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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 1

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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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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).

TheoryTheory: 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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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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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 wisdomThe 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’ methodIf 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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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 ArgumentsThe 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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3 If B, then C.4 If C, then not-A.5 Therefore, both A and not-A6 But 5 is a contradiction, so the original assumption must be false and not-A must be true.

Philosophical example of a Reductio ad AbsurdumSocrates’ 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.

TopicWhat is the practical value of philosophy?

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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 logicIn 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 logicAs 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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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.

NonargumentsArguing 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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The 3 Laws of ThoughtSome 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 É 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 that2 a=b :: b=aand 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 Ú ~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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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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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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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: SoundnessWhen 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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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 invalidity1 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 invalidityFirst, 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 pattern1 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.) Form1 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)

TopicsArgument and evidence: How do I decide what to believe?

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