names_predicates - Philosophy 220A: Symbolic Logic I...

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1 Philosophy 220A: Symbolic Logic I Department of Philosophy University of British Columbia Names, Predicates, Identity and Functions 1. Names and Predicates The term ‘atomic sentence’ applies only to sentences of FOL (First Order Logic). One cannot really talk about an English sentence being atomic. But here’s an English sentence that is easily translated into an atomic sentence of FOL: John Donne was a poet. The first thing to note about this sentence is that the two main parts, ‘John Donne’ and ‘poet’ have very different kinds of meaning. For the meaning of ‘John Donne’ is a particular thing , a certain man who lived in England in the 17 th century. The word ‘poet’, on the other hand, has no such meaning, for there have been many poets. (You might point at John Donne, but you cannot point at poet.) Logicians analyze sentences, which means that they break them down into smaller parts. In analyzing a sentence, the first thing to do is identify all the names , or individual constants , that it contains. An individual constant is a word, or sequence of words, whose meaning is some single, particular object, such as John Donne. Thus the following are all names, or individual constants: Calgary Mars The Lions Gate Bridge Larry Campbell Note that some objects in the world have no individual constant (in English, at least), and others have more than one name. The same is true of FOL, which can have multiple names for one object and no name for another. One difference between FOL and English is that FOL cannot have any names (like ‘Zeus’) that have no objective meaning, i.e. which don’t refer to anything real. Once all the names in a sentence have been identified, the analysis proceeds by removing it (or them) from the sentence, leaving a hole (or holes) behind. Thus the above sentence becomes: …………… was a poet.
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2 This sentence with a hole in it is called a predicate . In this case it’s a one-place predicate, as it has just one hole. Rather than using a row of dots to mark the hole, however, we use a ‘variable’, which is one of the (lower-case) letters t , u , v , w , x , y or z . (Usually we start with ‘ x ’ for the first hole, and then use ‘ y ’ and ‘ z ’ next.) So the predicate can be written: x was a poet. In FOL, this predicate would be written as something like: Poet(x). There are a few things to notice here. 1. A predicate in FOL is always a single word, in the sense that there are no spaces in it. 2. A predicate in FOL always begins with a capital letter. 3. The variable(s) that mark the hole(s) in the predicate are placed inside brackets that follow the predicate. How can John Donne be referred to in FOL? We can define a name in FOL that refers to him, such as donne . Note that: 1. A name (individual constant) in FOL is a single word (no spaces). 2.
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This note was uploaded on 11/03/2009 for the course ECON 210 taught by Professor James during the Spring '09 term at The University of British Columbia.

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names_predicates - Philosophy 220A: Symbolic Logic I...

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