Philosophy Radio! drlabasham777's Podcast
Society & Culture:Philosophy
Here we continue our logical deduction ("natural deduction"). Check the rules out again, both elimination and introduction and apply the rules: Success! This is what is going on in our heads, all of our heads. We just write it down. This is the basic system we use to do that. We will learn a few more and more powerful rules next time. Here are our rules and our problems now,
More natural deduction
Again,
Some basic rules of the game of Deduction (also known as (AKA) Life)
Basic valid elimination rules
p.q
p .E (“and” elimination)
or if you want,
q .E
P then q (“then” is our “arrow”: Podbean hates “special characters” so I have to write “then”)
P
q then E MP (which means: modus ponens) (hint: it’s easier to just write MP)
p then q
not q
not p then E MT (modus tollens: which means) (hint: it’s easier to just write MT)
Finally, remember disjunctive syllogism,
pvq
not p
q vE (or you just write, DS; that is easier for some people)
Basic valid introduction rules
P
q
p.q .I (“and” introduction)
p
pvq vI (“or” introduction)
Remember you can introduce anything with vI
r
rvt vI
or even something more complex,
(p.q) then (r.s)
(p.q) then (r.s) v (t.s) then (q.u) vI
Yes, it can do that: We start with anything we want and get anything that OR anything else we want. And yes, it makes sense. “I have a dog and a velociraptor” that is, p.q “I have a pig and a rabbit” that is, r.s So it is true that, “I have a dog and a velociraptor OR I have a pig and a rabbit”
p.q
(p.q) v (r.s) vI
So here’s some more basic problems. An example of a proof,
Quick note: You can draw a vertical line down lines 4, 5, and 6 to say, “this is my proof!”. Which it is. Traditionally we do this. But we don’t have to do that. You don’t either, unless you wish.
The problems,
a)
b)
c)
d)
e)
f)
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