REASON AND ARGUMENT
1.1 WHAT IS MODERN SYMBOLIC 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
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.
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.
Logic Unit 1: Introduction
©2011 Niko Scharer 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
Premise If you will study then you will pass. S P
Premise You will study.
Conclusion Therefore, you will pass. P
*This and other illustrations are the property of Gerald Grow, Professor of Journalism, Florida A&M University, and are
here by his permissiohttp://www.longleaf.net/ggrow/CartoonPhil.html
Logic Unit 1: Introduction 2
©2011 Niko Scharer 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
Premise Indicators: words or phrases showing that the sentence or clause is being given in support of
a conclusion, as reason or justification.
because as indicated by being that
since in the first place inasmuch as
as you can see from may be inferred from
for seeing that can be deduced from
as shown by for the reasons that whereas
follows from assuming that 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 accordingly we can conclude that
thus consequently we can deduce that
so as a result proves that
hence it follows that shows that
then for this reason we see that indicates that
in conclusion it can be inferred 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.
Logic Unit 1: Introduction 3
©2011 Niko Scharer 1.4 PUTTING ARGUMENTS IN STANDARD FORM
When you are analyzing a piece of writing think about what the piece as a whole is trying to do. If you
think that there is an argument, start by picking out the main conclusion (the conclusion indicators may
help with that). Then, try to use the premise indicators to pick out the premises from other bits of
writing (elaborations, illustrations, explanations, filleThink it through!
When you present it in standard form, only state the premises and conclusion (leave out inference
indicators and other filler). State the premises first, putting them in logical order and starting each one
on a new line. Then draw a line. After the line, state the conclusion. You may want to put a therefore
sign () before the conclusion.
Three Easy Steps!
State the premises.
Draw a line.
Then state the conclusion.
Extract the argument and rewrite it in standard form:
Either Professor Plum or the butler committed the murder. But, as
everybody knows, no sane person would commit murder without
some sort of a motive. So it has to be the Professor. After all, not
only is the butler sane but he couldn‟t possibly have had a motive
to kill him.
This argument has a clearly indicated conclusion, introduced by „so‟. “…it has
to be the Professor.” After that, it is just a matter of identifying the premises.
The first and second sentences are both premises. The last sentence has a
premise indicator, „after all,‟ introducing “not only is the butler sane.” And the
last premise is that the butler did not have a motive to kill the victim.
Either Professor Plum committed the murder or the butler committed the murder.
No sane person commits murder without a motive.
The butler is sane.
The butler had no motive to commit the murder.
Professor Plum committed the murder.
Logic Unit 1: Introduction 4
©2011 Niko Scharer A few more to try:
In each of the following, extract the argument and rewrite it in standard form:
1.4 E 1
Some students will undoubtedly pass this course. Hence it is clear that some students in this
class will do the exercises, since nobody passes who doesn‟t do at least some of the exercises.
1.4 E 2
Anybody who smokes is irrational. Any rational person knows that smoking can kill you, and
engaging in an activity that can kill you is suicide! No rational person commits suicide.
1.4 E 3
If I study, I won‟t have much free time in which to party. On the other hand, if I don‟t study,
my parents will cut off my funds. Without parental funds I‟m not going to be going out much at
all. So it looks like there won‟t be any partying for me.
1.4 E 4
At some point in the far distant past, the universe came into existence. But nothing can come
from nothing; nothing can come into existence unless there is something to create it.
Accordingly, there must be a God – a first creator, outside time. This follows from the fact
that there must exist, outside the universe, some being that caused the universe to exist. Such a
being must not have been created at all, unless there was some greater being that caused it that
creator to exist, and hence this being would be the first creator.
1.4 E 5
Some people think that Ms. Peacock murdered Mr. Green, but that is wrong! It‟s evident that
Ms. Peacock could not have murdered Mr. Green unless the murder occurred in the library.
Yet, there were signs of struggle and drops of blood in the dining room, indicating that the
murder occurred there and not in the library where the body was found.
1.4 E 6
I realized, as I lay in bed thinking, that we are not responsible for what we do. This is because
either determinism or indeterminism must be true. If determinism is true, we cannot do other
than we do. If so, we are but puppets on strings – our actions are not free. If indeterminism is
true, then human actions are random, and hence not free. If our actions are not free, it must be
conceded that we are not responsible for what we do.
1.4 E 7
From the way that people act, it would seem that some people desire power. It is true that all
people desire what is good, and that nobody desires what is evil. So if people do desire power
then it must be good. Yet, power leads to corruption and nobody can deny that corruption is
evil. So power cannot be desired for it‟s own sake. Those who think they want power are
mistaken, and rarely attain what they truly desire when they act to obtain power.
Logic Unit 1: Introduction 5
©2011 Niko Scharer 1.5 SENTENCES AND TRUTH-VALUE
Many sentences (i.e. statements or propositions) are either true or false at some particular time and
place. Such sentences have a truth-value.
Not all sentences have truth-value. Questions, commands, exclamations, proposals and requests are
neither true nor false, and have no truth-value.
True sentences have truth-value T.
False sentences have truth-value F.
These sentences have truth-value T (they are true)
Ottawa is the capital of Canada.
The volume of fixed mass of gas is proportional to its temperature at a fixed pressure.
The last living passenger pigeon was named Martha.
These sentences have truth-value F (they are false)
Toronto is the capital of Canada.
The volume of a gas is inversely proportional to its temperature.
A foreign oil company official wants to transfer millions of dollars into your bank account.
These sentences have no truth-value:
Take me to your leader! (An order or imperative sentence)
What planet are you from? (A question or interrogatory sentence)
Gee willikers! (An exclamation or exclamatory sentence)
In the arguments that we will be looking at, each sentence of the argument must have a truth-value – it
must be a statement. In real life, arguments often have imperatives for conclusions.
If you don‟t do the homework you‟ll fail the course.
You don‟t want to fail the course.
Therefore, do the homework!
Logic Unit 1: Introduction 6
©2011 Niko Scharer 1.6 IS IT A GOOD ARGUMENT? VALIDITY AND SOUNDNESS
Different kinds of a