Singular Propositions
Singular propositions are propositions about an individual to which some property is attributed. The individual is referred to by a name, and the property is referred to by a predicate. Here are some examples of singular propositions:
| 1. Walter is spiffy. |
| 2. Belinda is tall |
| 3. Tyler can dribble. |
In each of these examples, there is an individual, Walter, Belinda, and Tyler. Each has a property. Walter has the property of being spiffy, Belinda the property of being tall, and Tyler the property of being able to dribble. "Walter," "Belinda," and "Tyler" are names. The English expressions "is spiffy," "is tall," and "can dribble" are predicates.
To represent names in Quantificational Logic, we use lower case letters from the beginning of the alphabet. We call such an element an individual constant. So here are our translations of the three names from our three propositions above:
| a : Walter |
| b : Belinda |
| c : Tyler |
To represent the predicates, we use what we'll call a propositional function, which consists of an upper case letter, followed by a lower case letter from the end of the alphabet:
| Sx : x is spiffy |
| Tx : x is tall |
| Dx : x can dribble. |
We call the lower case letter from the end of the alphabet an individual variable, to distinguish it from the individual constants.Think of the individual variable as a placeholder, the position which could be occupied by an individual constant. The propositional function, by itself, does not express a proposition. It can be transformed into a proposition (something that can be true or false) when we replace the individual variable with an individual constant. Putting these two pieces together, we have the translation of a singular proposition into Quantificational Logic:
| English Sentence | Quantificational Logic Translation |
| 1. Walter is spiffy. | Sa |
| 2. Belinda is tall | Tb |
| 3. Tyler can dribble. | Dc |
The first skill you'll need to develop is the skill of recognizing singular propositions. Once you've recognized a sentence as a singular proposition, distinguish the name from the propositional function, select the appropriate abbreviations, and finish the translation. In the following exercise, you're just asked to pick out the singular propositions from a larger sample. In the second exercise, you'll translate singular propositions.
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