PHI 205 Exam 1

What is logic?

A normative practice about how to reason correctly

How is logic different from psychology of human reasoning?

People are subject to cognitive biases and regularly violate rules of logic

How does someone reason correctly?

By providing good arguments

What is a argument in logic?

A group of propositions where one is a premise and another a conclusion

What does the premise provide?

Evidence

What is the conclusion?

Supported by evidence

What does a good deductive argument conform to?

Valid rules with true premises

What is deductive logic?

reasoning where conclusions necessarily follow from premises

What is inductive logic?

reasoning based on probability and generalization

What is N-valued logic?

Systems that consider more than just true or false (not just black/white but grey)

What are the rules of deductive logic?

Modus Ponens, Modus Toellens and Disjunctive argument

What is Modus Ponens?

Known as the “mode affirming”

• affirms the antecedent P of the conditional Q

• if… then

• if a thing begins to exist, it must have cause

What is Modus Toellens?

Known as the mode denying

• denies antecedent of the conditional

• If P then Q, but not Q then not P

What is Disjunctive argument?

A rule for “either-or”, reasoning by process of elimination

• P or Q, not Q so P

• Subject to either-or fallacy, doesn’t include insufficient options so basically circle reasoning

What makes a good argument?

Uses a valid rule and has true premises (sound)

What makes an argument valid?

Conclusion follows from its premises, if the premises are true then the conclusion must be true

What makes an argument valid?

Validity is more about the form of the argument

What are the methods to test validity?

Diagram method

• Uses classes and membership relations

Truth table method

• Assigns truth values to premises and conclusion to check if the conclusion is true whenever premises are true

What are the common logical errors involving validity?

Denying the antecedent

• if P then Q, not P, therefore not Q

Affirming the consequent

• if P then Q, Q, therefore P

What is simple enumeration?

Observing multiple samples with a property and inferring the property applies to all members. (all swans have a long neck)

What is induction by analogy?

Observing that a sample has a property and inferring a similar and analogous sample shares it (next swan has a long neck, singular)

What is a classic example of induction by analogy?

The design argument for god’s existence

What are key differences between deduction and induction?

It lies in the strength of the relation between premises and conclusion

• deduction guarantees conclusion if premises are true

• induction supports conclusion with probability

What philosopher criticized induction as unjustified instinct?

David Hume

What philosopher highlighted induction’s limits with the example of a chicken fed daily but killed unexpectedly?

Bertrand Russell

What is the principle of quantity?

A large number of samples strengthens the inductive argument

• failing this leads to the fallacy of hasty generalization

• Ex. Drawing conclusion about all swans based on a few observations violates this principle

What is the principle of quality?

The sample should include a variety of kinds within the class

• failing this lead to fallacy of forgetful induction

• Ex. Observing many swans, but only from one location or only females

Describe and Provide Example: Consistency with Truths

Inductive conclusions should align with established scientific truths

• Principle of conservatism

• Ex. Observing apparent violations of gravity should prompt rechecking measurements before acceptance

Describe and Provide Example: Strong Analogy

In induction by analogy, premises and conclusion must share a strong similarity

• Ex Assessing whether the solar system is sufficiently like a watch to support the design argument

Describe and Provide Example: Ad Hominem

Rejecting an argument based on the arguer’s personal traits rather than the argument itself

• ex. dismissing a parent’s anti-smoking advice because the parent smokes

Describe and Provide Example: Begging the question

The conclusion is assumed in the premises or simply restated with no new evidence

• “Everyone wants the new iPhone because it is the hottest gadget”

Describe and Provide Example: Equivocation

Using ambiguous terms inconsistently between premises and conclusion

• Ex. “it’s wrong t kill a human being” vs “A fetus is a human being”, uses different senses of the word “human”

Describe and Provide Example: Hasty generalization

Violating the principle of quantity by generalizing from too few cases

• inferring all swans have long necks after seeing only a few

Describe and Provide Example: False Analogy

Violating the requirement of a strong analogy in induction by analogy

• Ex. Comparing the solar system to a watch with design but ignoring significant differences

Summarize key concepts of Inductive logic

• Conclusion is more probable but not guranteed

• Direction of reasoning is not strictly general to specific or vice versa

• Sample needs to be large and representative

• Weaker evidential link that depends on sample and analogy

• Seen as unjustified

• Common fallacies: hasty generalization, false analogy, forgetful induction

Summarize key concepts of deductive logic

• Conclusion must be true if premises are true

• Direction of reasoning is not strictly general to specific or vice versa

• no sample needed, it is based on logical structure

• Stronger, conclusion contained in the premises

• Generally accepted as valid reasoning

• Common fallacies: circular reasoning, equivocation

What is philosophy of religion?

Investigates the logical reasons underpinning fundamental religious issues

• reason provides evidence consistent with the rules of logic, distinguishing rational belief from propaganda, brainwashing or mental illness

Describe and Provide Example: Natural Theology

Uses logical arguments to establish positive religious propositions

• Aquinas: some truths about God are accessible to natural reason

Describe and Provide Example: Natural Atheology

Uses logical arguments to establish negative religious propositions

• Russell: no hypothesis about gods is more probable than another, hence none deserves preference

What are some variations on reason?

• Aquinas: division between truths of reason (accessible via logic) and articles of faith (beyond reason)

• SJ Gould: non-overlapping magisteria, distinguishing scientific truths (reason) from moral or faith truths

What are some “divine features” that creates the general idea of God in Western Philosophy?

• Omnipotent

• Omniscient

• Omnibenevolent

• Omnipresent

• Monotheistic

• Transcendent creator

• Eternal

What is the general idea of the cosmological argument?

Claim: there must be a God who is the cause of the cosmos

Argument: Plato, Aristotle, Al-Ghazali, Aquinas and Leibniz

What is the analogy for the cosmological argument?

Richard Taylor’s crystal ball story, just as a crystal ball mus have cause, so must the cosmos

How does the impossibility of an unending series support the cosmological argument?

Premise claims that an actual infinite series of causes cannot exist

• Craig argues that the concept of an actual infinite leads to counterintuitive paradoxes, such as Hilbert’s Hotel

• A hotel with an infinite number of occupied rooms can still accommodate more guests by shifting occupants

• This analogy shows the paradoxical nature of actual infinites

How does the Big Bang Theory support the cosmological argument?

Suggest that the universe began approximately 13-14 billion years ago, supporting the premise that the universe began to exist

• expansion of universe was observed by Hubble telescope, allowing defenders of cosmological argument that the universe has cause

What are some skeptical or scientific responses to the cosmological argument?

• Time itself began with the Big Bang, so there was no “before” or separate temporal dimension in which God could act.

• The early universe emerged from a singularity, where classical notions of space and time break down.

• Quantum physics allows for particles to appear and disappear spontaneously, suggesting something might come from “nothing” without a cause.

• Some propose a cyclic or oscillating universe model, with repeated Big Bangs, undermining the argument against an infinite regress.

Describe and Provide Example of criticism: Possible inconsistency

If everything that exists requires a cause, then God would also require a cause, contradicting the argument

• Russell’s critique; Schopenhauer’s “taxi” analogy

Describe and Provide Example of Cosmological Argument Criticism: Does Not Prove God as usually conceived

The first cause is not necessarily omnipotent, omniscient, or omnibenevolent

• Materialist challenge: theological mystery of eternity

Describe and Provide Example of Cosmological Argument Criticism: Dialectical Standoff

Both sides have strong intuitions: discomfort with infinite regress vs. Scientific models without God. No decisive proof either way.

• General philosophical and scientific debate

What are some theistic responses to criticisms of the cosmological argument?

• Craig refines premise (i) to “if a thing begins to exist, it must have a cause,” allowing God to be eternal and uncaused.

• Aquinas distinguishes causes and effects, arguing the first cause is not itself an effect, so it need not have a cause.

Define Term: Cosmological Argument

A philosophical argument asserting that there must be a first cause (God) to the cosmos

Define Term: Actual Infinite

An infinite set or series that is complete and existing as a whole, leading to paradoxes

Define Term: Potential Infinite

A process or series that can continue indefinitely but is never complete as a whole

Define Term: Singularity

A point at which physical quantities become undefined, such as the origin of the Big Bang

Define Term: First Cause

The initial cause in a causal chain, uncaused itself, traditionally identified with God

What is the basic idea of the teleological argument?

Suggests that the apparent design and purpose in nature imply an intelligent God as the designer

What are some key historical references for the Original Teleological Argument?

William Paley’s “Watchmaker Argument” and David Hume’s critiques

What is an example of Design in Nature?

The human eye is used as an example of biological design, having a specific function to perceive visual information

• The eye’s structure is analogous t a camera, with a lens focusing light and a film producing image

How does the teleological argument use inductive reasoning by analogy?

Observing artifacts with machine-like designs (A) known to be produced by intelligence B

• Given that natural entities also have machine-like designs

• It is probable they were also produced by intelligence

What is Limited Conclusion?

Even if analogy is sound, it does not conclusively prove the existence of God

• Intelligence responsible for design might not be infinite, good or singular

• Qualities are not supported by the argument itself

What is Weakness of the Analogy?

Hume argues that the universe doesn’t resemble a house or machine close enough for the analogy to be strong

• analogy may commit fallacy of false analogy, relying on superficial similarities without similar underlying causal mechanism

• part-whole problem, where the nature of the universe as a whole differs fundamentally from human-made artifacts

Describe the fine-tuning hypothesis

Modern proponents argue that the universe’s physical constants are so precisely balanced that life’s existence is highly improbable without intelligent design

What is cosmological constant of the fine-tuning parameter?

Must be within one part in 10^53 otherwise, no stars or rapid Big Bang would occur and therefore prevents life

What is the strong nuclear force of the fine-tuning parameter?

Altering by 0.4% would destroy carbon or oxygen which is essential for life

What is the Goldilocks principle of the fine-tuning parameter?

Planets must be an optimal distance from stars to support life

Describe the joint improbabilities argument

The combined likelihood of all necessary conditions for life is astronomically low

• An analogy is given with drawing pennies in perfect sequence, illustrating the improbability of these conditions occurring by chance

What are some responses to the fine-tuning argument?

Multiverse hypothesis: many universes exist, increases odds that one is life-supporting

Abundance of earth-like planets: estimates suggest there are 40-80 billion rocky, water-bearing planets in our galaxy alone

Improbably events occur naturally: improbability alone does not imply design, rare events happen by chance

Describe the differences between mind model and natural model

Mind/intelligence: traditional explanation, design attributed to conscious agents

Natural forces: explaining design through natural processes over extended timeframes

Describe and provide example of how they support the natural model: Fossil Records

Stratified layers showing progression from simple to complex organisms

• Siccar Point, Scotland

Describe and provide example of how they support the natural model: Genetic Similarities

Humans share 98.5% of DNA with chimpanzees

• Human chromosome 2 formed by fusion, explains difference from other primates

Describe and provide example of how they support the natural model: Observed Evolution

Viruses mutate over time, rendering some vaccines ineffective

• vaccine resistance studies

Describe and provide example of how they support the natural model: Patchwork Effects in Biology

Organisms show imperfect designs consistent with gradual evolutionary changes

• Panda’s thumb as an extended wrist bone, beneficial for feeding

What is a paradox?

An apparent contradiction that may be a puzzle, a counterintuitive truth or genuine contraction

What is a contradiction?

Occurs when a proposition and its negation are both affirmed

How is the basic skeptical claim about theism formulated?

If a belief is a contradictory, it must be false

traditional theistic belief is contradictory

traditional theistic belief must be false

What is divine perfection?

A specific interpretation of omnibenevolence

A being with divine perfection is:

always good and unable to do evil

What is omnipotence?

Power over created things, ability to do everything consistent with the laws of logic and ability to do everything consistent with logic plus the unchangeable past

What is the apparent contradiction?

Divine perfection implies god cannot do evil, therefore god can’t do everything (as implied by omnipotence)

What are theistic responses?

Reject one attribute: accept unrestricted omnipotence but reject divine perfection or vice versa

Add a moral proposition such as “whatever God does is good” to reframe “God cannot do evil”

What is the general logical structure of the paradox of omnipotence?

If God is unrestricted omnipotent, contradictory things could be true

Contradictory things cannot be true

Therefore, God cannot be unrestricted omnipotent

What is the paradox of the stone?

• Either God can create a stone God cannot lift, or cannot.

• If God can create such a stone, God cannot lift it, so not omnipotent.

• If God cannot create such a stone, God is not omnipotent.

• Hence, either way, God is not omnipotent.

Theistic Response to Paradox of Omnipotence: Aquinas

Omnipotence means ability to do anything logically possible, contradictions excluded such as the stone is too heavy

Theistic Response to Paradox of Omnipotence: Descartes/Voluntarists

God created laws of logic and can suspend them; God may allow contradictions to be true

• rejects necessity of logical consistency for omnipotence

Theistic Response to Paradox of Omnipotence: Wade Savage

Semantic analysis rejects the premise that inability to create a stone God cannot lift implies lack of omnipotence

Theistic Response to Paradox of Omnipotence: Richard Swinburn

God can make himself not omnipotent temporarily, enabling the stone paradox be resolved dynamically

What is the rough idea of the problem of evil?

The argument against the coexistence of God and evil is a posteriori, relying on observable facts rather than pure logic

What is the formal argument structure of the problem of evil?

Premise: If a being is omniscient, omnipotent and omnibenevolent, it could and would prevent evil

Premise: evil is not prevented

Conclusion: therefore, there is no being that is both omnipotent and omnibenevolent

Describe the assumption of evil?

“evil” is assumed to be objectively real, not merely subjective or a matter of personal preference

What is moral evil? Provide example.

Evil resulting from human free choices, such as atrocities (My Lai massacre)

What is natural evil? Provide example.

Natural evil is evil resulting from natural causes, such as disasters such as earthquakes, tsunamis.

What is the logical counterpart of the problem of evil?

evil is sometimes explained as logically necessary for good, analogous to pairs like right/left or up/down

Two senses:

• a) Good and evil are complementary and there can’t be one without the other

• b) Knowledge of good requires contrast with evil

Criticisms:

• a) an omnipotent God could create all good without evil; the existence of a purely good world is logically possible

• b) one can know good without experiencing evil directly, conceptual teaching suffices

What is the free will defense of the problem of evil?

• evil results from the free choices of agents, so God is not the direct cause

• A world with free will is better than one without, even if evil results

• Omnipotence cannot compel free creatures always to do good without contradicting free will

rejects premise by arguing God cannot prevent evil caused by free will without removing freedom

• doesn’t explain why God permits evil

• only explains moral evil, not natural

What is the greater good defense of the problem of evil?

Evil is allowed because it leads to greater goods that justify its existence

• for every evil, there is a logically necessary greater good

• the good outweighs the evil

criticism

• many evils seem unnecessary or could be avoided and still achieve greater good

• some greater goods do not justify the cost