7. “Or”
... Plato’s writings are dialogues, which are like small plays. In most of these, Plato made Socrates the protagonist of the philosophical drama that ensues. Several of the dialogues are named after the person who will be seen arguing with Socrates. In the dialogue Euthyphro, Socrates is standing in lin ...
... Plato’s writings are dialogues, which are like small plays. In most of these, Plato made Socrates the protagonist of the philosophical drama that ensues. Several of the dialogues are named after the person who will be seen arguing with Socrates. In the dialogue Euthyphro, Socrates is standing in lin ...
Why the “veridic” is not any better than the “liar”
... be done—by those lucky creatures who, as distinct from ideas, can sleep— furiously (again, in the sense intended here). When we try to actually think the thought that is pretendedly expressed in that sentence we find that we do not know how to go about it, and in particular, how to connect the parti ...
... be done—by those lucky creatures who, as distinct from ideas, can sleep— furiously (again, in the sense intended here). When we try to actually think the thought that is pretendedly expressed in that sentence we find that we do not know how to go about it, and in particular, how to connect the parti ...
What should we make of Wittgenstein`s paradoxical claim at the end
... meant to help us see that to ask “How can I justify such and such a belief?” is to ask the wrong question. In the previous example, Ian is trying to think of all the possible sources of worry and hopes not to find any but, through the paradoxical statement in (4), his friend points out that to do s ...
... meant to help us see that to ask “How can I justify such and such a belief?” is to ask the wrong question. In the previous example, Ian is trying to think of all the possible sources of worry and hopes not to find any but, through the paradoxical statement in (4), his friend points out that to do s ...
Metaphysics As Speculative Nonsense
... can do so in principle. We know how to show whether it is true or false, so it is ‘verifiable’ even though we can’t actually verify it. Why think these are the only two possibilities for meaning? Given that everyone accepts that empirical hypotheses are meaningful, the debate is, then, over a prior ...
... can do so in principle. We know how to show whether it is true or false, so it is ‘verifiable’ even though we can’t actually verify it. Why think these are the only two possibilities for meaning? Given that everyone accepts that empirical hypotheses are meaningful, the debate is, then, over a prior ...
(˜P ∨ ˜Q) are tautologically equivalent by constructing a truth
... 8. ˜R → P. ˜S → ˜P. R → S ∴ R 9. ˜Z. (R → ˜Z) → (Q ∧ P ) ∴ (Q ∧ P ) 10. ˜R. P ↔ (R ∧ (P ∨ S)) ∴ P → ˜S 11. ˜((P ↔ Q) ∨ ˜(Q → P )) ∴ ˜Q ∧ P ...
... 8. ˜R → P. ˜S → ˜P. R → S ∴ R 9. ˜Z. (R → ˜Z) → (Q ∧ P ) ∴ (Q ∧ P ) 10. ˜R. P ↔ (R ∧ (P ∨ S)) ∴ P → ˜S 11. ˜((P ↔ Q) ∨ ˜(Q → P )) ∴ ˜Q ∧ P ...
Relating Infinite Set Theory to Other Branches of Mathematics
... to Other Branches of Mathematics Roads to Infinity: The Mathematics of Truth and Proof. By John Stillwell, AK Peters, Natick, Massachusetts, 2010, 250 pages, $39.00. The infinite, wrote Jorge Luis Borges, is a concept that “corrupts and confuses the others.” Certainly, the theory of large infinite s ...
... to Other Branches of Mathematics Roads to Infinity: The Mathematics of Truth and Proof. By John Stillwell, AK Peters, Natick, Massachusetts, 2010, 250 pages, $39.00. The infinite, wrote Jorge Luis Borges, is a concept that “corrupts and confuses the others.” Certainly, the theory of large infinite s ...
Predicate Logic
... If P(x) denotes “x is an undergraduate student” and U is {Enorlled Students in COMPSCI 230}, then x P(x) is TRUE. If P(x) denotes “x > 0” and U is the integers, then x P(x) is FALSE. If P(x) denotes “x > 0” and U is the positive integers, then x P(x) is TRUE. If P(x) denotes “x is even” and U is ...
... If P(x) denotes “x is an undergraduate student” and U is {Enorlled Students in COMPSCI 230}, then x P(x) is TRUE. If P(x) denotes “x > 0” and U is the integers, then x P(x) is FALSE. If P(x) denotes “x > 0” and U is the positive integers, then x P(x) is TRUE. If P(x) denotes “x is even” and U is ...
Welcome to CS 245
... of our formal systems can be expressed in those systems themselves. This is unfortunately not always possible, and we will briefly examine the reasons. Our goal, however, will be to formalize enough of mathematics to be able to apply the formalisms of logic to proofs of program ...
... of our formal systems can be expressed in those systems themselves. This is unfortunately not always possible, and we will briefly examine the reasons. Our goal, however, will be to formalize enough of mathematics to be able to apply the formalisms of logic to proofs of program ...
x, y, x
... • P R(x, y) : course x is a prerequisite for course y . Q: Is ∀x, ∃y, P R(x, y) true? no, not every course is a prerequisite of some course. Q: Is ∃x, ∀y, P R(x, y) true? no. Q: Do ∃x, ∀y, P R(x, y) and ∀y, ∃x, P R(x, y) mean the same thing? I.e., are they logically equivalent? no. One says, there i ...
... • P R(x, y) : course x is a prerequisite for course y . Q: Is ∀x, ∃y, P R(x, y) true? no, not every course is a prerequisite of some course. Q: Is ∃x, ∀y, P R(x, y) true? no. Q: Do ∃x, ∀y, P R(x, y) and ∀y, ∃x, P R(x, y) mean the same thing? I.e., are they logically equivalent? no. One says, there i ...
