Add this site to your Home Screen by opening it in Safari, tapping and selecting "Add to home screen"

Our panel of 88 professional philosophers has responded to

- 267 Language
- 1224 Ethics
- 359 Religion
- 246 Justice
- 274 Mind
- 58 Abortion
- 79 Physics
- 113 Children
- 43 Color
- 334 Logic
- 73 Death
- 33 Sport
- 136 Existence
- 64 Happiness
- 29 Gender
- 69 Perception
- 262 Knowledge
- 147 Freedom
- 90 Time
- 71 Emotion
- 68 Business
- 128 Love
- 37 Race
- 75 Beauty
- 30 Space
- 58 Punishment
- 198 Science
- 560 Philosophy
- 77 Identity
- 1 Action
- 109 Art
- 5 Euthanasia
- 70 Feminism
- 31 Music
- 24 History
- 48 War
- 91 Law
- 126 Profession
- 2 Culture
- 101 Biology
- 214 Education
- 149 Sex
- 59 Truth
- 202 Value
- 21 Suicide
- 4 Economics
- 36 Literature
- 107 Animals
- 52 Medicine

To my knowledge, no. Ordinary first-order logic quantifies only over individuals (none of which are literally true) rather than over truth-valued things such as sentences or propositions. Thus there's nothing in first-order logic to which the predicate "is true" can apply. For that you need higher-order logic, which is a topic of controversy in its own right.

By "set of all true propositions," I take it you mean "a set of all the true propositions there are," i.e., the extension of the predicate "is a true proposition." A Cantorian argument due to Patrick Grim concludes that no such set is possible. It works by

reductio. Let T be any set containing all of the true propositions. If T exists, then it has infinitely many members, but that doesn't affect the argument. Now consider the power set of T -- P(T) -- which is the set whose members are all of thesubsetsof T. It's provable that any set has more subsets than it has members. With respect to each of those subsets in P(T), there is a true proposition concerning whether the propositionSnow is whitebelongs to that subset. It follows, then, that there are more true propositions than there are members of T, contrary to the assumption that T is the set ofallthe true propositions there are. So no such set as T exists.