Download deductive reasoning

LECTURE 3: REASONING AND
LOGIC
RECAP
In our previous lecture we:
1. Looked at the origins of philosophy
a) Investigated Thales’ metaphysical theory that everything is
composed of water.
b) Contrasted the rational thinking (logos) of Thales with the
mythical thinking (mythos) of his predecessors.
1. Discussed in further detail the similarities and differences between science
and philosophy
2. Discussed the methodological differences between science and philosophy
3. Concluded by discussing the value of philosophy
RECAP
Unresolved Discussions:
Q: Does ‘philosophy’ change over time?
 Throughout its history, science has undergone numerous changes
 These changes have often had big influences on society, philosophy etc.
Possible answers include:
Option 1: The discipline we call ‘Philosophy’ including its methods, scopes and
aims, undergoes historical changes.
Option 2: Although there was once a time before philosophy, philosophy does
not change.
Option 3: Some features of philosophy may change, but others do not.
The question, then, is; what remains constant and what changes?
Rationalism
RECAP
“The view that affirms reason, with its interest in evidence,
examination, and evaluation, as authoritative in all matters of belief
and conduct”
(Miller, Ed L. Questions that Matter, 2009. p.10)
Unresolved Discussions:
Q: Should we view religious texts and religions as based on
mythical or rational thinking?
Points for discussion:
 Some scientists might, for example, claim that religious belief is governed
entirely by mythical thinking.
 The appeal to supernatural beings might suggest a mythical dimension.
 Some philosophers, anthropologists, sociologists, etc. have asked whether
the distinction between mythical and rational thinking is valid. In
particular they ask whether the distinction is culturally biased.
Remember! Just because an account discusses God does not necessarily make
it mythical!
Rationalism
RECAP
“The view that affirms reason, with its interest in evidence,
examination, and evaluation, as authoritative in all matters of belief
and conduct”
(Miller, Ed L. Questions that Matter, 2009. p.10)
Unresolved Discussions:
Q: Should we view religious texts and religions as based on
mythical or rational thinking?
Possible answer: There are different ways of investigating the same
thing
For example, we could investigate the Bible in the following ways:
Mythically
Philosophically
Scientifically
The Bible is full of
mythical narratives that
explain our world. E.g.
The story of Adam &
Eve.
The Bible uses fables
and stories to teach us
valuable knowledge
about how we should
live.
Scientists might seek to
find physical evidence
that proves the truth of
the Bible. E.g. Pieces of
the Ark.
Rationalism
RECAP
“The view that affirms reason, with its interest in evidence,
examination, and evaluation, as authoritative in all matters of belief
and conduct”
(Miller, Ed L. Questions that Matter, 2009. p.10)
LOGIC AND REASONING
In today’s lecture we will:
1. Investigate an important tool used by philosophers: logic and reasoning
2. Examine the form of logic
3. Attempt to understand the distinction between Deductive and Inductive
reasoning.
4. Outline and examine a number of important argumentative fallacies
(invalid ways of arguing)
5. Apply what we have learned using a number of examples.
6. Conclude our investigation into the what/who/why/how of philosophy.
TODAY’S LECTURE
Logic & How Not to Argue
Philosophers often use logic to examine and evaluate arguments:
Logic is “The Formal Study of Valid Inferences”
Distinguishes between valid and invalid arguments
Also distinguishes between Sound and Unsound arguments
Powerful tool for analysis and criticism.
Analyzes the logical structure of an argument (not the truth of an
argument)
LOGICAL AND REASONING
Two Forms of Reasoning
Deductive Reasoning
In a valid deductive argument; if the premises are true, the
conclusion must be true, by virtue of a logically necessary inference.
[Deductive arguments tend to argue from the whole to the particular]
Inductive Reasoning
In a strong inductive argument: if the premises are true, the
conclusion is probably true, by virtue of a supportive inference.
[Inductive arguments tend to argue from the part to the whole]
(Miller, Ed L. Questions that Matter, 2008. p.23)
LOGICAL AND REASONING
A little clarification
Valid Arguments
Valid arguments display proper deductive form
True Statements
True statements are possible in any argument regardless of form
Sound Arguments
Sound arguments have both valid form and true premises
(Miller, Ed L. Questions that Matter, 2008. p.19)
LOGICAL AND REASONING
DEDUCTIVE REASONING
Deductive Reasoning
All men are mortal
Premises
Socrates is a man
Therefore Socrates is mortal
Conclusion
The premises logically entail the conclusion
The argument is valid and sound
(Both true and logically valid)
DEDUCTIVE REASONING
An example of a deductive, logical argument
All A’s are B’s
S is an A
Therefore S is a B
Remember: If the premises of a deductive argument are true
the conclusion must be true!
DEDUCTIVE REASONING
Is this argument logically valid?
All ducks float on water
Professor Harris is a duck
Therefore Professor Harris floats on water
Do the premises logically entail the conclusion?
Is the argument true?
Is the argument sound? (is it logically valid and true?)
DEDUCTIVE REASONING
How about this one?
If it is raining then the streets are wet
The streets are wet
Therefore it is raining
Do the premises logically entail the conclusion?
Is the argument true?
Is the argument sound? (is it logically valid and true?)
DEDUCTIVE REASONING
INDUCTIVE REASONING
An example of an inductive, argument
Instance 1 of A is observed to be X
Instance 2 of A is observed to be X
Instance 3 of A is observed to be X
Instance 4 of A is observed to be X
Instance 5 of A is observed to be X
...
Therefore, all A is X
INDUCTIVE REASONING
An example of inductive reasoning: Universal Generalization
Swan 1 is white
Swan 2 is white
Swan 3 is white
Swan 4 is white
Swan 5 is white
Swan 526 is white
...
Therefore all swans are white
Do the premises give supportive inference to the conclusion?
Is the argument true?
Is the argument sound? (is there sufficient supportive inference and is
the argument true?)
INDUCTIVE REASONING
Another example of inductive reasoning: Analogy
A is observed to be X and Y
B is observed to be X and Y
C is observed to be X and Y
D is observed to be X and Y
...
M is observed to be X
Therefore, M is Y
Do the premises give supportive inference to the conclusion?
Is the argument true?
Is the argument sound? (is there sufficient supportive inference and is
the argument true?)
INDUCTIVE REASONING
Deductive Reasoning
Inductive Reasoning
Argues from the Whole to the
Particular
Argues from the particular to the
whole
If the argument is valid and the
premises are true; the conclusion
MUST be true.
If the argument is sound and the
premises are true; the conclusion
MIGHT be true.
Deductive arguments are only
concerned with FORM
(An argument may be logically valid
but still false)
Doesn’t teach us anything new
SUMMARY
Inductive arguments rest on
‘supportive inferences’
Teaches us new things
Deductive Reasoning
Valid Arguments
In a valid deductive
argument; if the
premises are true, the
conclusion must be true,
by virtue of a logically
necessary inference.
Valid arguments display
proper deductive form
Inductive Reasoning
In a strong inductive
argument: if the
premises are true, the
conclusion is probably
true, by virtue of a
supportive inference.
True Statements
True statements are
possible in any
argument regardless of
form
Sound Arguments
Sound arguments have
both valid form and true
premises
LOGICAL FALLACIES
Some more clarification
Formal Fallacies
Mistakes in reasoning due to a failure in following the rules for the
formal structure of valid arguments. These fallacies do not concern
truth or falsity but validity.
Informal Fallacies
Mistakes in reasoning due to carelessness regarding relevance and
clarity of language. These fallacies bear directly on issues of truth
and falsity.
(Miller, Ed L. Questions that Matter, 2008. p.23)
LOGICAL FALLACIES
Argumentative Fallacies
1. Loaded Language is language with the sole purpose of swaying the
emotions of the audience for or against an argument.
2. Equivocation occurs when a word or expression changes its meaning in
the course of an argument, sometimes referred to as a “weasel word.”
3. Begging the Question occurs when the conclusion of an argument is
already present, usually disguised, in one of its premises.
4. Ad Hominem (appeal to the person) irrelevantly attacks the person
making a claim rather than attacking the claim itself.
5. Straw Man Inappropriately simplifies an opposing argument so that it
becomes a cartoon or caricature of the true argument and is easy to refute.
6. “Person who” is the fallacy of generalizing or drawing a conclusion from
too little information. Also called a hasty induction.
7. Ad populam (appeal to the masses) seeks to strengthen a claim by an
emotional appeal to the passions and prejudices of the listeners.
8. Ad ignorantium (appeal to ignorance) affirms the truth of something
on the basis of the lack of evidence to the contrary.
9. False Dilemma involves limiting the options considered to only two in a
way that is unfair to the person facing the dilemma.
(Miller, Ed L. Questions that Matter, 2008. pp. 22-24)
LOGICAL FALLACIES
TOPIC CONCLUSION
What is Philosophy?
A rational investigation into a range of topics and aspects of human existence
Who does Philosophy?
Everyone, particularly anyone that asks philosophical questions.
Why do we do Philosophy?
Many philosophical inquiries are important. Not everything can be investigated
scientifically.
Philosophy can provide us with important skills and knowledge.
How do we do Philosophy?
Philosophers use reason and rational thinking as their principle means of
conducting their inquiries; including logic; arguments; discussion; observation;
evaluation and more...
TOPIC CONCLUSION
Conclusions:
I.
Some questions do not have any definite answers but are still valid
questions!
II. Philosophy can be useful tool for critically examine the assumptions
implicit in other systems of thought.
III. Philosophy is a useful tool for examining the world. (beyond the natural
sciences.
IV. Like any tool, Philosophy has a limited role and application.
RECAP
Over the coming weeks we will be investigating:
1. What is Reality? (Metaphysics/Ontology)
(a) What is the relationship between mind and body?
2. Theory of Knowledge (Epistemology)
3. Natural Theology
4. Moral Philosophy
UPCOMING TOPICS
Perhaps ‘Philosophy’ Consists of “Family Resemblances”
And we can go through many, many other groups of games in the same way;
can see how similarities crop up and disappear.
And the result of this examination is: we see a complicated network of
similarities overlapping and criss-crossing: sometimes overall similarities,
sometimes similarities of detail.
I can think of no better expression to characterize these similarities than
“family resemblances”: for the various resemblances between members of a
family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and
criss-cross in the same way.—And I shall say “games” form a family.
Ludwig Wittgenstein, Philosophical Investigations, (New York: Macmillan, 1964), p.32
TOPIC CONCLUSION
DISCUSSION
Questions for Discussion:
1. Is the distinction between mythical and rational thinking valid? Or does
modern science constitute another form of myth-making?
2.
Could science do without philosophy or vice versa?
3. Defend one of these views:
a) “Philosophy” can be defined.
b) “Philosophy” cannot be defined.
4. Is philosophy a worthwhile subject?
5. What is significant about the form of deductive arguments?
DISCUSSION