Foundations of Philosophy
Jurian Traas
FW-TF2015
2022 – 2023
,Inhoudsopgave
LECTURE I – LOGIC......................................................................................................................................... 2
LECTURE 2 – THE MEANING OF LP'S CONNECTIVES......................................................................................... 4
ATOMIC VALUATIONS..............................................................................................................................................4
THE TRUTH VALUE OF A FORMULA.............................................................................................................................5
COMPUTING A TRUTH-TABLE....................................................................................................................................5
THREE WAYS OF USING I=........................................................................................................................................6
SHOWING THAT A NATURAL LANGUAGE ARGUMENT IS VALID...........................................................................................6
EXPLOSION............................................................................................................................................................6
LECTURE 4 – SYLLOGISTIC REASONING........................................................................................................... 6
VALIDITY OF SYLLOGISMS.........................................................................................................................................7
VENN DIAGRAM..................................................................................................................................................... 7
CHECKING SYLLOGISTIC VALIDITY................................................................................................................................8
PREDICATE LOGIC...................................................................................................................................................8
EXAMPLES OF SYLLOGISTIC PROPOSITIONS IN PREDICATE LANGUAGE.................................................................................9
EVALUATING LA FORMULAS...................................................................................................................................10
FREE AND BOUND VARIABLES..................................................................................................................................10
LECTURE 5 – CONCEPTS I.............................................................................................................................. 11
PREAMBLE..........................................................................................................................................................11
PHILOSOPHY OF LANGUAGE....................................................................................................................................11
PHILOSOPHY OF KNOWLEDGE (EPISTEMOLOGY)..........................................................................................................13
LECTURE 6 – CONCEPTS II............................................................................................................................. 14
PHILOSOPHY OF REALITY (METAPHYSICS)..................................................................................................................14
METHODOLOGY...................................................................................................................................................14
LECTURE 7 – CONCEPTS III............................................................................................................................ 15
BELIEF................................................................................................................................................................15
Lecture I – Logic
Logic is the study of (in)validity of argument forms. An Argument is a set of premises and a
conclusion given in support of an idea, action or theory. It contains a set of propositions, one
of which is called the conclusion, while the others are premises. These premises are
interpreted as offering reasons to believe or disbelieve the conclusion (propositions can be
either true or false).
2
, All musicians can read music.
John is a musician.
Therefore, John reads music.
Here, musician is an argument in standard form: first the premises, then the conclusion
follows. However, real life arguments typically do not occur in standard form but in order to
assess them, it is convenient to convert them into standard forms.
An argument can be good, valid, or both. A good argument provides a plausible conclusion
that follows from certain premises. On the other hand, a valid argument provides a
conclusion that necessarily follows from the premises if they are true. We call these
arguments deductive, valid arguments. It is impossible that all premises are true while the
conclusion is false.
An argument is sound when it is valid and when all the premises are true. In the musician
example, Jimi Hendrix did for example not read music, so the argument is valid, but not
sound.
Propositional arguments are formally written as Lp. Other symbols include:
The language Lp is a set of formulas such that:
3
Jurian Traas
FW-TF2015
2022 – 2023
,Inhoudsopgave
LECTURE I – LOGIC......................................................................................................................................... 2
LECTURE 2 – THE MEANING OF LP'S CONNECTIVES......................................................................................... 4
ATOMIC VALUATIONS..............................................................................................................................................4
THE TRUTH VALUE OF A FORMULA.............................................................................................................................5
COMPUTING A TRUTH-TABLE....................................................................................................................................5
THREE WAYS OF USING I=........................................................................................................................................6
SHOWING THAT A NATURAL LANGUAGE ARGUMENT IS VALID...........................................................................................6
EXPLOSION............................................................................................................................................................6
LECTURE 4 – SYLLOGISTIC REASONING........................................................................................................... 6
VALIDITY OF SYLLOGISMS.........................................................................................................................................7
VENN DIAGRAM..................................................................................................................................................... 7
CHECKING SYLLOGISTIC VALIDITY................................................................................................................................8
PREDICATE LOGIC...................................................................................................................................................8
EXAMPLES OF SYLLOGISTIC PROPOSITIONS IN PREDICATE LANGUAGE.................................................................................9
EVALUATING LA FORMULAS...................................................................................................................................10
FREE AND BOUND VARIABLES..................................................................................................................................10
LECTURE 5 – CONCEPTS I.............................................................................................................................. 11
PREAMBLE..........................................................................................................................................................11
PHILOSOPHY OF LANGUAGE....................................................................................................................................11
PHILOSOPHY OF KNOWLEDGE (EPISTEMOLOGY)..........................................................................................................13
LECTURE 6 – CONCEPTS II............................................................................................................................. 14
PHILOSOPHY OF REALITY (METAPHYSICS)..................................................................................................................14
METHODOLOGY...................................................................................................................................................14
LECTURE 7 – CONCEPTS III............................................................................................................................ 15
BELIEF................................................................................................................................................................15
Lecture I – Logic
Logic is the study of (in)validity of argument forms. An Argument is a set of premises and a
conclusion given in support of an idea, action or theory. It contains a set of propositions, one
of which is called the conclusion, while the others are premises. These premises are
interpreted as offering reasons to believe or disbelieve the conclusion (propositions can be
either true or false).
2
, All musicians can read music.
John is a musician.
Therefore, John reads music.
Here, musician is an argument in standard form: first the premises, then the conclusion
follows. However, real life arguments typically do not occur in standard form but in order to
assess them, it is convenient to convert them into standard forms.
An argument can be good, valid, or both. A good argument provides a plausible conclusion
that follows from certain premises. On the other hand, a valid argument provides a
conclusion that necessarily follows from the premises if they are true. We call these
arguments deductive, valid arguments. It is impossible that all premises are true while the
conclusion is false.
An argument is sound when it is valid and when all the premises are true. In the musician
example, Jimi Hendrix did for example not read music, so the argument is valid, but not
sound.
Propositional arguments are formally written as Lp. Other symbols include:
The language Lp is a set of formulas such that:
3
