HKBU, 2019. Introduction to epistemology and logic. Truth vs Reality. Statements Vs Knowledge. A priori. A posterior. Laws of Logic. Categorical argument, Disjunctive argument, Hypothetical argument

1. Formal Logic
Domenic Marbaniang, 2019

2. Definition of Knowledge
The classic definition was “Knowledge is Justified True Belief” (JTB).
If it’s not true, then it’s not knowledge, it’s misconception, false belief, or
ignorance.
The “justification” requirement was challenged by Gettier (1963) who noted
that sometimes, what one believes can turn out to be true, despite invalid
justifications.

3. Sources of Knowledge
1. Experience
2. Reason
3. Memory
4. Secondary sources (Testimony)
Do you think these can be combined into one or two?

4. Aristotle’s 3 Laws of Logic
1. Law of Identity
A is A
2. Law of Non-contradiction
A is not not-A
3. Law of Excluded Middle
Either A or Not-A

5. Types of knowledge
A priori - before experience (does not need experience to prove it)
E.g. Laws of logic
A posteriori - after experience (derives from experience)
E.g. At 14:30 hrs, there was traffic jam on Nathan Road, Mongkok.

6. Types of statements
Analytic - The predicate does not add to the subject
e.g. All bachelors are unmarried men.
Synthetic - the predicate adds something to the subject
E.g. The book is a mathematics text-book.

7. Statements expressing knowledge
1. Analytic a priori. e.g. All 14 year olds are
teenagers.
2. Synthetic a posteriori. e.g. It is raining.
3. Synthetic a priori. e.g. Every effect has a
cause.

8. Truth vs Reality
Epistemology deals with the meaning of Truth; Ontology deals with the
meaning of reality. True or false is predicated of statements only. Real or
unreal is predicated of existence. There are different kinds of truths that are
truthful only within their contexts. For instance, there are poetical truths
expressed in statements that would appear total falsehood in any other
linguistic context or genre. Truth is that which is known about reality. As such,
therefore, truth, in common experience, is substantial.

9. Statements Vs Arguments
Statements may be true or false
Arguments may be valid or invalid

10. 2 Types of Argument (Reasoning)
Deductive: From a general truth to a specific conclusion
E.g. All men are mortals
Socrates is a man
Therefore, Socrates is mortal.
Inductive: From a specific fact to a general conclusion (as in sampling
method)
E.g. Food: Taste a little of the dish to determine the taste of the whole dish.

11. Deductive argument:
1. Categorical
Examples:
All men* are mortals (All A is B) - Major Premise
Socrates is a man (C is A) - Minor Premise
Therefore, Socrates is mortal. (∴ C is B) - Conclusion
All drummers* like jazz. (All A is B) - Major Premise
Some singers are also drummers. (Some C are A) - Minor Premise
Therefore, some singers like jazz. (∴ Some C are B) - Conclusion
*”Man/men” in example 1 and “drummers” in example 2 (A in both) are known as middle terms, because
they occur in both the premises. According to rules of categorical argument, 1. One of the middle terms
must always be the major category (refer to all members). 2. Both the premises cannot be negative 3. If
one of the premise is a negative statement, then the conclusion should also be negative.
A=B
C
A=B
C

12. Deductive argument:
2. Hypothetical
1. If it rains, then the ground is wet (If A, then B)
2. It rained (A)
3. Therefore, the ground is wet (∴ B)
1. If it rains, then the ground is wet (If A, then B)
2. The ground is not wet (Not B)
3. Therefore, it did not rain (∴ Not A)
In both examples, A is antecedent and B is consequent. According to the rule of hypothetical argument,
the Minor Premise must also either be an affirmation of antecedent or denial of consequent. The above
are the only two valid forms of hypothetical arguments).

13. Deductive argument:
3. Disjunctive
1. Either he is happy or he is sad (Either A or B)
2. He is not happy (Not A)
3. Therefore, he is sad. (∴ B)
1. Either he is happy or he is sad (Either A or B)
2. He is not sad (Not B)
3. Therefore, he is happy. (∴ A)
A and B are known as the disjuncts. In a valid disjunctive argument, the minor premise will always be a
denial of one of the disjuncts; the conclusion, will be an affirmation of the other disjunct. The above are the
only two valid forms of disjunctive argument.

14. How do we know it's true?
Consistency Test:
1. Does it conform to the laws of logic?
2. Is the reasoning form valid?

15. How do we know it's true?
Correspondence test: Does it correspond to
what we know of reality?

16. How do we know it's true?
Coherence test: Does it cohere with the body of
established facts?

17. How do we know it's true?
Pragmatic test: Does it work or is it useful?

18. How do we know something is true?
1. Correspondence
2. Coherence
3. Consistency
4. Workability (mostly scientific theories)

19. Are we justified in holding beliefs?
1. Evidentialism: Don't believe anything unless you got sufficient evidence
to prove it's true
2. Foundationalism: There are some beliefs that are properly basic and
foundational (Alvin Plantinga). You are justified in holding a belief unless
you have a reason not to do so. (Richard Swinburne)

20. From the Readings (Marbaniang, Epistemics)
1. What are the two main sources of knowledge in Western philosophy?
Reason and Experience
2. What are the three types of deductive argument?
Categorical, Hypothetical, Disjunctive
3. What is the class of knowledge not dependent on experience?
A priori knowledge
4. What is the class of knowledge dependent on experience?
A posteriori knowledge
5. What is the difference between Truth and Reality?
Truth relates to our knowledge of reality (epistemological). Reality is what is as it is (ontological)
6. What are the four main tests of truth?
Consistency test, Correspondence test, Coherence test, Pragmatic test

21. From the Readings (Swinburne, Basicality)
1. What are the two ways of understanding a person’s “total available
evidence”?
(a) internalist: set of personal basic beliefs (b) externalist: set of public beliefs
2. What are four kinds of basic beliefs?
(a) perceptual (b) memory (c) awareness of mental states (d) beliefs not caused by other beliefs
3. What determines the strength of a basic belief?
The strength of a basic belief (or semi-belief or inclination to believe) is determined by how much it
fits well with the other beliefs (how coherent it is).
4. What happens when a “basic belief” loses strength?
It gets eliminated
5. What is the Principle of Credulity?
Things are probably as they seem to be. The rational person believes everything until she has reason not to do so.
Having a basic belief is a reason for having a belief.

22. Criteria
● Criterion of Scope: The greater the scope of a hypothesis, the less it is likely to be true.
● Criterion of Simplicity: Other things being equal, a simpler hypothesis is more probably true and so the simplest
hypothesis is the one most probably true.

23. Logic Review

24. 1. Categorical Argument
Examples:
All men* are mortals (All A is B) - Major Premise
Socrates is a man (C is A) - Minor Premise
Therefore, Socrates is mortal. (∴ C is B) - Conclusion
All drummers* like jazz. (All A is B) - Major Premise
Some singers are also drummers. (Some C are A) - Minor Premise
Therefore, some singers like jazz. (∴ Some C are B) - Conclusion
*”Man/men” in example 1 and “drummers” in example 2 (A in both) are known as middle
terms, because they occur in both the premises. According to rules of categorical
argument, 1. One of the middle terms must always be the major category (refer to all
members; i.e. the middle term must be distributed). 2. Both the premises cannot be
negative 3. If one of the premise is a negative statement, then the conclusion should also
be negative.
A=B
C
A=B
C

25. 2. Hypothetical
1. If it rains, then the ground is wet (If A, then B)
2. It rained (A)
3. Therefore, the ground is wet (∴ B)
1. If it rains, then the ground is wet (If A, then B)
2. The ground is not wet (Not B)
3. Therefore, it did not rain (∴ Not A)
In both examples, A is antecedent and B is consequent. According to the rule of hypothetical argument,
the Minor Premise must also either be an affirmation of antecedent or denial of consequent. The
above are the only two valid forms of hypothetical arguments).
Antecedent: If it rains
Consequent: the ground is wet
Valid forms:
If A, then B
A
Therefore, B
-----------
If A, then B
Not B
Therefore, not A
Invalid forms:
If A, then B
B
Therefore, A
----------
If A, then B
Not A
Therefore, not B

26. 3. Disjunctive
1. Either he is happy or he is sad (Either A or B)
2. He is not happy (Not A)
3. Therefore, he is sad. (∴ B)
1. Either he is happy or he is sad (Either A or B)
2. He is not sad (Not B)
3. Therefore, he is happy. (∴ A)
A and B are known as the disjuncts. In a valid disjunctive argument, the minor premise will always be a denial of
one of the disjuncts; the conclusion, will be an affirmation of the other disjunct. The above are the only two valid
forms of disjunctive argument.
Invalid forms:
Either A or B
A
Therefore, not B
----------------------
Either A or B
B
Therefore, not A

27. Internalism Vs Externalism (Epistemic Justification)
View Access Basis Responsibility
Internalism
(subjective)
A person always has
access to or can be
aware of why he
believes in
something
One’s internal
(mental) states are
important justifiers of
a belief
An internal sense of
conformity to
responsibility and
duty towards truth is
the justification for
one’s belief
Externalism
(objective)
It is not the case that
a person always has
access to or can be
aware of the
reasons or
justifications for his
belief
There are things
other than mental
states that act as
justifiers of belief
Belief is justified, not
by any sense of
duty, but by the
strength of
evidential support
and objectivity.