The most basic metaphysical question is: what is there? Metaphysics is not concerned to find
very specific answers to such questions. For example, it is not looking for answers like: There
are 25 desks in this room; there is water on Mars; there is a rece
In Meditations II and VI, Descartes argues for
Cartesian Dualism (df.): the mind and the body are two totally different things, capable of
Descartes held that
the mind is essentially something that thinks;
the body is essentially so
Degrees of Knowledge
Experience is the first and basic level of knowledge. The Greeks called
experience empeiria, which is at the basis of such English philosophical terms as:
empirical: which means based on the data of the senses, especially if that data
Question 3. Let P = cfw_p1, p2, . be a (possibly infinite) group of people and suppose that certain
finite non-empty subgroups Q1, Q2, . of P are incompatible. Call a subgroup P of P
harmonious if it contains no incompatible subgroup.
(i) Show that there
APPENDIX: GENERAL PREREQUISITES
In the body of this text we have assumed familiarity with several topics not specifically
connected with classical logic. In this appendix we present a brief introduction to these topics.
1. Sets and sequences
The Existence of Nonstandard Models for Arithmetic
An arithmetical model N is one whose domain is the set of natural numbers and for
which there is, for each natural number n, a formula An(x) such that N |= An(x)[m/x] iff m = n.
Recall that ThN = cfw_A: N
Mock Midterm (Logic S01)
Answer three questions.
1. (i) What is a formula of SL?
(ii) Let nc(A) be the number of occurrences of v in A and ns(A) the number of occurrences
of sentence-letters in A. Show by formula induction that ns(A) = nc(A) + 1.
2. (i) W
Meta-Logic (S01): Assignment
1. Give a rigorous proof on the basis of the truth-definition that the following formulas are valid:
(~xPx v ~xPx); ~x(Px v Px); ~x(Px v ~xPx).
2. (i) A formula A (possibly containing free variables) is said to be true under a
1. Let PL- be the same as PL but without the Axiom of Specification. Show that ~xPx H Px is
not a theorem of PL- . (Hint: consider extended valuations in which every universal formula is
made true. Show by induction that each theorem of PL- is
1. Merely use the Deduction Theorem, Modus Ponens and the basic structural properties of _ to
show that the following formulas are theorems:
(A H(B HB),
(A H A) H B) H B),
(A H (B H C) H (A H (C H D) H (A H (B H D).
2. Use the Deduction Theorem
Answer four questions.
1. Let SL + be the result of adding the formulas of as axioms to the system SL. Show the
following (you may presuppose that the system SL is complete):
(i) SL + is sound iff each formula of is a theorem of SL;
(ii) SL + i