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

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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

about the argument

- 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)

## 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.