The Art of Logic
logical explanations need to be independent of personal experiences.
Eugenia Cheng • The Art of Logic
It is important to note that this is logically different from concluding that the hypothesis is false, which would be the opposite rather than the negation. If you have insufficient evidence to support a hypothesis, it means that the truth value is still unknown. Maybe you need more data. Maybe you need a better experiment.
Eugenia Cheng • The Art of Logic
Like time, logic has a direction and we must not try to violate it.
Eugenia Cheng • The Art of Logic
Looking for axioms, or starting points, in my own system of beliefs has led me to a much clearer understanding of my own thinking.
Eugenia Cheng • The Art of Logic
Starting points in own system of thinking is the keyword . You have to relate to everything from your own beliefs
A is a sufficient condition for B. B is a necessary condition for A. • A is true only if B is true. Only if B is true is A true.
Eugenia Cheng • The Art of Logic
The two are linked, but in mathematics they are particularly cyclically linked.
Eugenia Cheng • The Art of Logic
soundly but starting from different basic beliefs. So two people can both be logical but still disagree about things.
Eugenia Cheng • The Art of Logic
A implies B. B is implied by A. • If A then B. B if A.
Eugenia Cheng • The Art of Logic
I will keep coming back to is that you can be alogical without being illogical, and indeed being alogical is unavoidable and sometimes beneficial or even crucial, whereas being illogical is undesirable.