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A formal language for propositional logic
A formal logical language; formal assertions; parse trees; induction on formulas; unique readability
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Joel David Hamkins
Classical propositional logic—introduction
Propositional logic as a clarification of ambiguity, truth tables, propositional worlds, logical entailment, validity, tautologies
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Joel David Hamkins
6
Infinite liars
Regrettably, this chapter consists entirely of lies—every sentence in it, including this one, is false.
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Joel David Hamkins
Epistemic logic and the problem of common knowledge
With the two generals, Cheryl's birthday, hidden surprises, blue-eyed islanders, pirate treasure division, philosopher's ruling council, coordination…
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Joel David Hamkins
3
Potential versus actual infinity
Potentialism and actualism offer radically different conceptions of the infinite—the dispute between them will lead us to ultrafinitism and the diverse…
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Joel David Hamkins
16
The paradox of giants
Galileo argued that the giants of folklore, taking human form but at much larger scale, are physically impossible. Similar ideas will lead us to many…
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Joel David Hamkins
Self-similar self-similarity
Let us explore the nature of symmetry, beginning simply, but moving steadily to abstraction, eventually to the symmetries of the symmetries themselves…
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Joel David Hamkins
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The mathematics and philosophy of the infinite
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