Course info

GODFREY OKOYE UNIVERSITY, ENUGU

FACULTY OF ART

DEPARTMENT OF PHILOSOPHY

PHI 121: INTRODUCTION TO LOGIC

Understanding Logic

There is no universal agreement as to the exact definition and boundaries of logic, hence the issue still remains one of the main subjects of research and debates in the field of philosophy. Logic is primarily an epistemological tool. Etymologically, logic is the anglicized form of the Greek word, logikḗ {(λογική) meaning: "possessed of reason, intellectual, dialectical, argumentative"} which has its root derived from logos {(λόγος) meaning: "word, discourse, rule, thought, idea, argument, account, reason, or principle"}. The New Testament Gospel recognizes logos as synonymous to God as used in the Gospel of John. This etymological derivations put together appropriately defines logic as the principles of correct reasoning. It is the method whoever wants to reason or argue correctly ought to follow but it’s not within the scope of logic to lure people into following these principles. Hence Frege states that it is the task of logic to discover the laws of truth. Uduma adds, ‘these laws of thought must be laws of correct reasoning’ such that appraisal of reasoning becomes the subject matter of logic.

According to Hegel, logic is the form taken by the science of thinking in general.The subject matter of logic is argument such that logic is indispensable to human existence. Quoting Spencer, Uduma maintained that while birds can fly, only human beings can argue. Hence argument for him, is the affirmation of our being. Like Spencer, he affirmed that human life is directed by argumentation. It is the disposition to fundamental ordered action. Thus it is the necessary condition for order and intelligibility in reality. Therefore, we boldly emphasize here that, human thought process, actions and inactions are bye products of human reasoned private arguments and judgements. Logic is indeed needful in life and existence.

Therefore, it is obvious that human life becomes wild and strange when one losses this essential and distinguishing element of being human. Even the Christians recognize that in creation, God made man different from animals just by the gift of reason. While he gave mere instinct to the lower animals, he gave reason to man. Little wonder when one acts without reason, he can be said to be inhuman. Thus in such situation, one may be said to have lost the quintessence of humanness. Uduigwomen sees logic as the science which “helps us to weigh the merits and demerits of an action or decision before we venture into it, and hence enables us to take a balanced action or decision. Instead of engaging in endless controversies of trivial matters, it enables us to sift the evidence before us”.

Logic is typically an element of culture. Whatever is judged, reasoned, thought or argued is according to the categories of the judging, thinking or reasoning mind as given by the environment. This mind is a product of a particular culture. Hence people’s background and temperaments influence their logic and thought process. Just as the Westerners have their ability to conduct their daily affairs following the givens of their environment, the Africans too have the same ability as regulated by their immediate experience and world views. This implies that the westerners, as well as the Africans are logical but their logic(s) is/are products of their varied experiences.

The discipline of logic has recently been invigorated by its merger with the discipline of mathematics. In 1854, George Boole wrote the book, "The Laws of Thought", in which he applied the methods of algebra to the study of logic. This marked the beginning of a revolution in the discipline. Now, the modern discipline of logic is incomplete without a background in mathematics.

In the Western World, logic was first developed by Aristotle, who called the subject 'analytics'. Aristotelian logic became widely accepted in science and mathematics and remained in wide use in the West until the early 19th century.  

Aristotle's system of logic was responsible for the introduction of hypothethetical syllogism, temporal modal logic and inductive logic, e.t.c.. In Europe during the later medieval period, major efforts were made to show that Aristotle's ideas were compatible with Christian faith. During the High Middle Ages, logic became a main focus of philosophers, who would engage in critical logical analyses of philosophical arguments, often using variations of the methodology of scholasticism. In 1323, William of Ockham’s 's influential Summa Logicae was released. By the 18th century, the structured approach to arguments had degenerated and fallen out of favour, as depicted in Holberg’s satirical play Erasmus Montanus. The Chinese logical philosopher Gongsun Long (c. 325–250 BCE) proposed the paradox "One and one cannot become two, since neither becomes two." In China, the tradition of scholarly investigation into logic, however, was repressed by the Quin Dynasty following the legalist philosophy of Han Feizi. In India, the Anyiksiki school of logic was founded by Medhatithi (c. 6th century BCE). Innovations in the scholastic school, called Nyaya, continued from ancient times into the early 18th century with the Navya-Nyaya school.

 

 

 

TYPES OF LOGIC.

Formal And Informal : Informal logic is the study of natural language arguments or referred as ordinary lay man logic. On the other hand, formal logic is concerned with specialties and specialization in logic. It can also be referred as Aristotelian, mathematical, artificial or critical logic. This is typical of western logic. The ancient times till 19^th century witnessed a wide acceptance of Aristotelian logic. Logic earlier this modern period was championed by the Aristotelian method as contained in the Organon. Philosophers and commentators after Aristotle grouped Aristotle’s six logical treatises into a manual they called the Organon which is the Greek translation for “tool”.  The Organon comprises the following works of Aristotle: the Categories, On Interpretation, Prior Analytics, Posterior Analytics, the Topics, and On Sophistical Refutations.  These works give us a good understanding of Aristotelian logic especially as it concerns; structure/rules of arguments and syllogisms, logical structure of propositions, difference between induction and deduction, the nature of scientific knowledge, basic fallacies, debate techniques, to mention but a few.

The basis of Aristotelian formal logic is anchored on his three fundamental laws of reason, namely; the law of Identity, the law of Contradiction and the law of Excluded Middle. The first law states that a thing is always equal to or identical with itself. The second law states that a thing cannot be unequal or different from itself. Also, the third law continues the former two laws; it states that if a thing is equal to itself, it cannot be unequal or different from itself. For example; if ‘y’ equals ‘z’, it cannot equal ‘non y’.  Formal logic is chiefly concerned with the processes of thinking and reasoning as well as the symbolic expression of such process in verbal or written form.

It is with reference to formal logic that Hegel purported that logic has its own proper content, and that content is not merely “subjective” in nature rather objective. For him, logical forms “are not mere forms of self-conscious thinking but also of objective understanding.” Here, it is obvious that Hegel being a racist ended up discussing and universalizing western logic. He was so short sighted on the thought pattern of diverse people across the globe and with particular reference to Africa.

Deductive and Inductive Logic:

Deductive logic makes arguments by drawing conclusions directly based on the premises. This is an argument that draws conclusion from general to particular. These arguments tend to resemble geometrical proofs. This type of logic gives us no new information, but as long as logical fallacies are avoided, it can be counted on to be correct. This is because the conclusion is necessarily valid, as long there is no fallacy. If the premises are true, the conclusion must be true. Don't confuse the validity of an argument, with the 'truth' of an argument. A valid argument can have premises that are false! If an argument has true premises, and is free from error (fallacy), it is considered "sound".

Inductive logic involves a certain amount of probability, assumption and generalization, but can give new information as well. It draws conclusion from particular to general.  A common example of inductive logic is the assumption by most of the people on the planet that the sun will rise tomorrow morning because it has risen every morning that anyone can remember. That certainly doesn't mean that the sun has to rise in the morning, but it probably will.

Propositional logic

A propositional calculus or logic (also a sentential calculus) is a formal system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives.

Predicate logic:

Predicate logic is the generic term for symbolic formal systems such as first-order logic, second-order logic, many-sorted logic, and infinitary logic. It provides an account of quantifiers general enough to express a wide set of arguments occurring in natural language. Whilst Aristotelian syllogistic logic specifies a small number of forms that the relevant part of the involved judgements may take, predicate logic allows sentences to be analysed into subject and argument in several additional ways—allowing predicate logic to solve the problem of multiple generality that had perplexed medieval logicians. The development of predicate logic is usually attributed to Gottlob Frege, who is also credited as one of the founders of analytic philosophy, but the formulation of predicate logic most often used today is the first-order logic presented in Principles of Mathematical Logic by David Hilbert and Wilhelm Ackermann in 1928. The analytical generality of predicate logic allowed the formalization of mathematics, drove the investigation of set theory, and allowed the development of Alfred Tarski's approach to model theory. It provides the foundation of modern mathematical logic.

 

 

 

Modal logic:

In languages, modality deals with the phenomenon that sub-parts of a sentence may have their semantics modified by special verbs or modal particles. For example, "We go to the games" can be modified to give "We should go to the games", and "We can go to the games" and perhaps "We will go to the games". More abstractly, we might say that modality affects the circumstances in which we take an assertion to be satisfied. Confusing modality is known as the modal fallacy.

Aristotle's logic is in large parts concerned with the theory of non-modalized logic. Although, there are passages in his work, such as the famous sea-battle argument in De Interpretatione § 9, that are now seen as anticipations of modal logic and its connection with potentiality and time, the earliest formal system of modal logic was developed by Avicenna, who ultimately developed a theory of "temporally modalized" syllogistic.^[41]

While the study of necessity and possibility remained important to philosophers, little logical innovation happened until the landmark investigations of C. I. Lewis in 1918, who formulated a family of rival axiomatizations of the alethic modalities. His work unleashed a torrent of new work on the topic, expanding the kinds of modality treated to include deontic logic and epistemic logic. The seminal work of Arthur Prior applied the same formal language to treat temporal logic and paved the way for the marriage of the two subjects. Saul Kripke discovered (contemporaneously with rivals) his theory of frame semantics, which revolutionized the formal technology available to modal logicians and gave a new graph-theoretic way of looking at modality that has driven many applications in computational linguistics and computer science, such as dynamic logic.

Mathematical logic:

Mathematical logic comprises two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic. The earliest use of mathematics and geometry in relation to logic and philosophy goes back to the ancient Greeks such as Euclid, Plato, and Aristotle. Many other ancient and medieval philosophers applied mathematical ideas and methods to their philosophical claims.

Computational Logic:

In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to create a machine that mimics the problem-solving skills of a human being. In 1956, John McCarthy, Marvin Minsky, Claude Shannon and Nathan Rochester organized a conference on the subject of what they called "artificial intelligence" (a term coined by McCarthy for the occasion). Today, logic is extensively applied in the field of artificial intelligence, and this field provides a rich source of problems in formal and informal logic. Argumentation theory is one good example of how logic is being applied to artificial intelligence. Furthermore, computers can be used as tools for logicians. For example, in symbolic logic and mathematical logic, proofs by humans can be computer-assisted.

 

Relevant and Deviant logic

orthodoxlogicinnotallowingasvalidthoseargumentswhosepremisesarenotrelatedinsubjectmattertotheirconclusions.

FALLACY IN LOGIC

Fallacy means common errors in reasoning that will undermine the logic of argument. Fallacies can be either illegitimate arguments or irrelevant points, and are often identified because they lack evidence that supports their claim. They can be seen as following:

1. Equivocation is an argument which exploits the ambiguity of a term or phrase which has occurred at least twice in an argument, such that on the first occurrence it has one meaning and on the second another meaning.

2. Amphiboly is similar to the fallacy of equivocation. In this case the ambiguity is due to indeterminate syntactic structure. In the argument:

The police were told to stop drinking on campus after midnight.
So, now they are able to respond to emergencies much better than before

There are several interpretations that can be given to the premise because it is grammatically ambiguous. On one reading it can be taken to mean that it is the police who have been drinking and are now to stop it; this makes for a plausible argument. On another reading what is meant is that the police were told to stop others (e.g., students) from drinking after midnight. If that is the sense in which the premise is intended, then the argument can be said to be a fallacy because despite initial appearances, it affords no support for the conclusion.

3. Composition and Division occur when the properties of parts and composites are mistakenly thought to be transferable from one to the other. Consider the two sentences:

a.     Every member of the investigative team was an excellent researcher.

b.    It was an excellent investigative team.

Here it is ‘excellence’ that is the property in question. The fallacy of composition is the inference from (a) to (b) but it need not hold if members of the team cannot work cooperatively with each other. The reverse inference from (b) to (a)—the fallacy of division—may also fail if some essential members of the team have a supportive or administrative role rather than a research role.

4. The fallacy of begging the question (petitio principii) This is an argument whose premises and conclusion are the very same proposition, albeit expressed in different words. It is a disguised instance of repetition which gives no reason for its apparent conclusion.

5. The fallacy of ignoratio elenchi, or irrelevant conclusion, is indicative of misdirection in argumentation rather than a weak inference.

6. The ad verecundiam fallacy concerns appeals to authority or expertise. Fundamentally, the fallacy involves accepting as evidence for a proposition the pronouncement of someone who is taken to be an authority but is not really an authority. This can happen when non-experts parade as experts in fields in which they have no special competence—when, for example, celebrities endorse commercial products or social movements. Similarly, when there is controversy, and authorities are divided, it is an error to base one’s view on the authority of just some of them.

7. The fallacy ad populum is similar to the ad verecundiam, the difference being that the source appealed to is popular opinion, or common knowledge, rather than a specified authority. So, for example:

These days everyone (except you) has a car and knows how to drive;
So, you too should have a car and know how to drive.

8. The ad baculum fallacy is one of the most controversial because it is hard to see that it is a fallacy or even that it involves bad reasoning. Ad baculum means “appeal to the stick” and is generally taken to involve a threat of injury of harm to the person addressed. So, for example,

9. The fallacy ad misericordiam is a companion to the ad baculum fallacy: it occurs not when threats are out of place but when appeals for sympathy or pity are mistakenly thought to be evidence. To what extent our sympathy for others should influence our actions depends on many factors, including circumstances and our ethical views. However, sympathy alone is generally not evidence for believing any proposition.

10. The ad hominem fallacy involves bringing negative aspects of an arguer, or their situation, to bear on the view they are advancing. There are three commonly recognized versions of the fallacy. The abusive ad hominem fallacy involves saying that someone’s view should not be accepted because they have some unfavorable property.

Another, more subtle version of the fallacy is the circumstantial ad hominem in which, given the circumstances in which the arguer finds him or herself, it is alleged that their position is supported by self-interest rather than by good evidence. Hence, the scientific studies produced by industrialists to show that the levels of pollution at their factories are within the law may be undeservedly rejected because they are thought to be self-serving. Yet it is possible that the studies are sound: just because what someone says is in their self-interest, does not mean it should be rejected.

The third version of the ad hominem fallacy is the tu quoque. It involves not accepting a view or a recommendation because the espouser him- or herself does not follow it. Thus, if our neighbor advises us to exercise regularly and we reject her advice on the basis that she does not exercise regularly, we commit the tu quoque fallacy: the value of advice is not wholly dependent on the integrity of the advisor.

We may finish our survey of the core fallacies by considering just two more.

11. The fallacy of faulty analogy occurs when analogies are used as arguments or explanations and the similarities between the two things compared are too remote to support the conclusion.

If a child gets a new toy he or she will want to play with it;
So, if a nation gets new weapons, it will want to use them.

12. The fallacy of slippery slope generally takes the form that from a given starting point one can by a series of incremental inferences arrive at an undesirable conclusion, and because of this unwanted result, the initial starting point should be rejected. The kinds of inferences involved in the step-by-step argument can be causal, as in:

You have decided not to go to college;
If you don’t go to college, you won’t get a degree;
If you don’t get a degree, you won’t get a good job;
If you don’t get a good job, you won’t be able to enjoy life;
But you should be able to enjoy life;
So, you should go to college.

SYMBIOSIS OF LANGUAGE, THOUGHT AND LOGIC

Undeniably, language is the vehicle of thought. Language is a tool of reason. In the words of Akwanya, language creates reality and representation of thought is the most important function of language. Language gives us access to the experiences and insights of our fellow men. Hence to a great extent, to know and master a language implies knowledge of the rules of logic in that language. It follows then that the connection between language and thought is profound. According to Hegel, the subject matter of logic is “thinking or more specifically conceptual thinking.” This form of thought is stored in human language. Hence the primary task of logic is to articulate those intelligible “categories” presupposed by and at work in the use of language. The majority of our everyday life involves the use of language. We tell our ideas to others with language; we access their responses and understand their meanings with language. Even when we soliloquize, we process the information and make logical conclusions in particular language. Hence our rational thinking unavoidably is meaningless without certain degree of the use of language.

Experts like Wittgenstein bemoaned the ordeal of private language thereby proving that language is a community property and a shared meaning in an environment. We emphasize here that every language belongs to a culture and every culture belongs to a people. In the words of Uduma, we claim here that ‘the cultural experiences of a people cannot be meaningful unless they are organized or co-ordinated in language, an activity which itself presupposes a logical ability, logic and language are fundamental or central to organizing reality and thus a characteristic of all human societies’. We affirm here that there cannot be a society without language or proper mode of communication.

The dependence between language and thought serves for better relation between logic and language. For Uduma, “thought is prior to language; but thought can make no progress without embodying itself in language.” By this relationship Uduma, rightly posited that there is a two-sided or reciprocal dependence between language and thought.

It should be noted at this point that logic makes language possible, language expresses culture, and since culture presupposes the existence of logic, logic is central in any culture. It is in language, we realize the true meaning of logic. The Greek etymological derivation of logic from logos, which means word or reason, bears testimony to the inseparable relationship between logic and language. Hence we can say that thought is prior to language; but thought can make no progress without embodying itself in language.  

 

Commenting on this form of relationship, Ogugua states;

 

language gives us the scheme of our ways of thinking; and thought remains the common background on which persons meet in the bid to have common and mutual understanding. Although language gives thought a cloak, that means it canalizes it, we need not conclude that without language, thoughts are not meaningful. Thoughts are meaningful in private minds, but we need language which is a social product in conveying our thoughts; and as such too logic to ensure that the meaning of our thoughts is not lost; and avoid our language being a hindrance to our getting at the real meaning of what is said as language can be the source of confusion or misunderstanding by fixing our emotions or even enrobing our tradition therein.

 

Logic considers language as a primary instrument of thinking and reason. Hence logic labours on the process of right reasoning through the help of language as environmentally created. Hence it is in language that the thinking mind does the thinking, describes, organizes e.t.c. Man’s capacity of language not only sets him apart from other animals, it also confers on him logical ability because human language makes human thought and conduct possible. It is worthy of note here that the logic of a people is not only discernable but discoverable in their language; that is why it is related to their metaphysics and ontology. It becomes obvious claiming that logic would have no content and form without language, and that language will be a dream, quite impossible without logic.

For Mellone, language forms the logical structures of thought. Language provides even a growing mind with the outline of thinking pattern as socially or culturally inherited. Thus here language provides both the framework for thought and manifest means of communicating thought. In the words of Uduma, ‘in logic, we are interested in words only as the visible and audible forms in which thought fixes and controls its own meaning’.

We have tried to show in a glance here, a symbiotic relationship between logic, language and thought. It is irrevocably proven that logic makes language possible while language is an expression of logical thought(s). Also, we state here, without equivocation that language is the vehicle of culture. Culture finds perfect expression in the language of the cultural group. Therefore, we make bold to claim at this point that if Africa has her own culture expressed in language and thought pattern, it would be fallacious denying her an African Logic. 

 

 

FURTHER READING

·       Alfred North Whitehead, An Introduction to Mathematics, (New York: H. Holt and Company publishers, 1861

·       Copi, Irving. Introduction to Logic. 6th (ed). New York: Macmillan, 1982

·       Georg Wilhelm Friedrich Hegel; The Science of Logic, (Cambridge: University Press, 2010), p.30

·       S. H. Mellon, Elements of Modern Logic, (London: University Press, 1952), p. 18

·       Uduma O. Uduma, Introduction to Logic. Lagos: Obaroh & Ogbinaka Pub., Ltd, 1997.

·       Uduma Orji Uduma, “Explicating the Formal Nature of Logic”, in The Nigerian Journal of Philosophy, Vol., 23, No. 2, Lagos: University Press, 2009

·       Uduigwomen, A.F., How to Think: An Introductory Text on Logic, Argumentation and Evidence. Aba: A.A.U. Vitalis Books Co., 2003.