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PHIL 201-Logic Notes
Philosophy and Contemporary Ideas (Liberty
University)
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PHIL 201
•Definition of Philosophy
o“Philosophy” from Greek “philos” (friend) and “sophia” (wisdom), etymologically
means “friend of wisdom”
▪Quest for understanding
oPhilosophy is the activity of thinking carefully about the deep issues of life, taking
into consideration the insights of the greatest thinkers who have preceded us, in
an attempt to better understand these issues and perhaps resolve any associated
problems.
▪Understanding precedes resolving
•Philosophy and worldview
oSet of fundamental beliefs about the nature of reality that determine how you
interpret your experiences and view the world
oEveryone has a worldview
oPhilosophy gives you the tools to critically evaluate and reconstruct
your worldview, to decide for yourself what you want to believe
•Faith = belief + trust
oBelief needs evidence
oTrust needs willpower
•Logic
oBasic symbols:
▪Negation ~
▪Conjunction .
▪Disjunction v
▪Equivalence =
▪Inequality ≠
▪Implication >
▪Biconditional (If and only if) =
▪Conditional :.
oSymbols help because they take away the theory laden words and emotions and
leave the argument
January 22, 2019
•Three Laws of Thought
oThe Law of Identity (A = A)
oThe Law of Excluded Middle (A v ~A)
▪Either A or not A
oThe Law of Non-Contradiction (A > ~~ A)
▪If it’s Tuesday, then it’s not not Tuesday
•Why does logic exist at all?
oIf God designed the universe and gave us the laws of thought, then we can trust
them because God has our best in mind
▪Where does logic come from, and why does it work so well? Given by
an omnibenevolent God
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•The Elements of an Argument
oArgument: An argument is a group of propositions in logical sequences that lead
to the conclusion the philosopher is trying to support
▪Premises: the propositions from which the conclusion follows
•Show that the conclusion is true or likely to be true
▪Conclusion: the proposition that follows from the premises (what you
are trying to prove
▪Logic ties the premise and the conclusion together
▪Entailment (deductive)/Inference (inductive): the relationship between
the premises and the conclusion by which the conclusion can be said
to
follow from the premises
oDeductive Argument: an argument wherein the premises logically entail
(require, necessitate) the conclusion.
▪3 types of deductive syllogisms (major premise, minor
premise, conclusion)
•Categorical syllogism:
oIn a categorical syllogism the premises are categorical
propositions
▪Statement that assigns things to categories
•Disjunctive syllogism
oSyllogism contains a disjunctive statement (either/or)
▪x v y
▪~x
▪:. Y
▪In a disjunctive syllogism, the minor premise
ALWAYS denies one half of the major
premise
•If the minor premise affirms half of the
major premise, that’s called the fallacy
of affirmation
•Hypothetical syllogism
oPremises contain a hypothetical or conditional statement
▪Pure H.S.
•All of the statements are hypothetical
▪Mixed H.S.
•Only one of the statements is hypothetical
oX>Y
oX
o:. Y
•Two valid/logical forms
oAffirming the antecedent (modus
ponens, the way of affirmation)
▪X>Y
▪X
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▪:. Y
oDenying the consequent (modus
tollens, the way of denial)
▪X>Y
▪~Y
▪:.~X
•Major premise always has
two terms/phrases
oFirst is called antecedent
oSecond is called consequent
•Two formal fallacies of mixed H.S.
oAffirming the Consequent
▪X>Y
▪Y
▪:. X
oDenying the Antecedent
▪X>Y
▪~X
▪:. ~Y
▪Truth applies to propositions, not arguments (homework due next
class; premises, conclusion)
▪Validity applies to logical form (a valid argument is a logical
argument; arguments)
▪Soundness applies to the entire argument (combines truth and validity
to create a good argument: true premises + sound logic = absolutely true
conclusion)
▪True premises plus valid logical form yield sound arguments
(and therefore true conclusions)!
oInductive Argument
▪Induction is an argument or form of reasoning wherein the premises
(the evidence) support and make probable the conclusion
•Deductive arguments are usually clear it’s an argument,
whereas inductive looks more like a method of thinking that
eventually leads to a conclusion
•The stronger your evidence, the higher your levels of
probability, never 100% guaranteed
▪Two forms of inductive reasoning:
▪Generalization: x’. x’’. x’’’. x’’’’ etc., :.x
•The method of generalization is a form of induction that works
by generalizing or universalizing on the basis of repeated,
particular
instances.
▪Analogy: x; = a,b,c,d,e; x” = a,b,c,d; :.x” = e
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•You conclude that things similar/analogues in several respects
are likely to be similar in other ways as well.
▪In an inductive argument, the conclusion is never certain. At best it is
very highly probable.
•Hasty induction
oBasing a conclusion on an insufficient number of premises
oDon’t jump to conclusions
•Lazy induction
oNot drawing a conclusion as strong as the evidence
suggests
•Forgetful induction
oNeglecting some relevant data that might change the
conclusion
oAbduction Argument (Inference to the best explanation)
▪Abduction is a form of reasoning that argues for the truth of some theory
by showing that it is better able to account for the known data than is
any competing theory.
▪Criteria:
•Coherence
oNo internal contradictions
•Factual adequacy
oAccounts for all of the known data
•Simplicity
oAll things being equal the theory that requires fewer
assumptions and less complexity is preferable
oDon’t make things more complex than they need to be
•Explanatory power
oThe theory provides an explanation of the phenomena in
question
•Elegance
oThe theory’s ability to cover the first four criteria
▪Examples:
•Medical diagnosis
oLooking at symptoms, various illnesses, to lead to which
illness would deliver those symptoms with no other
•A criminal case
oThe prosecution or the defense has the best explanation to
cover all of the evidence uncovered
•The resurrection of Jesus of Nazareth
▪Comments:
•This is not “affirming the consequent”
•Like induction, abduction does not guarantee its conclusion
but rather raises their degree of probability
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January 29, 2019
•It can never lead to the same degree of certainty that
deductive arguments do
•Three Formal Fallacies of Deduction
oAffirming the Consequent
▪X>Y
▪Y
▪:. X
oDenying the Antecedent
▪X>Y
▪~X
▪:. ~Y
oAffirming a Disjunct
▪X v Y
▪X
▪:. ~Y
•Three (informal) Fallacies of Induction
oHasty induction
▪Basing a conclusion on an insufficient number of premises
▪Don’t jump to conclusions
oLazy induction
▪Not drawing a conclusion as strong as the evidence suggests
oForgetful induction
▪Neglecting some relevant data that might change the conclusion
•Formal vs. Informal Fallacies
oFormal fallacies involve mistakes in the logical form of an argument
oInformal fallacies involve problems of language or inattention to some
important aspect of the argument
•Additional Informal Fallacies:
oFallacies of “relevance” (resulting from inattention to some aspect of the
argument)
▪Appeal to force
•Attempts to settle intellectual agreements using force rather
than logic
•Appeal to strength not the truth
▪Argumentum ad hominem (appeal to the man)
•Attacks the person rather than the position
•Abusive
oPointing out shortcomings
•Circumstantial
oPosition is false by pointing irrelevant details about
opponents
▪Argument from silence
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•Something is true because it cannot be proven to be false
▪Appeal to the crowd
•Group think
•Appeal to emotion instead of reason
▪Appeal to pity
•Arouses sympathy in the listener
▪Appeal to Authority
•Appeals to an unqualified expert
▪Begging (Beggaring) the question
•The proof that you offer assumes the very thing you are
supposed to prove
•Involves circular reasoning
▪False Cause (post hoc)
•Mistakenly attributing causality to something
▪Complex question (loaded question)
•Asking a question that assumes the answer to
another, unexpressed question
▪False dilemma
•Posing the question in such a way that the response is limited
to fewer options than are really possible
▪Genetic fallacy
•A position is false because of some detail of its origin
•Something began a certain way and therefore it will end that way
▪Straw man
•Setting up an argument in such a way that the opposing view
is easy to defeat
▪Red Herring
•Introduces some extraneous issue into the discussion to
draw attention away from the real issue
▪Self-referential incoherence
•Statement not living up to its own standard
▪Non-sequitur
•A conclusion not logically following from the evidence
oFallacies of “ambiguity” (involving problems of unclear language)
▪Equivocation
•Using a word in more than one way without acknowledging
the change in meaning
▪Amphiboly
•Grammatically ambiguity that allows a phrase to be interpreted
in more than one way
▪Composition
•Attributing the characteristics of the part to the whole
▪Division
•Attributing the characteristics of the whole to its parts
