# PHL232H1 Lecture Notes - Lecture 1: Relevance Logic, Truth Table, Classical Logic

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Published on 8 Jan 2015
School
UTSG
Department
Philosophy
Course
PHL232H1
Professor
PHL232 Tutorial Week 1
Validity and Soundness
- validity
only arguments are valid/invalid – not statements
if all the premises are true then the conclusion must be true
- soundness
validity and true premises
- there are many arguments that are valid but not sound
- many very odd arguments can be considered valid
- if the premises are not all true at the same time then the argument is automatically trivially valid (and the
conclusion must be true)
- example:
Premise 1: grass is green
Premise 2: grass is not green
Conclusion: God exists
- while the argument is valid, it is likely not a very good idea
- definition of soundess – must be valid and true – contradictory premises cannot all be true and therefore the
conclusion cannot be sound
- soundness, not validity is what makes arguments good/true
- example – conclusion that cannot be false (no matter the premises because the conclusion is true no matter
what)
Conclusion 1: 2 + 2 = 4
Conclusion 2: grass is purple or grass is not purple
Conclusion 3: everything is self-identical
- conclusion 2 is disjunctive
- if 2 + 2 = 7 is a premise, then the argument cannot be sound, despite the true conclusion
- but id “Winnipeg is in Manitoba” is the premise, then it meets the criteria for soundness – still something odd
- limit of classical logic – in response, there is relevant logic – in order for an argument to be good then they
premise and conclusion have to be relevant
Truth Table
- p and negation of p
- must be either true or false, but not both or neither
- the negation creates the opposite of the truth value
- p and q, can be joined together as p&q – four possible combinations (both true, both false, one true and one
false)
- whether or not p&q are true depends on whether or not individual p and q are true
- p or q, pvq – the opposite of p&q
- if p then q, p q (conditional)
- for p q, if the first is true then the second must be as well, if the first is not true then it does not matter
(trivial true)
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## Document Summary

Validity and soundness validity soundness only arguments are valid/invalid not statements if all the premises are true then the conclusion must be true validity and true premises there are many arguments that are valid but not sound. Many very odd arguments can be considered valid if the premises are not all true at the same time then the argument is automatically trivially valid (and the conclusion must be true) example: Conclusion 2: grass is purple or grass is not purple.