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Philosophy 103
Linguistics 103
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Introductory Logic:
Critical Thinking
Dr. Robert Barnard
Last Time:
• Syllabus:
Home.olemiss.edu/~rwbjr/rbphil103.htm
• Basic Concepts:
1) Arguments ( Premise/Conclusion)
2) Propositions (Simple/Complex)
- Conditional Props. (Antecedent/Consequent)
-Truth values
Why Logic?
• One way to support a theory is to offer an
argument in its favor.
• One way to criticize a theory is to offer an
argument against that theory.
• Which arguments should we take seriously?
Logic answers this Question!
Talking about Arguments
• We need to have a specific
vocabulary for talking about different
kinds of arguments and when an
argument works and when it doesn’t
work.
• We will use different terms to
describe failures of structure and
failures of content.
Deduction
In DEDUCTIVE ARGUMENTS the CONCLUSION
is supposed to follow NECESSARILY from the
PREMISES.
A DEDUCTIVE INFERENCE is one which takes us
from evidence or reasons to a conclusion
with necessity.
A Deductive Argument
All Cars have engines
My Honda is a car
Therefore, …
My Honda has an engine.
Premise 1
Premise 2
Conclusion INDICATOR
THE CONCLUSION!
Note:
If I tell you what the premises are, you know what the conclusion
would be before I told you!!! It is impossible for the conclusion
to be false, given these premises!
Induction
In INDUCTIVE ARGUMENTS the CONCLUSION is
supposed to follow with HIGH PROBABILITY
from the PREMISES.
An INDUCTIVE INFERENCE is one which takes us
from evidence or reasons to the likelihood of
the conclusion.
An Inductive Argument
Every person I have met from Poland loves
potato soup.
Karlov is from Poland.
Therefore,…
i) Karlov will love potato soup.
ii) Karlov will probably love potato soup.
A Quick review…
• Deductive vs. Inductive Arguments
• Deductive: The truth of the premises is
supposed to require the truth of the
conclusion (Necessary Support)
• Inductive: The truth of the premises is
supposed to increase the probability of the
conclusion (Probability)
Good vs. Bad Arguments
• Deductive Validity – IF the premises are true
THEN the conclusion MUST be true.
• Inductive Strength – IF the premises are true
THEN the conclusion WILL BE PROBABLE.
• Deductive Soundness – the deductive
argument is valid AND premises are all true
• Inductive Cogency—The inductive argument
is strong and the premises are all true
Argument Family Tree
Argument
Deductive
Valid
Invalid
Sound
Inductive
Strong
Weak
Cogent
Deductive Arguments
• Deductive Validity – IF the premises are true
THEN the conclusion MUST be true.
• Deductive Soundness – the deductive
argument is valid AND premises are all true
Failure of Structure: INVALID
Failure of Content: UNSOUND
Validity
Validity is the central concept in deductive logic.
Validity is related to structure or form.
Validity =df A deductive argument is
valid iff it is impossible for the
premises to be true and the
conclusion false (at the same time).
Soundness
Soundness is the secondary mode of evaluation
in deductive logic. Soundness is related to
content.
Soundness =df A deductive argument
is sound iff the argument is valid and
the premises are all true (at the
same time).
Kinds of Deductive Arguments
• Arguments from Mathematics
• Arguments from Definition
• Categorical Syllogism
• Hypothetical Syllogism
• Disjunctive Syllogism
Argument Family Tree (D)
Argument
Deductive
Valid
Invalid
Sound
Inductive
Strong
Weak
Cogent
Evaluating Deductive Arguments
• To determine VALIDITY you must first identify
the form of the argument.
– Try to develop counter-examples with the same
logical form, or…
– Employ methods of formal logical analysis.
• Determining SOUNDNESS depends upon the
truth of the premises (beyond logic)
Inductive Arguments
• Inductive Strength – IF the premises are true
THEN the conclusion WILL BE PROBABLE.
• Inductive Cogency—The inductive argument is
strong and the premises are all true
Failure of Structure: WEAKNESS
Failure of Content: NON-COGENT
Strength
• Inductive STRENGTH is the central mode
of evaluation for inductive arguments.
Strength=df An inductive argument is
strong iff it is improbable that the
conclusion is false when the premises are
all assumed to be true.
Cogency
• Inductive COGENCY is the secondary
mode of evaluation for inductive
arguments.
Cogency=df An inductive argument is
cogent iff it is inductively strong and
the premises are all true.
Kinds of Inductive Arguments
• Prediction
• Arguments from Analogy
• Generalization
• Arguments from Authority
• Arguments based upon signs
• Causal Inferences
Argument Family Tree (I)
Argument
Deductive
Valid
Invalid
Sound
Inductive
Strong
Weak
Cogent
Evaluating Inductive Arguments
• To determine STRENGTH you must evaluate
whether the truth of the premises would in
fact enhance the probability of the conclusion.
This requires knowledge of how things work
and how they are related.
• To determine COGENCY you must know the
truth of the premises (beyond logic)
Induction?
The evaluation of inductive arguments is
less clear. If you can give determinate
quantitative values to probabilities, then
the rules of statistics apply.
Otherwise you need to try and reflect on
the probabilities to the best of your
ability.
Induction
Some factors to keep in mind about inductive
data:
• Typicality (How common?)
• Generality (How General?)
• Frequency (How Frequent?)
• Analogy / Dis-analogy?
Arguments
1. All ARGUMENTS have a CONCLUSION and
PREMISES that are supposed to support the
conclusion.
2. Deductive and Inductive arguments differ
with respect to the type of support they are
intended to provide.
3. Deductive arguments provide NECESSARY
SUPPORT
4. Inductive arguments provide PROBABLE
SUPPORT
Pause and reflect…
New Topic:
Informal Fallacies
The study of informal fallacies goes back to
Ancient Greece, where the first philosophers
and logicians sought to control the
demagogues and their teachers (the so-called
Sophists).
What is a Fallacy?
A fallacy is a mistake in an
argument which consists in
something other than merely
false premises.
Formal Fallacies
A formal fallacy is simply an
invalid deductive argument form.
Informal = Material
Informal fallacies depend on the
content of the fallacious
argument: either the argument
depends upon a shift or ambiguity
in linguistic meaning or the
substitution of an non-logical
basis for a logical justification.
There are many varieties.
Fallacies of Relevance
Fallacies of Relevance
•The conclusion is logically irrelevant to
the premises, even if it is psychologically or
emotionally relevant.
•The key to spotting a fallacy of relevance
is to distinguish genuine evidence from
emotional appeal.
1. Appeal to Force
(Argumentum Ad Bacculum)
Arguing via threat: "I deserve a good
grade, wouldn't you agree? If you don't
agree, I'm afraid about what might
happen: I just can't control Bruno here".
2. Appeal to Pity
(Argumentum ad Misericordium)
Trying to support a conclusion by evoking
pity in the listener. I need to pass this
class in order to graduate, if I don't
graduate,, my parents will kill me.
Therefore, I should receive a passing grade
in the class".
3. Appeal to the People
(argumentum ad populum)
Attempting to convince by appealing to the
natural desire we all have to be included, or
liked, or recognized. This type of fallacy breaks
down into several sub-types.
Bandwagon: Of course God exists. Every real
American believes that. Other related types:
Appeal to Vanity; Appeal to Snobbery ("Of
course you should cheat; all the cool people are
doing it").
3. Appeal to the People (argumentum
ad populum) (2)
In general, accepting a claim only because someone
else believes it is a fallacy (not because you find them to
be a credible source for instance . . .). So, we could say
that another example of an ad populum is:
Appeal to Belief. Example: "90% of those surveyed think
we should not convict Clinton, so you should too".
Closely related is the…
Appeal to Common Practice. Example: "Hey, everyone
speeds. So speeding isn't wrong".