) a 1-2 sentence summary of the idea, (3) a single pointer to find out more, and (4) a pointer to the tweet, in case some weeks produce fun conversation. Please feel free to reach out to discuss :)

Here is the list in reverse chronological order:

• Brief Summary: How do we prove a claim? The trilemma says there are three ways to provide justification:
1. A circular argument (\(A\) implies \(B\), \(B\) implies \(A\)).
2. An infinite argument (\(X_i\) implies \(X_{i+1}\), for all \(i\)).
3. Invoking "brute facts" or assumptions (Brute fact \(A\) implies \(B\))
But, Agrippa, Popper, and others stipulate that these are each problematic (with the third requiring a break from the principle of sufficient reason). How are we to determine which of the three is the appropriate way to justify our claims? (Note: closely related to Caroll's skepticism about Modus Ponens, coming soon to the list).
• Links: SEP on Foundationalist Epistemology, which takes the third prong of the trilemma (as many do, I believe).
• Tweet

• Links: SEP snippet by Ichikawa and Steup, or The Inescapability of Gettier Problems by Zagzebski.
• Quick Summary: What is knowledge? One classical view dating back to Plato's Meno is that knowledge is justified, true, belief. Gettier problems are a kind of counterexample to this definition of knowledge. They work by by showing there are routes for an agent to come to justified, true, belief, purely by chance in a way that leaves skepticism as to whether knowledge is really at play. See Gettier's short two page paper for such examples.
• Tweet
• Origins: Gettier (1963).

• Links: SEP snippet by Bridges, or the pair of books by Stillwell (more high level) or Simpson (more technical detail).
• Quick Summary: Much of math is about committing to a set of axioms and determining what other statements are provable from those axioms. Reverse math takes the alternate approach, instead starting with the desirable theorems, then determining which axioms are strictly required to support proof of the desired theorems.
• Tweet
• Origins: Friedman (1975).

• Links: SEP Article by Daniels
• Quick Summary: Daniel's says it quite nicely: "the end-point of a deliberative process in which we reflect on and revise our beliefs about an area of inquiry". In this sense one could view it as a possible gold standard of belief maintenance: All of an individual's views about a particular domain cohere with one another. My only addendum is that it is likely fair to replace "we" with "an agent", as we might imagine the same deliberative process (and the fixed points resulting from its application) being relevant to artificial agents, too.
• Tweet
• Origins: Goodman and Rawls

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