PHIL1005 Lecture Notes - Lecture 7: Definite Description, Universal Quantification, Existential Quantification
7.1 PREDICATES AND DESIGNATORS
Propositional Logic
- We have been dealing with whole atomic propositions.
- A, B, C…
- These represent statements that are independently truth apt.
- This allows us to tabulate and consider the truth conditions of compound propositions made up of
these atomic propositions and connectives
Connectives in Propositional Logic
, &, v, ~,
- These connectives all interact with atomic propositions truth-functionally
- They take the truth values of some other set of propositions and deliver a truth value
Predicate Logic
- Using Predicate Logic we can look more closely at the structure of propositions
- Consider the following argument.
- Conclusion must be identical to antecedent of conditional premise
Singular Terms
- Some words and phrases pick out a particular object.
- ‘Sophie’ picks out a particular object
- Can’t assign a truth value to an object
- Other particular object designators include definite descriptions: ‘the meanest swan in the ACT’ picks
out a particular swan
Non-specific Singluar Terms
- ‘The meanest swan in the ACT is a singular term. It is what is called a definite description.
- ‘Jill saw a swan’
- ‘a swan’ is singular but not specific. It is sometimes called an ambiguous description.
- It picks out a swan but not a specific swan. Many different swans could help make ‘Jill saw a swan’ term
Predicates
- Predicates are terms or phrases that pick out properties and relations.
- ‘Sophie is angry’
- ‘Jill has more money than Alex’
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- E.g. being taller than.
- Can have more than 2 relations
Notations for Predicates and Singular
- Lower case letters (exluding w, x, y and z) will stand for particular objects
- Capital letters will stand for predicates
- ‘Sophie is angry’ will be represented as ‘As’
- ‘Jill has more money than Alex’ will be represented as ‘jRa’
- Capital without any adjacent lower case letters stand for whole propositions.
Truth of Simple Predicative Propositions
- ‘Alex is a frog’ Fa
- Fa is truth just in case Alex really is a frog.
- ‘Jill has more money than Alex’ jRa
- jRa is truth just in case Jill really has more money than Alex
Set of Things
- ‘Alex is a frog’
- Fa
- Has to be in the box and in the selected area
Connectives
- ‘Alex is a frog or he is a lamppost’
- Fa v La
- ‘Donald is horrible and orange’
- Hd & Od
Truth in a Situation
- ‘Alex is a frog or he is a lamppost’
oFa v La
oBoth a and b are in the circle. Truth vale is truth.
- ‘If Alex is a frog then he eats flies.’
oFa Ea
oINSERT DIAGRAM
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Document Summary
We have been dealing with whole atomic propositions. These represent statements that are independently truth apt. This allows us to tabulate and consider the truth conditions of compound propositions made up of these atomic propositions and connectives. These connectives all interact with atomic propositions truth-functionally. They take the truth values of some other set of propositions and deliver a truth value. Using predicate logic we can look more closely at the structure of propositions. Conclusion must be identical to antecedent of conditional premise. Some words and phrases pick out a particular object. Can"t assign a truth value to an object. Other particular object designators include definite descriptions: the meanest swan in the act" picks out a particular swan. The meanest swan in the act is a singular term. It is what is called a definite description. It picks out a swan but not a specific swan. Many different swans could help make jill saw a swan" term.
