Review+Notes+for+Exam+3+_optional+exam+5_

Review+Notes+for+Exam+3+_optional+exam+5_ - Translations in...

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Translations in Predicate Logic: Difference from sentential logic: Recall that in sentential logic (what we did for the first two exams) we used upper case letters to translate declarative sentences (that is, sentences that are true or false). For example (I have used arbitrary letters below): Jon is a teacher : J Everyone loves Simon : E Jon is the cousin of Mike : C Every teacher is an idiot : T London is between Chicago and New Delhi : L Added complexity was noted only where there were truth functional connectives: E.g. If Jon is a teacher then everyone loves Simon : J E Every teacher is an idiot unless Jon is a teacher : ~J T Jon is not the cousin of Mike : ~C Another way to put this is to say that the basic unit of sentential logic was the sentence. Atomic formulas (individual upper case letters) represented whole sentences. Compound formulas were formed by combining an atomic formula (or formulas) with connectives. Predicate logic goes deeper. It analyzes each declarative sentence into a subject and a predicate . In other words, the atomic formulas of predicate logic are always made up of two components- the subject (or subjects) and the predicate. Predicates tell you something about the subject(s). They come in different degrees. If they are degree one, then they are called one-place predicates, and they describe something about the subject (the subject is always an individual thing): Examples of one place predicates: _____ is happy _____ is a teacher If they are degree two, then they are called two-place predicates, and they describe relations between two subjects (or individuals): _____ is the cousin of ________ _____ loves ________ If they are degree three, then they are called three-place predicates, and they also describe relationships: ______ is between ________ and __________ Predicates are symbolized using an upper case letter: e.g. ____ is happy : H _____is the cousin of : C
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As I said above, the basic unit of predicate logic has two components, so a predicate by itself is not a legitimate formula in predicate logic. What is required in addition is a subject. How many subjects attach to the predicate depend on how many places it has. A one-place predicate will be attached to one subject; a two-place predicate to two subjects and so on. Subjects are always individuals of some sort- subjects are always singular terms . A subject can be a person, or a city, or a number. Indeed, it can be any kind of singular thing at all. What is crucial to keep in mind is that a legitimate subject is never plural. So, for example, ‘the five winners of the lottery this week’ is not a legitimate subject because it picks out more than one thing. Subjects are either
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This note was uploaded on 09/15/2011 for the course PHILOSOPHY 201 taught by Professor Morgan during the Spring '08 term at Rutgers.

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Review+Notes+for+Exam+3+_optional+exam+5_ - Translations in...

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