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What is the logic?
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The primary concern in logic is to identify and classify valid
form of inference.
The notions of 'validity' ,'form' and 'inference' are the key
ones.
They can be explained in the following way.Consider these
two arguments:
'Either Tom broke the clock or Harry did.Harry did not break
the clock. Therefore Tom did'
'Either is rained on Thuesday or on Wednesday. But on
Wednesday there was no rain, Therefore it rained on Tuesday'
Each has two premisses from wich a
conclusion
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The conclusion: therefore.
To drawn a conclusion from premisses is to infer it from them.;the
conclusion follow from the premisses.
: 'Either Tom broke the clock or Harry did.Harry did not break the
clock. Therefore Tom did'
'Either is rained on Thuesday or on Wednesday. But on Wednesday
there was no rain. Therefore it rained on Tuesday
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Structure= Either p or q; not q; Therefore p.
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The letters 'p' 'q' are formulae wich 'stand for' propositions
Simple,atomic,complex,
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'p' and 'q' also stand for atomic propositions
'p or q' is a proposition complex made up of two
simple propositions or atomic propositions
Why? Because stand for Either Tom broke the
clock or Harry did
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Tom broke the clock= simple=p
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Harry did= simple=q
If the premisses are true, the truth of
the conclusion are guaranteed
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Why? Because the propositions are logical.Ma this must be
explained.
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Either p or q; not q; Therefore p. Why this is logical proposition?
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Because we compute (just as in mathematics).
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[(Either p or q) not q] therefore p.
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In mathematical logic 'or' becomes the symbol v
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In mathematical logic 'not' becomes the symbol ¬
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In mathematical logic 'therefore' becomes the symbol ⊃
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[(p v q) ¬ q] ⊃ p (Either disappears)
The logical calculus
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You could say we just put new symbols.
It true, but these new symbols allow you to
calculate the true and false.
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p can be true and can be false as q
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True-p-False ; True-q-False
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T-p-F; T-q-F
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2 +2 = 4 but what gives true + false ?
The scholastic sense of Wittgenstein
W= true
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Wittgenstein had the idea to connect
the two propositions
But we can report exactly the picture
of Wittgenstein's also so
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p q
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WF
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WW
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FW
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FF
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The first hookup of Wittgenstein is
the first line, the second the second
line,etc.
The negation
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¬ p
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FW
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WF
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F-
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W-p-FW
If you deny it a true
statement is false,
a false proposition if
you deny it becomes
true
the disjunction or, v
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The disjunction here is
done with two
propositions
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pq
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WF = W
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WW=W
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FW = W
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FF = F
The conjuction (and) ^ (new symbol)
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The conjunction is true
only if the two
propositions are true
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pq
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WF = F
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WW= W
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FW= F
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FF= F
Implication (therefore ⊃)
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The implication is
false only if the
antecedent is true and
the consequent is false
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pq
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WF = F
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WW =W
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FW = W
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FF = W
we now write p and q and calculate all possible values
(true,false) ​we see that the proposition is logical because the
implication is always true.
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[(p v
q) ^
¬ q]
⊃
p
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W
W
F W
WF
W
W
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W
W
W F
FW
W
W
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F
W
W F
FW
W
F
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F
F
F F
WF
W
F
we now write p and q and calculate all possible values
(true,false) ​we see that the proposition is logical because the
implication is always true.
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Calculus
[(p
V
V
F
F
V
V
V
V
F
q)
V
F
V
F
^
F
V
F
F
~
F
V
F
V
q]
V
F
V
F
V
V
V
V
p
V
V
F
F