1. What is Philosophy?
Philosophy may be regarded as a search for wisdom and understanding and it is an
evaluative discipline that in the course of time has started to be seen as becoming
more and more concerned with evaluating theories about facts than with being
concerned with facts in themselves. In this sense, philosophy may be regarded as a
second order discipline, in contrast to first order disciplines which deal with empirical
subjects. In other words, philosophy is not so much concerned with revealing truth in
the manner of science, as with asking secondary questions about how knowledge is
acquired and about how understanding is expressed. Unlike the sciences, philosophy
does not discover new empirical facts, but instead reflects on the facts we are already
familiar with, or those given to us by the empirical sciences, to see what they lead to
and how they all hang together, and in doing that philosophy tries to discover the most
fundamental, underlying principles.
What is Philosophy? Why should we learn it?
What is philosophy? Philosophy can mean different things to different people.
Etymologically speaking, philosophy means ‘Love of Wisdom.’ It includes both
theory and practise, view and way, end and means, beginning (alpha) and end
(omega), or science and art. Its meanings seem to depend on each school of thought.
Philosophers, therefore, may be considered as sages, lovers of wisdom, lovers of
argument, theorists, practitioners, or even artists.
Philosophy may be regarded as a search for wisdom and understanding and it is an
evaluative discipline that in the course of time has started to be seen as becoming
more and more concerned with evaluating theories about facts than with being
concerned with facts in themselves. In this sense, philosophy may be regarded as a
second order discipline, in contrast to first order disciplines which deal with empirical
subjects. In other words, philosophy is not so much concerned with revealing truth in
the manner of science, as with asking secondary questions about how knowledge is
acquired and about how understanding is expressed. Unlike the sciences, philosophy
does not discover new empirical facts, but instead reflects on the facts we are already
familiar with, or those given to us by the empirical sciences, to see what they lead to
and how they all hang together, and in doing that philosophy tries to discover the most
fundamental, underlying principles.
Philosophy ‘as the thought of the world’, it appears only when actuality is already
there cut and dried after its process of formation has been completed… When
philosophy paints its grey in grey, then has a shape of life grown old. By philosophy’s
grey in grey it cannot be rejuvenated but only understood. ‘The owl of Minerva
spreads its wings only with the falling of the dusk’. (Hegel, pp.12-13, Philosophy of
Right)
There are various currents of academic philosophy. We can speak of Eastern and
Western philosophy. Western philosophy at the moment can be divided into two main
kinds: analytic (Anglo-American or English speaking) and continental (European)
philosophy. The two kinds of philosophy pay attention to language and being.
However, while analytic philosophy mainly deals with truths and knowledge,
continental philosophy (primarily) deals with values and life. From these
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2. observations, it may be said that analytic philosophy is a close friend of science
whereas most school of continental philosophy are close friend of religion. Turning to
Eastern philosophy, we may surprisingly discover that all schools of thought believe
that reality is a social process. In other words, according to Eastern philosophy, all
actual realities are becomings, not beings.
Useful glossary
- Idea: Something such as a thought or conception, that potentially or actually exists
in the mind as product of mental activity.
- Concept: A general idea derived or inferred from specific instances or occurrences.
- Conception: The ability to form or understand mental concepts and abstractions;
something conceived in the mind; a concept, plan, design, idea, or thought.
Synonyms: idea, thought, notion, concept, conception.
These nouns refer to what is formed or represented in the mind as the product of
mental activity. Idea has the widest range: ‘Human history is in essence a history of
ideas’ (H.G. Wells).
Thought is applied to what is distinctively intellectual and thus especially to what is
produced by contemplation and reasoning as distinguished from mere perceiving,
feeling, or willing: Quiet – she’s trying to collect her thoughts. I have no thought of
going to Europe. ‘Language is the dress of thought’ (Samuel Johnson).
Notion often refers to a vague, general, or even fanciful idea: ‘She certainly has some
notion of drawing’ (Rudyard Kipling).
Concept and conception are applied to mental formulation on a broad scale: He seems
to have absolutely no concept of time. ‘Every succeeding scientific discovery makes
greater nonsense of old-time conceptions of sovereignty’ (Anthony Eden).
Theory
Theory: Systematically organized knowledge applicable in a relatively wide variety of
circumstances, especially a system of assumptions, accepted principles, and rules of
procedure devised to analyse, predict, or otherwise explain the nature or behaviour of
a specified set of phenomena.
[Source for the definitions: The American Heritage Dictionary of the English
Language. Third Edition. Boston, New York, London: Houghton Mifflin Company,
1992.]
George Wilhelm Friedrich Hegel (1770-1831)
German philosopher, Hegel was the founder of modern idealism and developed the
notion that consciousness and natural objects are in fact unified. In Phenomenology of
Spirit (1807), he sought to develop a rational system that would substitute for
traditional Christianity by interpreting the entire process of human history, and indeed
the universe itself, in terms of the progress of absolute Mind towards self-realization.
In his view, history is, in essence, a march of human spirit towards a determinant end-
point.
Hegel’s principal political work, Philosophy of Right (1821), advanced an organic
theory of the state that portrayed it as the highest expression of human freedom. He
identified three moments of social existence: the family, civil society, and the state.
Within the family, he argued, a particular altruism operates, encouraging people to
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3. set aside their own interests for the good of their relatives. He named civil society as a
sphere of universal egoism in which individuals place their own interests before
those of others. However, he held that the state is an ethical community underpinned
by mutual sympathy, and is thus characterized by universal altruism. This stance
was reflected in Hegel’s admiration for the Prussian state of his day, and helped to
convert liberal thinkers to the cause of state intervention. Hegel’s philosophy also had
considerable impact upon Marx and other so-called ‘Young Hegelians’.
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4. Philosophy literally means love of wisdom, the Greek words philia meaning love or
friendship, and Sophia meaning wisdom. Philosophy is concerned basically with three
areas: epistemology (the study of knowledge), metaphysics (the study of the nature of
reality), and ethics (the study of morality).
Epistemology deals with the following questions: what is knowledge? What are truth
and falsity, and to what do they apply? What is required for someone to actually know
something? What is the nature of perception, and how reliable is it? What are logic
and logical reasoning, and how can human beings attain them? What is the difference
between knowledge and belief? Is there anything as “certain knowledge”?
Metaphysics is the study of the nature of reality, asking the questions: What exists in
reality and what is the nature of what exists? Specifically, such questions as the
following are asked: Is there really cause and effect in reality, and if so, how does it
work? What is the nature of the physical world, and is there anything other than the
physical such as the mental or spiritual? What is the nature of human beings? Is there
freedom in reality or is everything predetermined?
Ethics deals with what is right or wrong in human behaviour and conduct. It asks such
questions as what constitutes any person or action being good, bad, right, or wrong,
and how do we know (epistemology)? What part does self-interest or the interest of
others play in the making of moral decisions and judgements? What theories of
conduct are valid or invalid, and why? Should we use principles or rules or laws, or
should we let each situation decide our morality? Are killing, lying, cheating, stealing,
and sexual acts right or wrong, and why or why not?
Lecture 2: Love of wisdom
The term philosophy literally means the love of wisdom. It is said that the first one to
call himself a philosopher was Pythagoras, a Greek who lived somewhere between
570 and 495 B.C. and spent most of his life in southern Italy. He is, of course, best
known for his famous mathematical theorem. When once asked is he was wise, he
replied that no one could be wise but a god, but that he was a lover of wisdom. To
love something does not mean to possess it but to focus our life on it. Whereas
Pythagoras introduced the term philosopher, it was Socrates who made it famous. He
said that the philosopher was one who had a passion for wisdom and who was
intoxicated by this love. This description makes quite a contrast with the image of the
philosopher as being cold and analytical – sort of a walking and talking computer. On
the contrary, the cognitive and the emotional are combined in philosophy, for we do
not rationally deliberate about those issues in life that are deeply trivial. Those issues
that are most important to us are such things as our religious commitments (or lack of
them), our moral values, our political commitments, our career, or (perhaps) who we
will share our lives with. Such issues as our deepest loves, convictions, and
commitments demand our deepest thought and most through rational reflection.
Philosophy, in part, is the search for that kind of wisdom that will inform the beliefs
and values that enter into these crucial decisions.
Socrates’ method
If wisdom is the most important goal in life to Socrates, how did he go about pursuing
it? Socrates method of doing philosophy was to ask questions. That method was so
effective that it has become one of the classic techniques of education; it is known as
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5. the Socratic method, or Socratic questioning. Plato referred to the method as dialectic,
which comes from a Greek word for conversation. Typically, Socrates’ philosophical
conversations go through seven stages as he and his partner continually move toward
a greater understanding of the truth:
1 Socrates unpacks the philosophical issues in an everyday conversation. (The genius
of Socrates was his ability to find the philosophical issues lurking in even the most
mundane of topics.)
2 Socrates isolates a key philosophical term that needs analysis.
3 Socrates professes ignorance and requests the help of his companion.
4 Socrates’ companion proposes a definition of the key term.
5 Socrates analyzes the definition by asking questions that expose its weaknesses.
6 The subject produces another definition, one that improves on the earlier one. (This
new definition leads back to step 5, and on close examination the new definition is
once again found to fail. Steps 5 and 6 are repeated several times.)
7 The subject is made to face his own ignorance. (Finally, the subject realizes he is
ignorant and is now ready to begin the search for true wisdom. Often, however, the
subject finds some excuse to end the conversation or someone else makes an attempt
at a new definition.)
Socrates’ hope in utilizing this method was that in weeding out incorrect
understandings, he and his conversational partner would be moving toward a clearer
picture of the true answer. Since Socrates believed that the truth about the ultimate
issues in life lay deeply hidden within us, this process of unpacking the truth within
was like that of a midwife helping a mother in labour bring forth her child.
One of Socrates’ most skilful techniques for showing the weakness of someone’s
position was his use of the reductio ad absurdum form of argument. This term means
“reducing to an absurdity.” Socrates would begin by assuming that his opponent’s
position is true and then show that it logically implies either an absurdity or a
conclusion that contradicts other conclusions held by the opponent. Deducing a false
statement from a proposition proves that the original assumption was false.
Reductio ad Absurdum Arguments
The label of the reduction ad absurdum argument, a valid argument form, means
reducing to an absurdity. To use this technique, you begin by assuming that your
opponent’s position is true and then you show that it logically implies either an absurd
conclusion or one that contradicts itself or that it contradicts other conclusions held by
your opponent. Deducing a clearly false statement from a proposition is definitive
proof that the original assumption was false and is a way of exposing an inconsistency
that is lurking in an opponent’s position. When the reduction ad absurdum argument
is done well, it is an effective way to refute a position.
1 Suppose the truth of A (the position that you wish to refute).
2 If A, then B.
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6. 3 If B, then C.
4 If C, then not-A.
5 Therefore, both A and not-A
6 But 5 is a contradiction, so the original assumption must be false and not-A must be
true.
Philosophical example of a Reductio ad Absurdum
Socrates’ philosophical opponents, the Sophists, believed that all truth was subjective
and relative. Protagoras, one the most famous Sophists, argued that one opinion is just
as true as another opinion. The following is a summary of the argument that Socrates
used to refute this position as Plato tell us (Theaetetus, 171a,b):
1 One opinion is just as true as another opinion. Socrates assumes the truth of
Protagoras’s position.)
2 Protagoras’s critics have the following opinion: Protagoras’s opinion is false and
that of his critics is true.
3 Since Protagoras believe premise 1, he believes that the opinion of his critics in
premise 2 is true.
4 Hence, Protagoras also believes it is true that: Protagoras’s opinion is false and that
of his critics is true.
5 Since individual opinion determines what is true and everyone (both Protagoras and
his critics) believe the statement “Protagoras’s opinion is false”, it follows that
6 Protagoras’s opinion is false.
Topic
What is the practical value of philosophy?
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7. The basic concepts of logic
Logic is the study of the methods and principles used to distinguish correct reasoning
from incorrect reasoning and is a tool for figuring out everything that can truthfully be
said, based on what is already known to be true. For this reason, it is related to
epistemology, i.e., the theory of knowledge, but its range of application cover the
evaluations of arguments in every field of knowledge including metaphysics and
ethics. There are objective criteria with which correct reasoning may be defined. If
these criteria are not known, they cannot be used. The aim of logic is to discover and
make available those criteria that that can be used to test arguments, and to sort good
arguments from bad ones.
The logician is concerned with reasoning on every subject: science and medicine,
metaphysics, ethics and law, politics and commerce, sports and games, and even the
simple affairs of everyday life. Very different kinds of reasoning may be used, and all
are of interest to the logician, but his concern throughout will be not with the subject
matter of those arguments, but with their form and quality. His aim is how to test
arguments and evaluate them.
It is not the thought processes called reasoning that are the logician’s concern, but the
outcomes of these processes, the arguments that are the products of reasoning, and
that can be formulated in writing, examined, and analyzed. Each argument confronted
raises this question for the logician: Does the conclusion reached follow from the
premises used or assumed? Do the premises provide good reasons for accepting the
conclusion drawn?
The origins of logic
In Western intellectual history there have been three great periods of development in
logic, with somewhat barren periods sandwiched between them. The first great period
was ancient Greece between about 400 BC and 200 CE. The most influential figure
here is Aristotle (384-322) who developed a systematic theory of inferences called
“syllogisms”.
It should also be mentioned that at around the same time as all this was happening in
Greece, theories of logic were being developed in India, principally by Buddhist
logicians.
The second growth period in Western logic was the in the medieval European
universities, such as Paris and Oxford, from the 12th
to the 14th
centuries.
After this period, logic largely stagnated till the second half of the 19th
century.
The development of abstract algebra in the 19th
century triggered the start of third and
possibly the greatest of the three periods. The logical theories developed in the third
period are normally referred as modern logic, as opposed to the traditional logic that
preceded it. Developments in logic continued apace throughout the 20th century and
show no sign of slowing down yet.
“Arguments” in logic
As we have seen, it is with arguments that logic is chiefly concerned. An argument is
a cluster of propositions in which one is the conclusion and the other(s) are premises
offered in its support. This means that in understanding and constructing arguments, it
is particularly important to distinguish the conclusion from the premises. Indicator
words can help us to do this: words like therefore, thus, so, consequently tell us which
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8. claims are to be justified by evidence and reasons, and since, because, for, as, as
indicated by, in view of the fact that which other claims are put forward as premises to
support them. However, indicator words are not infallible signs of argument because
some arguments do not contain indicator words, and some indicator words may
appear outside the context of arguments.
Arguments may be analyzed and illustrated either by paraphrasing, in which the
propositions are reformulated and arranged in logical order; or by diagramming, in
which the propositions are numbered and the numbers are laid out on a page and
connected in ways that exhibit the logical relations among the propositions. To
diagram we number each proposition in the order in which it appears, circling the
numbers. This avoids the need to restate the premises.
Nonarguments
Arguing and arguments are important as rational ways of approaching disputes and as
careful critical methods of trying to arrive at the truth. Speeches and texts that do not
contain arguments can be regarded as nonarguments. There are many different types
of nonarguments – including description, exclamation, question, joke, and
explanation. Explanation are sometimes easily confused with arguments because they
have a somewhat similar structure and some of the major indicator words for
arguments are also used in explanations. Explanations should be distinguished from
arguments, however, because they do not attempt to justify a claim, or prove it to be
true.
Recognizing arguments: deduction and induction
The difference between inductive and deductive arguments is deep, Because an
inductive argument can yield no more than some degree of probability for its
conclusion it is always possible that additional information will strengthen or weaken
it. Newly discovered facts may cause us to change our estimate of probabilities, and
thus may lead us to judge the argument to be better or worse than we thought it was.
In the world of inductive argument – even when the conclusion is thought to be very
highly probable – all the evidence is never in. It is this possibility of new data,
perhaps conflicting with what was believed earlier, that keeps us from asserting that
any inductive conclusion is absolutely certain.
Deductive arguments, on the other hand, cannot gradually become better or worse.
They either succeed or do not succeed in exhibiting a compelling relation between
premises and conclusion. The fundamental difference between deduction and
induction is revealed by this contrast. If a deductive argument is valid, no additional
premises could possibly add to the strength of that argument. For example, if all
humans are mortal, and is Socrates is human, we may conclude without reservation
that Socrates is mortal – and that conclusion will follow from that premises no matter
what else may be true in the world, and no matter what other information may be
discovered or added.
Topics:
Try to formulate some general principles or criteria that you use in deciding whether
the truth of a statement is more or less certain;
Define philosophy and explain the role of logic within it specifying how it differs
from or relate to epistemology, metaphysics and ethics.
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9. The 3 Laws of Thought
Some early thinkers, after having defined logic as the science of the laws of thought,
went on to assert that there are exactly three basic laws of thought, laws so
fundamental that obedience to them is both the necessary and the sufficient condition
of correct thinking. These three laws have traditionally been called:
1 The principle of identity.
This principle asserts that if any statement is true, then it is true. Using our notation
we may rephrase it by saying that the principle of identity asserts that every statement
of the form
p ⊃ p must be true, that every such statement is a tautology (a tautology is a statement
which uses different words to same the same thing). From this follows that
1 Prem.
a=a [This is an axiom – a basic assertion that is not proved but can be used to prove
other things. The rule of self-identity says that that we may assert a self-identity as a
derived step anywhere in a proof, no matter what the earlier lines are.]
and that
2 a=b :: b=a
and that
3 Fa
a = b
Fb [This is the equals may substitute for equals rule which is based on the idea that
identicals are interchangeable. If a=b, then whatever is true of a is also true of b, and
vice versa. This rule holds regardless of what constants replace a and b and what well
formed formulas replace Fa and Fb provided that the two well formed formulas are
alike except that the constants are interchanged in one or more occurrences.]
2 The principle of non contradiction.
This principle assets that no statement can be both true and false. Using our notation
we may rephrase it by saying that the principle of non contradiction asserts that every
statement of the form p ∙ ∼p must be false, that every such statement is self
contradictory.
3 The principle of excluded middle.
This principle asserts that every statement is either true or false.
Using our notation we may rephrase it by saying that the principle of excluded middle
asserts that every statement of the form p ∨ ∼p must be true, that every such statement
is a tautology.
It is obvious that these 3 principles are indeed true, logically true – but the claim that
they deserve a privileged status as the most fundamental laws of thought is doubtful.
The first (identity) and the third (excluded middle) are tautologies, but there are many
other tautologous forms whose truth is equally certain. And the second (non
contradiction) is by no means the only self-contradictory form of statement.
We do use these principles in completing truth tables. In the initial columns of each
row of a table we place either a T or an F, being guided by the principle of excluded
middle. Nowhere do we put both T and F together, being guided by the principle of
non-contradiction. And once having put a T under a symbol in a given row, then
(being guided by the principle of identity) when we encounter that symbol in other
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10. columns of that row we regard it as still being assigned a T. So we could regard the
three laws of thought as principles governing the construction of truth tables.
Nevertheless, some thinkers, believing themselves to have devised a new and
different logic, have claimed that these 3 principles are in fact not true, and that
obedience to them has been needlessly confining.
The principle of identity has been attacked on the ground that things change, and are
always changing. Thus for example, statements that were true of the United States
when it consisted of the 13 original states are no longer true of the United States today
with 50 states. But this does not undermine the principle of identity. The sentence
“There are only thirteen states in the United States” is incomplete, an elliptical
formulation of the statement that “There were only 13 states in the United States in
1790” and that statement is as true today as it was in 1790. When we confine our
attention to complete, non-elliptical formulation of propositions, we see that their
truth (or falsity) does not change over time. The principle of identity is true, and does
not interfere with our recognition of continuing change.
The principle of non-contradiction has been attacked by Hegelian and Marxists on the
ground that genuine contradiction is everywhere pervasive, that the world is replete
with the inevitable conflict of contradictory forces. That there are conflicting forces in
the real world is true, of course - but to call these conflicting forces contradictory is a
loose and misleading use of that term. Labour unions and the private owners of
industrial plants may indeed find themselves in conflict – but neither the owner nor
the union is the negation or the denial or the contradictory of the other. The principle
of contradiction, understood in the straightforward sense in which it is intended by
logicians, is unobjectionable and perfectly true.
The principle of excluded middle has been the object of much criticism, on the
grounds that it leads to a two-valued orientation which implies that things in the world
must be either white or black, and which therefore hinders the realization of
compromise and less than absolute gradations. This objection also arises from
misunderstanding. Of course the statement “This is black” cannot be jointly true with
the statement “This is white” – where “this” refers to exactly the same thing. But
although these two statements cannot both be true, they can both be false. “This” may
be neither black nor white; the two statements are contraries, not contradictories. The
contradictory of the statement “This is white” is the statement “It is not the case that
this is white” and (if “white” is used in precisely the same sense in both of these
statements) one of them must be true and the other false. The principle of excluded
middle is inescapable.
Deductive arguments: Validity and truth
A successful deductive argument is valid. This means that the conclusion follows with
logical necessity from the premises.
Remember that truth and falsity are attributes of individual propositions or statements;
validity and invalidity are attributes of arguments.
Just as the concept of validity does not apply to single propositions, the concept of
truth does not apply to arguments.
There are many possible combinations of true and false premises a conclusions in
both valid and invalid arguments. Consider the following illustrative deductive
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11. arguments, each of which is prefaced by the statement of the combination it
represents.
I Some valid arguments contain only true propositions – true premises and a true
conclusion:
All mammals have lungs.
All whales are mammals.
Therefore all whales have lungs.
II Some valid arguments contain only false propositions:
All four-legged creatures have wings.
All spiders have four legs.
Therefore all spiders have wings.
This argument is valid because, if its premises were true, its conclusion would have to
be true also – even though we know that in fact both the premises and the conclusion
of this argument are false.
III Some invalid arguments contain only true propositions – all their premises are
true, and their conclusion are true as well:
If I owned all the gold in Fort Knox, then I would be wealthy.
I do not own all the gold in Fort Knox.
Therefore I am not wealthy.
IV Some invalid arguments contain only true premises and have a false conclusion.
This can be illustrated with an argument exactly like the previous one (III) in form,
changed only enough to make the conclusion false:
If Bill Gates owned all the gold in Fort Knox, then Bill Gates would be wealthy.
Bill Gates does not own all the gold in Fort Knox.
Therefore Bill Gates is not wealthy.
The premises of this argument are true, but its conclusion is false.
Such an argument cannot be valid because it is impossible for the premises of a valid
argument to be true and its conclusion to be false.
V Some valid arguments have false premises and a true conclusion:
All fishes are mammals.
All whales are fishes.
Therefore all whales are mammals.
The conclusion of this argument is true, as we know; moreover it may be validly
inferred from the two premises, both of which are wildly false.
VI Some invalid arguments also have false premises and a true conclusion:
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12. All mammals have wings.
All whales have wings.
Therefore all whales are mammals.
From examples V and VI taken together, it is clear that we cannot tell from the fact
that an argument has false premises and a true conclusion whether it is valid or
invalid.
VII Some invalid arguments, of course, contain all false propositions – false premises
and a false conclusion:
All mammals have wings.
All whales have wings.
Therefore all mammals are whales.
Deductive arguments: Soundness
When an argument is valid, and all of its premises are true, we call it sound.
All whales are mammals.
All mammals are animals.
Hence, all whales are animals.
If the president does live in the White House, then he lives in Washington, D.C.
The president does live in the White House.
So, the president lives in Washington, D.C.
The conclusion of a sound argument obviously must be true – and only a sound
argument can establish the truth of its conclusion. If a deductive argument is not
sound – that is, if the argument is not valid, or if not all of its premises are true – it
fails to establish the truth of its conclusion even if in fact the conclusion is true.
To test the truth or falsehood of premises is the task of science in general, since
premises may deal with any subject matter at all. The logician is not interested in the
truth or falsehood of propositions so much as in the logical relations between them.
By “logical” relations between propositions we mean those relations that determine
the correctness or incorrectness of the arguments in which they occur. The task of
determining the correctness or incorrectness of arguments falls squarely within the
province of logic. The logician is interested in the correctness even of arguments
whose premises may be false.
Why not confine ourselves to arguments with true premises, ignoring all others?
Because the correctness of arguments whose premises are not known to be true may
be of great importance. In science, for example, we verify theories by deducing
testable consequences – but we cannot beforehand which theories are true. In
everyday life as well, we must often choose between alternative courses of action,
deducing the consequences of each. To avoid deceiving ourselves we must reason
correctly about the consequences of the alternatives, taking each as a premise. If we
were interested only in arguments with true premises, we would not know which set
of consequences to trace out until we knew which of the alternative premises was
true. But if we knew which of the alternative premises was true, we would not need to
reason about it at all, since our purpose in reasoning was to help us decide which
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13. alternative premise to make true. To confine our attention to arguments with premises
known to be true would therefore be self-defeating.
Deductive arguments: Proving invalidity
1 See whether the premises are actually true and the conclusion is actually false. If
they are, then the argument is invalid. If they are not, or if you can’t determine
whether the premises and the conclusion are actually true or false, then go on to step
2.
2 See if you can conceive a possible scenario in which the premises would be true and
the conclusion false. If you can, then the argument is invalid. If you can’t, and it is not
obvious to you that the argument is valid, then go on to step 3.
3 Try to construct a counterexample to the argument – that is, a second argument that
has exactly the same form as the first argument, but whose premises are obviously
true and whose conclusion is obviously false. If you can construct such a
counterexample, then the argument is invalid. If you can’t, then it is usually safe to
assume that the argument is valid.
Counterexample method of proving invalidity
First, determine the logical pattern, then the form of the argument that you are testing
for invalidity, using letters (A,B,C,D) to represent the various terms of the argument.
Then, construct a second argument that has exactly the same form as the argument
you are testing but that has premises that are obviously true and a conclusion that is
obviously false.
Example: Some Republicans are conservative, and some Republicans are in favour of
capital punishment. Therefore, some conservatives are in favour of capital
punishment.
Logical pattern
1 Some Republicans are conservatives.
2 Some Republicans are in favour of capital punishment.
3 Therefore, some conservatives are in favour of capital punishment.
(Note that in logic some means at least one it does not mean some but not all.)
Form
1 Some A’s are B.
2 Some A’s are C.
3 Therefore, some B’s are C’s.
Construct a second argument that has exactly the same form and that has obviously
true premises and an obviously false conclusion.
1 Some A’s are B. 1 Some fruits are apples (true)
2 Some A’s are C. 2 Some fruits are pears (true)
3 Therefore, some B’s are C’s. 3 Some apples are pear (false)
Topics
Argument and evidence: How do I decide what to believe?
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