1. How to Think Logically

2. Chapter Three
The Virtues of Belief

3. Belief, Disbelief, and Nonbelief
Belief = the cognitive attitude of accepting a proposition.
Disbelief = the cognitive attitude of rejecting a proposition.
Nonbelief = the lack of a cognitive attitude of accepting or rejecting a proposition.
Note: In order to identify a particular statement as a belief, disbelief, or nonbelief, we must assume normal circumstances and the speaker’s sincerity.

4. Belief, Disbelief, and Nonbelief

5. Belief’s Virtues and Vices
Among the traits or features of beliefs, some contribute to good reasoning and others to bad.
The good-making features are virtues. The supervirtue is rationality.
Other virtues: accuracy, truth, reasonableness, consistency, conservatism, revisability
The bad-making features are vices. The supervice is irrationality.
Other vices: inaccuracy, falsity, unreasonableness, inconsistency, relativism, dogmatism

6. Accuracy and Inaccuracy
To have an acceptable degree of accuracy, a belief must either represent, or come close to representing, the facts.
If a belief represents the facts, then it is true.
If a belief gets close to representing the facts, then it is approximately true.
When a belief is true it has maximal accuracy; when it is false it has maximal inaccuracy.
Accuracy is a matter of degree.

7. Truth and Falsity
Truth is a belief’s virtue of representing the facts as they are.
Truth, unlike accuracy, is not a matter of degree.

8. Reasonableness
A belief is reasonable if, and only if, it has adequate support.
For an empirical belief, reasonableness is the virtue of being supported by evidence or inference from evidence.
For a conceptual belief, reasonableness is the virtue of being based on good reasons.
Reasonableness is a matter of degree.

9. Two Kinds of Reasonable Belief

10. Consistency
Consistency is a virtue that only a set of beliefs can have.
A set of beliefs is consistent if, and only if, its members could all be true at once.
A set of beliefs is inconsistent if, and only if, its members could not all be true at once.
As a shorthand, a set of beliefs is consistent as long as it is not inconsistent.

11. Propositions
Propositions are true when things are as represented by them and false when they are not.
Thus, propositions have truth conditions, which are the conditions that have to be met for a proposition to be true.
Propositions can be contrasted with concepts, which have no truth conditions.

12. Logical Possibility
Compatible beliefs need not, in fact, be true. Beliefs that are actually false would be consistent if they could all be true in some possible scenario.
A proposition is logically possible if, and only if, it involves no contradiction.
Two propositions are contradictory if they cannot have the same truth value; if one is true, the other must be false and vice versa.

13. Consistency and Possible Worlds
A set of beliefs is consistent if, and only if, there is a logically possible world where its members could all be true at once.
A set of beliefs is inconsistent if, and only if, there is no logically possible world where its members could all be true at once.

14. Consistency and Inconsistency
The following are all inconsistent:
All pigs are mammals, but some pigs are not mammals (Logically Self-Contradictory).
Arnold Schwarzenegger is a doctor and he isn’t (Logically Self-Contradictory).
Arnold Schwarzenegger is a married bachelor (Conceptually Self-Contradictory).
The following is consistent:
Arnold Schwarzenegger is a medical doctor. Pigs fly.

15. Consistency in Logical Thinking
In logical thinking, inconsistent beliefs are to be avoided completely.
A salient feature of logical thinkers is that they reflect upon their beliefs (or the statements they make) and try to make them consistent.

16. Conservatism and Revisability
Conservatism is a belief’s virtue of being compatible with other beliefs we already have.
Revisability is a virtue that beliefs have insofar as they are open to change.
Too little revisability leads to dogmatism.
Too much revisability leads to extreme relativism.

17. Rational Belief A thinker’s belief is rational only if the believer:
has it presently and consciously in his mind
could provide evidence or reasons for it
is not aware of the belief’s failing any of the virtues already discussed

18. Rational vs. Irrational Belief