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PHL245H1 Chapter Notes -Dark Chocolate, Formal Methods, Kurt Cobain


Department
Philosophy
Course Code
PHL245H1
Professor
Niko Scharer

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Logic Unit 1: Introduction
©2011 Niko Scharer
UNIT 1
REASON AND ARGUMENT
1.1 WHAT IS MODERN SYMBOLIC LOGIC?
Logic.
The Study & Evaluation of Reasoning & Argument
An argument probably seems logical if it look likes the conclusion
must be true, based on what you are told is the case and what you
already know to be true.
This is because logical deductive arguments are truth-preserving:
if the premises are true, then the conclusions must be true.
Studying logic can help you recognize which arguments are good
ones, and thus improve your ability to distinguish truths or
probable claims from ones that are poorly supported by the
evidence.
Symbolic.
Use Tidy Symbols instead of Messy Words!
Using symbols instead of words lets you to focus on the logical form of the argument, so you can
evaluate the reasoning of the argument without being distracted by other considerations, e.g. whether
you agree with it, whether it‟s interesting or has true premises, etc.
Symbolization also can clear up ambiguities in meaning. Sometimes sentences, phrases and words can
be interpreted different ways. Symbolization can force you to be more precise and consider exactly
what is meant.
Modern.
After such people as ...
Aristotle (384-322 BC). Aristotelian or syllogistic logic is
the earliest system intended to classify and evaluate a wide
range of arguments.
Chrysippus (c.280-c.205 BC) developed a system of
propositional logic that anticipates modern logic.
Gottfried Wilhelm Leibniz (1646-1716), perhaps the father
of symbolic logic, developed some of the first logical calculi.
Gottlob Frege (1848-1925) laid foundations for mathematical
logic, further developed by Alfred North Whitehead (1861-1947)
and Bertrand Russell (1872-1970) in their Principia Mathematica.

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Logic Unit 1: Introduction
©2011 Niko Scharer
2
1.2 WHAT IS AN ARGUMENT?
In philosophy, logic, essays and many other contexts,
arguments are bits of reasoning which present
justifications for certain statements a conclusion (a
statement, opinion, thesis, etc.) supported by a
justification or evidence.
An argument is a discourse in which some statements
(the premises) are presented in support of another
statement (the conclusion). In a valid deductive
argument, the logical structure of that discourse is
such that if the premises are true, then the conclusion
must also be true. It is truth-preserving!
*
Two parts of an Argument
Premises or assumptions: reasons or justification for the conclusion.
Conclusion: the statement, thesis or opinion being argued for.
Premises and conclusions are sentences, statements or propositions that can be true or false they have
truth-value. Arguments are generally composed of statements and usually don‟t include questions,
commands and other sentences without truth-value.
„Premise‟ and „conclusion‟ are relative terms. The same sentence can serve as a premise in one
argument and as the conclusion in another.
STRUCTURE OF AN ARGUMENT
This argument (center) is in standard form. The premises are stated above a horizontal
line, and the conclusion is stated below. The argument is presented on the right in
symbolic form.
Premise
Premise
Conclusion
If you will study then you will pass.
You will study.
Therefore, you will pass.
*
This and other illustrations are the property of Gerald Grow, Professor of Journalism, Florida A&M University, and are
here by his permission. http://www.longleaf.net/ggrow/CartoonPhil.html

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Logic Unit 1: Introduction
©2011 Niko Scharer
3
1.3 IDENTIFYING THE ARGUMENT
What to look for ... Signs of Reasoning or Inference Indicators
Some words or phrases at the beginning of sentences or clauses tell us that the sentence or clause is
part of an argument. Some introduce premises (premise indicators) and others introduce conclusions
(conclusion indicators).
Premise Indicators: words or phrases showing that the sentence or clause is being given in support of
a conclusion, as reason or justification.
because
since
as
for
as shown by
follows from
as indicated by
in the first place
you can see from
seeing that
for the reasons that
assuming that
being that
inasmuch as
may be inferred from
can be deduced from
whereas
on account of
Conclusion Indicators: words or phrases showing that the sentence or clause is the conclusion for
which reasons or justification will be given.
therefore
thus
so
hence
then
in conclusion
accordingly
consequently
as a result
it follows that
for this reason we see that
it can be inferred that
we can conclude that
we can deduce that
proves that
shows that
indicates that
this makes it clear that
BE CAREFUL THINK ABOUT HOW WORDS ARE BEING USED!
Inference indicators are just words and words perform different functions in
different contexts. In arguments, words like “because,” “for,” “thus,” and “then”
are often inference indicators. But, in explanations, descriptions, or even in
arguments, they perform many other functions.
Consider the different ways that „since‟ can be used:
I realize that I haven‟t seen my cousin since we were kids.
Since I was sick, I have to turn my essay in late.
Clearly Sam will win since he has the support of the party.
In the third sentence „since‟ acts as a premise indicator, introducing a reason
for accepting the conclusion (that Sam will win). In the other sentences, „since‟
is not a premise indicator. In the first, it introduces a clause that provides
information; in the second sentence, it introduces an explanation.
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