46 lines
1.6 KiB
Markdown
46 lines
1.6 KiB
Markdown
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---
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tags:
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- propositional-logic
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- logic
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---
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# Object and metalanguages
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When we talk about a language we call that language the **object language**. A
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**metalanguage** is a language used to describe some object language.
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When we are developing a formal logical language (which we may call SL or PL for
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'sentential' and 'propositional' logic respectively), the formal language is the
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object language and natural language (e.g. English) is the metalanguage.
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**Demonstration**
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If we talk about German in English, German in the object language and English is
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the metalanguage.
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## Use and mention
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There is an associated distinction: that of use and mention.
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When we create an expression in a language we are said to _use_ that language.
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When we remark upon said expression we are said to be _mentioning_ the language.
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This distinction may correspond to the object and metalanguage difference above
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but doesn't have to; use and mention can happen in the same language. For
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example:
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```
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'London' is the word that denotes the capital of the UK.
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```
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## Metavariables
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A metalinguistic variable (metavariable for short) is an expression in the
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metalanguage that is used to talk generally about expressions of the object
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language. The convention in these notes will be to embolden single letters when
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these letters are used as metavariables.
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For example, instead of saying _'P & Q' is an expression comprising two atomic
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sentences and a conjunction_ we might say **\*P** is an expression comprising
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two atomic sentences and a conjunction. In this instance **P** is a metavariable
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in the metalanguage mentioning the expression P & Q in the object language
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