69 lines
2 KiB
Markdown
69 lines
2 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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# Atomic and molecular propositions
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Propositions are expressions **that have truth values**, either true or false.
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We call a proposition which does not contain a logical connective (or
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'sentential connective') a **simple proposition**.
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We call a proposition that does contain a logical connective, a **compound
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proposition**.
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Simple propositions are represented within a formal language of sentential logic
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with a single character, customarily _P_ or _Q_. When we refer to the formal
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representation of such propositions in our system of sentential logic (SL) we
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call them **atomic propositions**.
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Compound propositions consist in single characters for each atomic proposition
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that they comprise, combined with a symbol for the logical connective. When we
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refer to the formal representation of such propositions in SL we call them
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**molecular propositions**.
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### Demonstration
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Atomic proposition:
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```
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Socrates was a philosopher.
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(P)
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```
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Molecular proposition:
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```
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Socrates was a philosopher and a drinker.
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(P & Q)
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```
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Connectives in natural language often obscure the logical basis of the
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proposition being expressed (where such a proposition contains a proposition,
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i.e. excluding propositions that are _logically indeterminate_. The molecular
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proposition is above is such an example. In this instance the proposition can be
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expressed more precisely as:
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```
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Socrates was a philosopher and Socrates was a drinker.
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```
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Where propositions in natural language cannot be elucidated by the addition of
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implied logical connectives in the manner above, they must be treated not as
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molecular propositions but as atomic proposition. Example:
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```
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Two splashes of gin and a few drops of vermouth make a great martini.
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```
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If we were to formalise this as:
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```
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Two splashes of gin make a great martini and a few drops of vermouth make a great martini.
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```
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We would lose the sense of the original and we would not be uncovering any logic
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that is in the original.
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