- (1), (2), and (3)(logic and argumentation)
- Numbered statements or propositions referenced earlier in a larger argument (not shown in this excerpt).
- Error is logically excluded(epistemology)
- It's impossible for something to be false or wrong—the claim rules out any possibility of mistake by the rules of logic alone.
- Infallibilism(epistemology (the study of knowledge))
- The philosophical position that knowledge only counts as real knowledge if it's completely certain and impossible to be wrong about.
- Jointly inconsistent(logic)
- Two or more statements cannot all be true at the same time; accepting one means you have to reject the others.
- Jointly refuting(logic)
- Two or more statements proving that a third statement is false by being true together.
- Ludwig Wittgenstein(the philosopher whose critique is referenced)
- An influential 20th-century philosopher who revolutionized thinking about language by claiming that words get their meaning from everyday use, not from representing fixed ideas.
- René Descartes(the philosopher the Cartesian Circle is named after)
- A French philosopher from the 1600s famous for saying 'I think, therefore I am.' He tried to find absolutely certain knowledge by doubting everything he could, and argued that God's existence was needed to guarantee our thinking is reliable.
- knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
- Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.