Philosophy 120: Introduction to Logic (Autumn 2015)
Handwritten Exercise Week 2
Exercise 1: Translate the following English sentences into the language of
sentential logic. Be sure to indicate what each sentential variable represents.
A. Julio shouted.
B.

Weller/120
Conditionals have different uses depending on the context.
If Mitt is a mammal he has lungs.
If Bob passed the course he showed up for the exams.
One would typically utter these sentences to indicate that the consequents
express a necessary con

PHIL 120/Weller
1
29: P P
1
(1) P
A
This constitutes the circular but obviously valid proof of a
proposition from itself as assumption. This move shows up in
hinky uses of v-E in 32 and 33.
We introduce a new symbol, to stand for is interderivable
with. S

Phil 120/ Weller
page1
Consider the following argument:
If Florida State won Oregon isnt happy. Oregon is happy. Therefore, Florida
State didnt win.
1 (1) P Q
2 (2) Q
1,2 (3) P
A
A
?
MTT requires the negation of the consequent of a conditional. But the in

Phil 120/weller
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&-Introduction
In our system a conjunction is a compound proposition formed by conjoining
two propositions (of whatever complexity) with an ampersand, '&',. It
corresponds to a statement formed by conjoining two statements with the word

Weller/Phil120
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Indirect Proof and RAA
Heres an argument attributed to Zeno of Elea circa 450 BCE
To be proven: that motion is impossible.
(1)
Now lets just assume that its possible to traverse the finite
distance AB.
(2)
A finite distance, AB, is infini