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January 3, 2010 10:52
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Here are the logic symbols I use, roughly in order of frequency, along with a | |
brief description of what they do. The main logical paradigms used by philosophers are | |
sentential logic (that is the logic of sentences), predicate logic and modal logic | |
(which deals with necessity and possibility). Each is roughly a superset of the former. | |
∀ [predicate] | |
- the universal or 'for all' quantifier. This is used to specify that some | |
statement applies to all things which match. | |
- Example: (∀x)(Fx→Gx) means for all things x, all x's that are F are G. | |
e.g. for all things x, if x is frosty (F), x is cold (G). | |
∃ [predicate] | |
- the existential or 'for at least one' quantifier. This is used to | |
specify that some statement applies to at least one thing. | |
- Example: (∃x)(Fx) means for at least one thing x, x is F. | |
e.g. there is at least one dog that can bark. | |
¬ [sentential] | |
- negation. ¬P just means "not P". | |
in programming, this would be !expr. | |
∧ [sentential] | |
- logical and. Think about it the same way you would | |
([Expr foo] && [Expr bar]) in C/Java-style languages. | |
∨ [sentential] | |
- logical or. Equivalent to "||" in C/Java-style programming languages. | |
→ [sentential] | |
- conditional. P→Q means "if P, then Q" | |
▢ [modal] | |
- a square is the symbol for 'necessarily'. | |
Example: ▢P means it's necessarily so that P. | |
◇ [modal] | |
- a diamond is the symbol for 'possibly'. | |
Example: ◇Q→P means "if Q is possibly true, then P is true" | |
∴ [sentential] | |
- therefore. Often used in both sentential and predicate logic to specify | |
a conclusion in a multiple step logical formulation. | |
Many philosophers since Russell also use set theory to express their ideas: | |
⊂ | |
- union | |
⊃ | |
- intersection | |
∪ | |
- subset of | |
∩ | |
- superset of | |
Further reading | |
--------------- | |
Basic logic textbooks: Samuel Guttenplan's "Languages of Logic", Wilfrid Hodge's | |
"Logic" or John Pollock's "Technical Methods in Philosophy". | |
Online resources: | |
http://philosophy.hku.hk/think/sl/ | |
http://www.rbjones.com/rbjpub/logic/log019.htm | |
http://www.jgsee.kmutt.ac.th/exell/Logic/Logic31.htm | |
http://plato.stanford.edu/entries/set-theory/primer.html |
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