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Unit 1: Logic and Epistemology
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Critical Thinking: The Basics
“There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are
necessary and their opposite is impossible; the truths of fact are contingent and their opposites are
possible.”
G. Wilhelm Leibniz
In order for something to be considered knowledge it must meet three criteria: 1) You must believe it to
be true, 2) it must be justified and 3) it must be true.
Types of Knowing
Empirical Evidence: Evidence derived from experience (also called A Posterior)
Eg: I observe that the sun comes up.
Inductive Reasoning: Using a series of Empirical Evidence to predict outcomes.
Eg: Every morning the sun comes up, thus I know the sun will come up tomorrow.
Scientific Method: A form of inductive reasoning in which we create a hypothesis and then testing by
process of collecting empirical evidence.
Eg: I suspect that the sun will rise tomorrow, and will test this theory by observation.
Deductive Reasoning: Drawing conclusions using from either assumptions or definitions independent of
any experience. It is when we use general principals to arrive at specific conclusions.
Eg. The sun is defined as that which rises each morning, thus if there is a sun, then it must rise
each morning.
Education: When we come to know something because someone has taught us about it. It is important
to note that in order for education to work the source of that information must hold some
authority.
Eg. The sun will rise tomorrow because my teacher, whom I trust, tells me that it will.
Indirect Experience: When one comes to know something because it is related to something else that
that person has experienced.
Eg. If I drop the book it will fall because when I dropped my pencil it fell.
Faith Knowledge or Intuitive knowledge: When something is considered true based on a feeling of some
sort.
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Unit 1: Logic and Epistemology
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Theories of Truth
Correspondence Theory of Truth
Theory: Truth is the correspondence between truth and reality:
Belief
Reality
Empiricism All knowledge
derives from the senses or
sensory experience.
Truth
Problems:
How do we know what corresponds to what?
How do we know what is real?
How can one be certain of a truth that is consistent, not relative
and not changing?
Coherence Theory of Truth
Theory: True ideas are ideas that make sense or hold together logically.
Truth
Truth
Truth
Some Beliefs about knowing:
Truth
Problems:
Any given proof must have a starting point by which we can
derive truth, what is it?
To who’s belief system must thing be coherent?
No one system can comprehend the whole of human
understanding.
What if all coherent truths are derived from an inherently false
principle?
Nativism We are born with
predispositions that enable
knowledge or complex
behaviour to arise in
response to experience.
Rationalism Reason is
productive of truth apart
from the senses.
Empirical Relativity
Knowledge is derived
through experience, but
experience is a subjective
matter. Is the car coming
toward you or are you
coming toward the car is a
matter of perspective.
Pragmatic Theory of Truth
Theory: Truth is an idea that “works”. True ideas work when utilized or tested.
Idea
Application
Truth
Problems:
If applied, it reduces truth to things that are simply what is expedient.
The theory is circular. Things are true because they work and they work because they are
true.
Some things are true but are useless (i.e. have no function to test)
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Unit 1: Logic and Epistemology
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Elements of Arguments
Assumption: Any point which is not proven, but it utilized as proof
Premise: A point used to come to a conclusion.
Conclusion: Any point which is derived logically.
Das Falsum (): A logical contradiction where something is both true and not true at the same time.
This proves a logical error.
The Process of Argumentation
Creating an argument:
1- Determine a question to be explored
2- Determine a criteria by which to assess the question
3- Define your terms
4- Apply your criteria to your question and draw a conclusion utilizing your terms of discussion.
5- Generate proof for your argument using deductive or inductive reasoning
a.
Avoid Fallacies
b.
Utilize your criteria and definitions in your proof
c.
Be sure that your proof follows logically
Defeating an Argument (some tactics)
Reductio Ad Absurdum – The process by which you assume your opponents position is correct and prove that it
leads to a logical contradiction. This my also be used as a proof where you assume the opposite of your position
then prove that it leads to a contradiction.
False Definition – Assume that a definition or criteria used by your opponent is correct then show that by utilizing
that definition or criteria you can prove something your opponent objects to.
Prove the Opposite – By proving the negation of your opponents argument, then your opponent must either
surrender his or her point or accept a stale mate.
Fallacious Reasoning – Point out that your opponent has used a logical fallacy to prove his or her point
Principal of Proof- Show that an argument your opponent has used proves too much. That is to say the principal is
“Anything which justifies everything, justifies nothing.” This is true because it also justifies .
Other Argumentation Tactics
Prove that your opponent has used and incorrect assumption
Prove that your opponent has used an invalid definition
Prove that your opponent has used incorrect reasoning (i.e. the conclusion does not follow from the
premises)
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Unit 1: Logic and Epistemology
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Fallacies
“Fallacy” - a misconception resulting from incorrect reasoning
“Fanatic” – One who holds firm to a belief in spite of the fact that that belief has been
disproved or does not support that belief with evidence.
Common Fallacies People Use
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Ad Hominem: an argument that attacks the person who holds a view or advances an argument,
rather than commenting on the view or responding to the argument.
Appeal to authority: an assertion that one is right based on some kind of authority or
qualification.
Appeal to ignorance: The assertion that something is true because we do not know for a fact
that it isn’t true. It asserts that that, because a premise cannot be proven false, the premise
must be true; or that, because a premise cannot be proven true, the premise must be false. This
is also known as negative proof fallacy.
Appeal to tradition: this is the assertion that because things were or have been done a certain
way, this ought to continue. Tradition has not logical validity.
Argument from Consequences: this is the assertion that something, if considered true, may lead
to undesirable consequences and thus ought to be considered false.
Argument from fallacy: if an argument for some conclusion is fallacious, then the conclusion
must necessarily be false.
Argument from omniscience: an assertion in which an arguer would need omniscience in order
to know. These generally contain words like "all," "everyone," "everything," "absolute."
Association-Causation Fallacy: (also called Post-hoc ergo propter hoc, which means ” after this,
therefore because of this” this fallacy is where one assumes that because two things are
associated (generally associated in time), there is a causal relationship.
Begging the question: when one presents a question that implies a premise in the question
itself. i.e. “Have you stopped beating your wife yet?” This question cannot be answered
without asserting that one is in fact beating ones wife.
Circular Logic: When the conclusion is explicitly or implicitly implied in the premises themselves.
Cherry picking: act of pointing at individual cases or data that seem to confirm a particular
position, while ignoring a significant portion of related cases or data that may contradict that
position
Composition: where one infers that something is true of the whole from the fact that it is true
of some (or even every) part of the whole
Definition Fallacy: (also known as “no true Scotsman”) when one uses a specific definition that
implies what one is trying to prove.
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14. False Analogy analogies are useful for explaining ideas, but just because there is a logical
problem with the analogy, does not mean there is a problem with the idea.
15. False attribution: occurs when an advocate appeals to an irrelevant, unqualified, unidentified,
biased or fabricated source in support of an argument
16. False Continuum this is the idea that because there is no definitive demarcation line between
two extremes, that the distinction between the extremes is not real or meaningful.
17. False dilemma (false dichotomy): where two alternative statements are held to be the only
possible options, when in reality there are several or more.
18. Historian's fallacy: occurs when one assumes that decision makers of the past viewed events
from the same perspective and having the same information as those subsequently analyzing
the decision
19. Inconsistency Fallacy: applying different rules, standards of proof or validations to different
arguments
20. Loki's Wager: the unreasonable insistence that a concept cannot be defined, and therefore
cannot be discussed.
21. Moving Goalpost Fallacy: the moving goalpost refers to when someone changes the criteria of
discussion to one that better suites them.
22. Naturalistic fallacy: a fallacy that claims that if something is natural, then it is "good" or "right".
23. Non-Sequiter: in Latin this term translates to "doesn't follow". This refers to an argument in
which the conclusion does not necessarily follow from the premises. In other words, a logical
connection is implied where none exists
24. Proof by verbosity (argumentum verbosium) Shouting down your opponent or refusing to hear
their side.
25. Package-deal fallacy: consists of assuming that things often grouped together by tradition or
culture must always be grouped that way
26. Reductio Ad Absurdum: In formal logic, the reductio ad absurdum is a legitimate argument. It
follows the form that if the premises are assumed to be true it necessarily leads to an absurd
(false) conclusion and therefore one or more premises must be false. The term is now often
used to refer to the abuse of this style of argument, by stretching the logic in order to force an
absurd conclusion
27. Red Herring: also called a "fallacy of relevance." This occurs when the speaker is trying to
distract the audience by arguing some new topic, or just generally going off topic with an
argument.
28. Slippery Slope: this logical fallacy is the argument that a position is not consistent or tenable
because accepting the position means that the extreme of the position must also be accepted.
But moderate positions do not necessarily lead down the slippery slope to the extreme.
29. Straw Man Fallacy: This is where one argues with a position that is similar to but not the same
as ones opponent. Usually this means creating a caricature of ones opponent’s position by using
an extreme example of a similar position.
30. Tu Quoque: also called a "you to" fallacy. This occurs when the speaker appeals to the notion
of hierocracy. The speaker accuses the arguer of going against his or her own beliefs. This is
fallacious because the application of the belief is irrelevant to its validity.
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Unit 1: Logic and Epistemology
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Logical Symbols
Types of Deductive Reasoning
 = Implication
A  B means “If A then B” or “B if A)
Modus Ponens:
1. If Socrates is Yellow then Socrates is a Banana
2. Socrates is tallow
3. Therefore, Socrates is a Banana (MP 1 & 2)
Or a more complicated version
1. If Socrates is yellow then Socrates has yellow skin.
2. If something has yellow skin, then it is delicious
3. If it is delicious and has yellow skin, then it is a banana.
4. Socrates is yellow
5. Therefore Socrates has yellow skin (MP 1&4)
6. Therefore Socrates is delicious (MP 2 &5)
7. Therefore, Socrates is a Banana (MP 5,6 & 3)
Modus Tollens
1. If Socrates is not a banana then Socrates is an orange
2. Socrates is not an orange
3. Therefore Socrates is a banana (MT 1&2)
Double Negation
1. It is not the case the Socrates is not a banana
2. Therefore Socrates is a Banana
And Addition
1. Socrates is a Banana
2. Socrates is Yellow
3. Therefore Socrates is yellow and a banana
And Elimination
1. Socrates is yellow and a banana
2. Therefore Socrates is a banana
Or Addition
1. Socrates is a banana
2. Therefore Socrates is a banana or an artichoke
Or Elimination
1. Either Socrates is a banana or Socrates is an artichoke
2. Socrates is not an artichoke
3. Therefore Socrates is a banana
 = Bi-Implication
A  B means “A if and only if B” or “If
A then B and if B then A”
¬ = Negation
¬A means “not A”
ˆ = Addition
A ˆ B means “A and B”
ˇ = Or
A ˇ B mean “Either A or B”
Note: In Logic ˇ is the inclusive, often
written and/or.
 = Das Falsum
-
This means that the system is
logically in correct.
-
You get  whenever you can
prove a contradiction
-
A contradiction looks like this
(A ˆ ¬A) regardless of what A
is.
QED = It is proven
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Unit 1: Logic and Epistemology
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All and Some
Note the special case of “all and some
For the following premises, mark whether the conclusions below can be considered true (T) knowingly
false (F) or undetermined (U)
All Philosophers are bananas
Socrates is a philosopher
Therefore Socrates is a banana
T
F
U
Therefore some philosophers are bananas
T
F
U
Therefore some bananas are philosophers
T
F
U
Therefore all bananas are philosophers
T
F
U
Therefore Socrates is a banana
T
F
U
Therefore some bananas are philosophers
T
F
U
Therefore all bananas are philosophers
T
F
U
Therefore Socrates may be a banana
T
F
U
Some Philosophers are bananas
Socrates is a philosopher
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Unit 1: Logic and Epistemology
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Logic Terms and Conditions
“I am quite sure now that often, very often, in matters concerning religion and politics a man's reasoning
powers are not above the monkey's”
Mark Twain
Truth Tables
Fill in the following truth tables:
Not A
T
F
A
T
T
F
F
and
B
T
F
T
F
A
T
T
F
F
or
B
T
F
T
F
If A
T
T
F
F
then
Venn Diagrams
Shade the diagrams in the way indicated
A or B
A and B
A
B
A
B
Not A
A
B
B
T
F
T
F
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Unit 1: Logic and Epistemology
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Conditions
If
A
Antecedent
Sufficient condition
Premise Set
Then
B
Consequence
Necessary Condition
Conclusion
All and Some
All and some are quantifiers and have a special effect on reasoning:
All A are B
Some Terms You Need to Know
A
Tautology: A tautology is a statement that is always true by
definition of the statement itself. For example to say “If this
statement is true, then the statement is not false.” This
sentence must logically be true because it proves itself.
B
Some A are B
A
Contradiction: A contradiction is a statement that cannot
possibly be true because it contradicts itself. To say “I am both
lying and telling the truth” is a contradiction because it cannot
possibly be true.
Paradox: A paradox is a statement where the possibility of
truth of falsity cannot be assessed because it leads to a logical
“loop” where its truth makes it false. The statement “This
statement is false” is a paradox.
B
The only
thing we
know from
the above
statement is
that this
part is true.
Either of these
areas may or
may not be
true. They are
not addressed
in the above
statement .
Skepticism: All things are uncertain. One cannot KNOW
anything. Scepticism does not say that there is no absolute
truth (like Existentialists) but that no absolute truth can be
known.
Nihilism: There is no absolute truth.
Futile Statement of Circular Logic: A futile statement is a
statement that leads us to no conclusion at all because if the
statement is true then it is true and if false, then the statement
is false. “This sentence is true” is a futile statement.