PHIL 101 Exam 2 JMU Lupher

Logical Problem of Evil

The existence of God is logically incompatible with the existence of any suffering or evil whatsoever

Evidential Problem of Evil

If there exists an omnipotent, omniscient, and omnibenevolent God, why is there quite so much suffering and evil? (abductive argument)

Omnipotent

Willing but not able

Malevolent

Able but not willing

First Argument from Evil

-If God exists, then it would be PKG

-If a PKG-being existed, then there would be no evil

-There is evil

Hence, there is no God

(Logical, supposed to be sound, valid, denying the consequent twice)

Reject Premise 1 or Premise 3

-Moral categories are illusory (moral skeptic)

-Most religious traditions accept 3

-(Not likely to be attacked)

2 Types of Evil

Natural: Doesn't occur due to human actions

Human: Only occurs due to human actions

Theodicy

-Reconcile the existence of a PKG-being and the existence of evil

-No=none, 0% evil in the world

Tough Love?

-Evil makes us better

-Evil creates benefits for your future

-Helps spiritual growth, soul-building

Second Argument from Evil

-If God exists, then it would be PKG

-If a PKG-being existed, then the amount of evil would not exceed a soul-building minimum

-The amount of evil exceeds the soul-building minimum

Hence, there is no God

(Structure is same as 1 argument, valid, denying the consequent twice)

(Minimum means it gives people what they need to be a better person but no more evil than that - Response: free will allows for more evil than required for soul-building)

Free Will

Basic Idea: Because free will is so great a good, its better for God to make a world with free will in it than without it - even if that free will is occasionally used badly

-Natural evil has no connection to free will

Third Argument from Evil

-If God exists, then it would be PKG

-If a PKG-being existed, then there would be no more than the minimum anoubt of evil for soul-building and as a consequence of human freedom

-The amount of evil in human hisory exceeds the minimum required for soul-building and as a consequence of human freedom

Hence, there is no God

(Valid, denying the consequent twice)

(Possible Response: Human being cannot know why God decided to let that amount of evil into the world. For arguments from evil to succeed, need to know what an all PKG-being would do. If that cannot be done, then cannot test that premise.)

Evidential Argument from Evil

E: A proposition that describes the kinds and quantities of evil that exist

(Weaker argument and weaker conclusion)

Paradoxes

-Paradox: An apparently unaccpetable conclusion derived by apparently acceptable premises

-Acceptable > Unacceptable choices

1. Accept the conclusion

2. Reject the reasoning as faulty

3. Reject one or more premises

Change is what?

An illusion

The Continuous and Discrete

Continuous: -No gaps ->Unity -Limitlessy divisble (dense)

-Geometry: lines, circles, spheres -Concepts: time, space, extension

Discrete: -To be separate ->Plurality -Cannot be divided w/out changing its essential nature -Arithmetic: whole number or positive integer -Concept of point

Geometry and Arithmetic

Z: -Infinite in both directions

Q: -Infinite in both directions -Dense

R: -Infinite in both directions -Dense -Gap-free

A geometrical line is a continuum

Treat geometrical lines arithmetically

A real number line is also a conitinuum

Physical continua are modeled on the mathematical contiuum

Allows for calculus: rates of change at a point in space and time

The Dichotomy

Continue covering half of the distance you have left. You never get to your end goal (finish line)

The Regressive Dichotomy

Covering half the distance from before, closer to where you started, you never get back to your original starting point (start line)

The Dichotomy Argument

-Premise 4 ~finite arithmetic doesn't tell us what a sum of an infinite collection of number is

-Until we have a theory of how to add up an infinite senes of terms, we can't conclude that an infinite sum of finite quantities is infinite

Infinitesimal

A number that is not zero, but less than any assignable (finite) value

Berkeley's Critism

He thought calcius led people to atheism

Limit

An infinite sequence of increasing positive numbers converges to a finite limit L if and only if, for all numbers e>0, there is some number @ such that for all (integers) if c>@, then |L -ne|

What is Cauchy's definition of an infinite sum?

Not all infinite sums of finite quantities are infinite

What is the limit of Zeno's sequence?

A limit of 1

Limits

If the points have zero length, then the total length of segment is zero.

If the points have a finite nonzero length l, then the total length of the segment is zero

Same Size

1 - to - 1 correspondence

Cardinality and Countably Infinite

Cardinality: The size of a set

-The cardinal number of the set of natural numbers N is the smallest infinite cardinal: N0

-Also called denumerable or countably infinite

Cantor's Diagonal Argument

-Indirect argument (reductio ad absurdum)

-How to find a number in (0,1) with a natural number

-Look at a number in the first column and the first row

-Take the number and add 1

-Do the same for the next step in the diagonal, the number in the second column, second row, and so on

-We are going down the diagonal

Countable and Uncountable Infinites

-N0 is the smallest infinity

-The cardinality of R is nondenumerable or uncountably |R|=N1>N0

-N1 is the cardinality of the continuum

-Row #/Column #

Cantor's Reaction

-He doesn't believe it himself

-The number of real numbers in an interval is independent of the dimensions of the space

-The real numbers is not the biggest infinite set

-Can always create bigger infinite sets by taking the power set

~There is no biggest infinite set

Summing the Uncountable

-Same size but length is different, they have the same number of points

~The length of a line is not a function of the number of points very deep point. Length, and other metrical notions, aren't intrinsic features of collections of points

-Points have no length to them individually

Summing Up

-Summation of finite numbers: ok

-Summation of countable number: use limit concept

-Summation of uncountable number: undefined

-Conclusion: restrict the notion of addition

Measure Theory

-Extends notion of length from finite intervals to measurable sets

-A measure is a generalization of length, area, and volume

Length and Measure

-Does the open interval (0,1) have the same length as the closed interval [0,1]?

~Yes, adding 2 points makes no difference to the length (same length as [0,1) and (0,1]

-Points have zero measure

Measure and Addition

-Measures are countably additive

-A countably additive number of zero-sized points also has zero measure

-Adding up an uncountable (continuum) of zero-sized ponts does consitute an intercal whose measure is non-zero

Take Home Points

-In geometry, length is not an intrinsic property of points

-To determine the length of an interval, you need a collection of points plus a metric (distance function)

-Assign coordinates to points in form of real numbers

-Euclidean metric: (x,y) and use Pythagorean metric

-In topology, a 1-dimensional line is composed of mothing but 0-dimensional points, yet an uncountable number of 0-D points make up something 1-D

What do Zeno's paradoxes concern?

Physical change, physical motion, and physical plurality

Banach-Tarski Paradox

-Most paradoxal of mathematics

-Key idea: the finite sized pieces are unmeasurable sets (allowed by the Axxiom of choice)

-The apparent absurdity of BT can be used as an argument that real space is not described by Cantor's continuum

Euclid's Theory of Space

-General form of Zeno's Paradoxes

~Euclid's theory of space is true of actual world.... motion is impossible

Motivation

Advantage: Valid arguments provide an absolute guarantee that the conclusion must be true if the premises are true

Disadvantage: Valid arguments tell us nothing new

Types of Arguments

Good Arguments (Not deductively valid -abductively strong -inductively strong) (Deductively valid)

Types of Nondeductively Valid Arguments

-Analogy

-Probable/Statistical/Bayesian inference

-Abductive interence (inference to the best explanation)

~There is no (uncontroversial) notion of validity for inductive arguments

Nondecutively Valid Argument

-Strong: If the premises are true, then the conlusion is probably true

-Cognent: An argument is cognent if (1) it is a strong inductive argument and (2) all of the premises are true

Inductive Arguments

-AKA enumerative induction

-Involves sampling from a population and extending the results outside of the sample

Adding Premises

-Inductive arguments deals with probability

-Adding info to argument won't change validity except when changing information about the world

Differences Between Inductive and Valid

-Valid are 'yes', 'no', there is no inbetween

-Inductive can have a large range in probability

-You need enough evidence to make the conclusion probably true, but the premises will never guarantee it's true

-Scientific theories can never be absolutely proven through experimental data

-New experimental results can increase or decrease the probability of some scientific theory being proven true

Evaluating Inductive Arguments

-Sampling size

-Randomization

Abductive Arguments

-AKA inference to the best explanation

-Involves inferring an explanation for the observations one has made

-Answers a "why question"

-Typically with cause and effects

-Reconstruct why something happened the way it did

Evaluating Abductive Arguments

-Surprise Principle

-Only Game in Town Fallacy

Advantages of Surprise Principle

The greater the difference between the two hypotheses, the higher probability of one than the other

Only Game in Town Fallacy

-The error in thinking that you are obliges to believe a proposed explanation of an observation just because it's the only explanation that has been proposed

-Alternative: admit that you don't know or have an explanation

-You are not obliged to accept someone's explanation just because you don't have an alternative one

Predictions

-Typical scientific inference: predictions

-Predictions: inferences of observations from a theory

-Predictions are tests of a theory

-A correct prediction might count as evidence for a theory

WARNING: A successful prediction is not conclusive proof that the theory is true (A successful prediction is not conclusive proof that the theory is true)

Scientific Conformation and Falsification

-Conformation: does not give conclusive truth theory is true, confirms or provides evidence for theory, affirming the consequent (valid)

-Falsification: Denying the consequent (valid)

2 Rival Theories

-Special case: A deductively valid argument for the truth of a theory can be made

Requirement: need two theories that make different predictions

Advantages of Dating System

Time is marked by a number

Time

Familiarity with time comes from two sources:

-clocks

-our inner psychological experience of time

Clocks

Physical object that exhibits regular periodic (i.e., movement that returns to original state) movement, e.g., a pendulum

Measuring Time

-A clock is measuring time

-You don't see time

-Best physical clock: NIST F-1 cesium clock still loses 1 second every 20 million years

Psychological Time

-We feel time pass

-We have memories of the past and anticipate the future

-Can estimate how much time has past

-Different people have different inner clocks

-Manifest Image of Time: constant changes and activities

Which Times Exist?

-Presentism: only the present moment exists

-Four dimensionalism: presentism is false

Real Time vs. Manifest Image of Time

-Manifest Image of Time: our experience of time is active and complicated

-'Explanatory gap' between time as we find it in experience and time as we find it in science

-Physicists TIme: 't' in the fundamental equations of physics doesn't differentiate between past and future, nor does it speed up or slow down, nor does it pick out which time is now

-Time = 't' is constant

H.G. Wells

-Tme is the 4th dimension

-Time machines give us the same freedom to move in the temporal direction: like a hot air balloon

Types of Four Dimensionalism

-4 coordiantes: (x, y, z, t)

-Universe is 4 dimensionalism block

-Types of 4 dimensionalism: Eternalism, Growing block, Shrinking Block

Albert Einstein

Fusing space and time together into 'spacetime'

Eternalism

Past, present, and future objects and events are all equally real

Growing and Shrinking Blocks

Growing Block: past and present objects and events exist but future objects and events do not exist

Shrinking Block: present and future objects and events exist but past objects and events do not exist

3 Metaphysics of Time

-Presentism: "Nowism" The Present

-Possibilism: "The Tree Model" Past & Present

-Eternalism: "The Block Universe" Past, Present, Future

Defining Time Travel

-When personal time and external time don't line up, time travel happens

Lewis's Modal Inconsistency

Attempt to change the past will fail every time

Consistency Constraints

-Past can be changed: multiverse, 2x dimensions

-Crucial distinction: changing the past vs. participating (aka affecting or influencing) the past

General Relativity

-Spacetime geometry <-> distribution of matter and energy

-Einstein general relativity: curvature of spacetime

Key Idea

-Closed timelike curves permit time travel into the past

-2 sources: spacetime structure and wormhole

Timelike Curves

-Closed timelike curves are required for time travel

-Closed: curves intersects itself

-Timelike: roughly, not going faster than the speed of light

-CTCs take advantage of the geometrical structure of spacetime, i.e. of curvature

Wormholes

-Wormhole: tunnel between 2 different points of spacetime

-Could be a shortcut between 2 different times

-For a time machine, there must be a temporal difference between the different mouths of the wormhole