# PHILOS 2 Lecture Notes - Lecture 3: Billiard Ball, Logical Form, Discrete Series Representation

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Published on 14 Jan 2016
School
UC-Irvine
Department
Philosophy
Course
PHILOS 2

 !"!"#\$%&'\$&()*+#
",-
.
o/!"#.".!#!
"
"0"( ",
o1#"*/
o2"**".!"*/
"!"!"#!
3#/"/.!.
4
!".!!/.
*""##"*".!!"
*
o*"!*5*'"
*""/.'
o6""/./"!""/'
."/*""!!'!/7
!7.
"!*\$&/./".#.
*""*2*/"
/.
o6"!!*/!
""6 
8/
9 "*
(:
6""/!/#*""
continuous series
o;!!"/"".!<-#
*""**.."#
"".."
6"...)**<"
..
o,discrete series*<*.."*
"/*"*.
6"rational.continuous2.!
*"!.'#=>\$0?=>\$0@'*""
/""".*".
6"natural.#"""#discreteA
2.!*"!.'>'
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*""/""".*
".
,!B
,!continuous#"**!!"
"!
oC!/*"#

/"#"""/""/"!!.#
"*"..#""
"/"".#"**..
""
,!discrete#""/"*""
/"-
o,.#""!.*"""
"".*".

-
6*5//
/*"".!!.."
3"!"*"either
.!""..!
!.B
D
(
D
:
""6 "8/
9 "*
(EF=
!"/!"*/C
 :<.<!B
 "*!B
C. Are space and time continuous or discrete?
: ,!<B
 ,!.B
""6
6"/.!!"*"if!.
continuous#"..!
6""""/"
#"*#"/"

oAchilles, ."/#"*""64
2""/*3.
,
"*""642#
*""".""*"*
""..*""#"
."""..!!
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*6"""/
""
2.*"/""
o;#"*some amount of time
/
o#"#"/"*#C!)
!#".#""
some distance.#."*
.".
o9.."*./"!.
<)"."
....
6"/"."!*""
")"..<..
".=
o6"#*"*#!'""
../".6"
."#".
o#"=#"""
"'""/"!*""
6""""!"""=
"#*"C#<)"4
"...".>
o3"*/""#">BGC
6"##"../>*
G##"'""
/
o#">#"""
!!"*#\$#0#'**/
."*""""/""B
,.#*".<.
.""#/"<..#"
**".
o**"",#."if motion
is possible at all#!"/""
"/."".*"""*
.!
H#""*"".!"
!!"!.continuous3*#"*#
!/.!.*
#B
I!/"!".!.*"!
*"//""!/"
.!"!."9
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## Document Summary

Lecture 3: zeno"s paradoxes by prof. sven bernecker. Zeno of elea (ancient greek philosopher, 490 430 bc; elea is now velia, southern italy) Paradoxes of motion credited to zeno of elea: a group of the oldest, and most historically important, paradoxes ever set forth. Hence, reconstructing his arguments is partly a matter of conjecture. Zeno had upwards of 40 arguments against the reality of motion, most of which are unknown to us. We will be discussing four of his arguments: these four paradoxes can be separated into two groups: There is no smallest member; you will always find another: in a discrete series you will find two members and there will be. The series of rational numbers is continuous. We can never come up with a pair of rational numbers say, 1. 23456 and 1. 23457 which are so close together that there is no rational number in between them.

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