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Lesson 1: Introduction to PHILOSOPHY

"Philosophy" (philosophia, from philein, to love, and sophia, wisdom) means "the love of wisdom" Introduction to the Five Branches of Philosophy

Metaphysics Study of Existence What's out there?

Epistemology Study of Knowledge How do I know about it?

Ethics Study of Action What should I do?

Politics Study of Force What actions are permissible?

Esthetics Study of Art What can life be like?

1. Epistemology Epistemology is the study of knowledge. Epistemology deals with the process by which we can know that something is true. It addresses questions such as: --What can I know? --How is knowledge acquired? --Can we be certain of anything? 2. Metaphysics Metaphysics is the study of reality. More specifically it is the study of reality that is beyond the scientific or mathematical realms. The term metaphysics itself literally means beyond the physical. The metaphysical issues most discussed are the existence of God, the soul, and the afterlife. 3. Ethics Ethics is the study of moral value, right and wrong. Ethics is involved with placing value to personal actions, decisions, and relations. Important ethical issues today include abortion, sexual morality, the death penalty, euthanasia, pornography, and the environment. 4. Logic Logic is the study of right reasoning. It is the tool philosophers use to study other philosophical categories. Good logic includes the use of good thinking skills and the avoidance of logic fallacies. 5. Aesthetics Aesthetics is the study of art and beauty. It attempts to address such issues as: --What is art? --What is the relationship between beauty and art? --Are there objective standards by which art can be judged? --Is beauty in the eye of the beholder?

Difference Between Eastern and Western Philosophy

Eastern philosophy=> Hinduism, Buddhism, and Taoism Western Philosophy=> Greek School of Thoughts, Socrates, Plato, Aristotle

East (Oriental) West

Spherical thinking Linear thinking

Region = Philosophy Religion vs Philosophy Intuition and mysticism Theory and speculation

Logic, aesthetics, politics > ethics 5 divisions of Philosophy

Cycle or rebirth Different theories of Universe

To be one with ABSOLUTE Different concept of Absolute

Socratic Philosophy

Socrates (470-399) was the son of a sculptor and a midwife, and served with distinction in the Athenian army during Athens clash with Sparta. He married, but had a tendency to fall in love with handsome young men, in particular a young soldier named Alcibiades. He was, by all accounts, short and stout, not given to good grooming, and a lover of wine and conversation.

- His unorthodox religious views (that there was only one god behind the variety of Greek gods) gave the leading citizens of Athens the excuse they needed to sentence him to death for corrupting the morals of the youth of the city. In 399, he was ordered to drink hemlock, which he did in the company of his students.

MORAL THOUGHT SOUL > PSYCHE

Not a thing or ghostly substance capacity for intelligence and character persons conscious personality that within us in virtue o f which we are pronounced wise or

foolish, good or bad

MAKING THE SOUL AS GOOD AS POSSIBLE VIRTUE Arete = grk, Ares- god of war (Mars roman name) = machismo/manliness COURAGE = prime component of virtue

VIRTUE = KNOWLEDGE > GOODNESS

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VICE = IGNORANCE Ignorance> product of wrongdoing. It is done w/hope that it will do what is cannot do Ex. Thieves know stealing is wrong but they steal in hope that it will bring happiness

It is ignorance about ones soul, about what it takes to make t soul as good as possible

Plato (424-347)

Theory of SOUL

Three parts of the soul 1.. Rational (logos) > Reason > head 2. Irascible (thumos) > courage >the heart 3. Appetitive (epithumia) > desire > the abdomen

These are not faculties or powers of one substance, but parts (mer) the distinction of which is proved by the fact that appetite strives against reason, and anger against reason and appetite

Theory of knowledge

Knowledge begins with sense-perception. The senses, however, cannot attain a knowledge of truth. They contemplate the imperfect copies of the Ideas; as long as we look upon the objects of sense we are merely gazing at the shadows of things which, according to the celebrated Allegory of the Cave, are moving where we cannot see them, namely, in the world of Ideas from which the soul has fallen. (Yet though the sense perceived world cannot lead us to a knowledge of Ideas, it can and does remind us of the Ideas which we saw in a previous existence. Theory of Freedom of the will

o The will is free. o Not only is freedom of choice a quality of adult human activity, but it is

free choice also that decides our parentage, hereditary tendencies, physical constitution, and early education, for all these are the result of actions freely performed during the previous existence of the soul.

o Socratic principle that no one is voluntarily bad. Theory of Ethics.

o Study of the Idea in human action and human society. o All Platonic, as well as Socratic, speculation starts with an inquiry about the

good and the beautiful, and proceeds, in the case of Plato, through the doctrine of concepts to the theory of Ideas.

1. The highest good = happiness

o The Idea of good > God. o The aim of man's actions should be to free himself from the bonds of

the flesh, from the trammels of the body in which the soul is confined, and by means of virtue and wisdom to become like to God, even in this life.

2. Virtue > essential > the order, harmony, and health of the soul, o all virtue with wisdom highest place among virtues, reducing o all virtues to four supreme kinds, -- wisdom, fortitude, temperance, and

justice. 3. State that > the most important applications of Plato's doctrine of virtue.

o Man should aim at being virtuous, and could, even in his savage condition, attain virtue. Without education, however, virtue would be a matter of mere chance, and without the State education would be impossible. While, therefore, the State is not the aim and end of human action, it is the indispensable condition of knowledge and Virtue.

ARISTOTLE (384-327 BC)

Platos great pupil born at Stagira, in Thrace, in 384 B.C. His father was a physician to the king of Macedon, so science was in

his background. At the age of seventeen, he went to Athens and joined Plato's school,

where he stayed until Plato's death in 347 he became the tutor to the young prince of Macedon, Alexander the

Great the world could be understood at a fundamental level through the

detailed observation and cataloging of phenomenon knowledge (which is what the word science means) is fundamentally

empirical the first person to really think out the problem of evidence

The Theory of Soul

the perfect expression or realization of a natural body 3 Kinds 1. Nutritive Soul > Plants > grow and reproduce 2. Sensitive > Animals > sensitive cognition, appetition, local

movement 3. Rational > Man > Reason

Soul cannot be a body = but cant be without body

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Reason

source of the first principles of knowledge

realizes something of the essential characteristic of absolute thought > GOD

The human ability to properly control these desires is called moral virtue, and is the focus of morality

Aristotle notes that there is a purely rational part of the soul, the calculative, which is responsible for the human ability to contemplate, reason logically, and formulate scientific principles.

The mastery of these abilities is called intellectual virtue. Theory of Freedom of the will

An instrument of free choice

Its the power of everyone to be good or bad, worthy or worthless

Do good, avoid evil

The development of potentiality to actuality is one of the most important aspects of Aristotle's philosophy.

It was intended to solve the difficulties which earlier thinkers had raised with reference to the beginnings of existence and the relations of the one and many.

The actual vs. potential state of things is explained in terms of the causes which act on things.

There are four causes:

1. Material cause, or the elements out of which an object is created; 2. Efficient cause, or the means by which it is created; 3. Formal cause, or the expression of what it is; 4. Final cause, or the end for which it is.

Example, bronze statue material cause > bronze efficient cause > sculptor > he forces the bronze into shape. formal cause > the idea of the completed statue final cause > the idea of the statue as it prompts the sculptor to act on the bronze.

The final cause tends to be the same as the formal cause, and both of these can be subsumed by the efficient cause.

Of the four, it is the formal and final which is the most important, and which most truly gives the explanation of an object.

The final end (purpose, or teleology) of a thing is realized in the full perfection of the object itself, not in our conception of it.

Final cause is thus internal to the nature of the object itself, and not something we subjectively impose on it.

God to Aristotle is the first of all substances, the necessary first source of movement who is himself unmoved. God is a being with everlasting life, and perfect blessedness, engaged in never-ending contemplation. Theory of Ethics.

viewed by Aristotle, is an attempt to find out our chief end or highest good: an end which he maintains is really final.

Though many ends of life are only means to further ends, our aspirations and desires must have some final object or pursuit. > HAPPINESS

For starters, happiness must be based on human nature, and must begin from the facts of personal experience.

Thus, happiness

cannot be found in any abstract or ideal notion, like Plato's self-existing good.

It must be something practical in human. It must then be found in the work and life which is unique to humans.

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Lesson 2: Definition of Logic and its scope

LOGIC

from the Greek (logikos) the study of the methods and principles used in distinguishing

correct from incorrect reasoning (Copi and Cohen 1994: 2). the science that investigates the principles governing correct or

reliable inference Division of Logic

Induction => drawing general conclusions from specific examples conclusion is probable from a set of specific facts to a general conclusion Ex: All of your friends are good therefore you can be good, too.

Deduction => drawing logical conclusions from definitions and axioms.

=> conclusion is absolutely necessary => we start our reasoning from the general to the particular or less general => one absolutely necessary conclusion that follows from the premises for the argument to be valid

Ex: All men are mortal, Socrates is a man (Therefore,) Socrates is mortal A similar dichotomy, used by Aristotle, is analysis and synthesis. Here the first takes an object of study and examines its component parts, the second considers how parts can be combined to form a whole.

Nature of logic Informal logic = the study of natural language arguments.

= The study of fallacies is an especially important branch of informal logic.

Formal logic = the study of inference with purely formal content. Symbolic logic = the study of symbolic abstractions that capture the formal

features of logical inference.

=2 Divisions > propositional logic and predicate logic.

Mathematical logic =an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.

HISTORY OF LOGIC

ARISTOTLE => FATHER OF LOGIC

Organon (6 treaties) Zeno the Stoic => coined the name LOGIC Thomas Aquinas => Doctor Angelicus

Aristotelian Logic 5 Ways of Gods Existence

The First Way: Argument from Motion

1. Our senses prove that some things are in motion. 2. Things move when potential motion becomes actual motion. 3. Nothing can be at once in both actuality and potentiality in the same

respect (i.e., if both actual and potential, it is actual in one respect and potential in another).

4. Therefore nothing can move itself. 5. Therefore it is necessary to arrive at a first mover, put in motion by no

other; and this everyone understands to be God. The Second Way: Argument from Efficient Causes

1. Nothing exists prior to itself. 2. Therefore it is necessary to admit a first efficient cause, to which everyone

gives the name of God. The Third Way: Argument from Possibility and Necessity (Reductio argument)

1. We find in nature things that are possible to be and not to be, that come into being and go out of being i.e., contingent beings.

2. Assume that every being is a dependent being. 3. For each contingent being, there is a time it does not exist. 4. Therefore there could have been a time when no things existed. 5. Therefore some being exists of its own necessity, and does not receive its

existence from another being, but rather causes them. This all men speak of as God.

The Fourth Way: Argument from Gradation of Being

1. There is a gradation to be found in things: some are better or worse than others.

2. Predications of degree require reference to the uttermost case (e.g., a thing is said to be hotter according as it more nearly resembles that which is hottest).

3. The maximum in any genus is the cause of all in that genus. 4. Therefore there must also be something which is to all beings the cause of

their being, goodness, and every other perfection; and this we call God.

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The Fifth Way: Argument from Design 1. We see that natural bodies work toward some goal, and do not do so by

chance. 2. Most natural things lack knowledge. 3. But as an arrow reaches its target because it is directed by an archer, what

lacks intelligence achieves goals by being directed by something intelligence.

4. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God.

Francis Bacon/ John Stuart Mill=> Novum Organum => Scientific Method Early Modern Period (1600-1850 A.D.): Leibnitz (1646-1716) is considered a great logician and his work exhibits a respect for traditional Aristotelean logic but also an interest in general theories of arrangements, plans for an ideal language, and general science of method. The German philosopher Kant (1724-1804) made the distinction between types of statements a key to understanding his philosophy; he distinguished between analytic statements whose truth can be determined on the basis of the meanings of the words in the statements, and synthetic statements, which require a direct appeal to experience. Bolzano (1781-1848) continued to examine the analytic-synthetic distinction in his chief work Wissenschaftslehre. Modern and Contemporary Period (1850-present) The 19th and 20th centuries have involved great activity and discovery in logic, including the rediscovery of the Stoic type of logic or logic of propositions. De Morgan (1806-1871) discovered the theorems that bear his name and that are now routinely part of the logic of propositions. George Boole (1815-1864), considered the founder of symbolic logic, used symbols to depict arguments; he wrote the Analysis of the Laws of Thought and Mathematical Analysis of Logic, in which he argues that math is the basis of logic; and his use of numbers to express the truth values of compound statements (conjunctions, disjunctions, etc.) directly influenced the development of computers. PIERRE DE LA RAMEE (1515-1572)

Made a criticism to Aristotelian Logic => ACTS OF THE MIND

LESSON 3 : DIVISIONS OF LOGIC ACCORDING TO 3 ACTS OF THE MIND

Mental Act Mental Product External Sign Logical Issues

Apprehension Concept/Idea Terms Predicability

Judgment Enunciation Proposition Predication

Reasoning Arguments Syllogism Inference

Simple Apprehension: o the act by which the intellect knows an essence (what a thing is), and

produces a concept; o is the grasp of a concept. o A concept is also called an idea, a species, an intelligible form, and a

mental word. A concept has an extension, which is the group of things included under the concept

o the mind understands the essence or general meaning of a thing w/out affirming or denying anything about it Ex: Man, horse, bag, book If the Statement is this book is for children > Judgment

Judgment: o the act by which the intellect affirms or denies the truth of something,

putting together or dividing apart concepts; o is expressed in a complete sentence or proposition. o Attributive and either true or false. o Ex. "A is B", where A is a subject and B is a predicate, or existential, as

when we say "A exists". o Affirmation or affirmative judgment is called composition, because we

are putting two concepts together. Negation is called division, because we are taking two concepts apart.

Reasoning: o the act whereby the intellect compares two concepts with one third

concept, and perceives whether the two concepts go together. o involves three terms or concepts, and two judgments.. The major term

is the most broad, the minor term is the most narrow, and the middle term is between the two, included in the meaning of the major term, and including in itself the meaning of the minor term.

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CONCEPT/IDEA

Theres nothing in the intellect that doesnt pass first through the sense IDEA = begins w/sense data > sense organs = its the building block of knowledge

- its the intellectual representation or IMAGE of a thing - its the same thing as CONCEPT (BUT CONCEPT S ARE VIEWD AS

PURIFIED IDEAS) STEP FOR THE FORMATION OF IDEA

1. All knowledge starts with senses a. Thus, man is able to produce the sensible image of a thing =>

PHANTASM ( sensible representation of the material features of a thing)

2. IN the presence of image mans mind begins to think a. =>SENSE IMAGE a representation of a thing

=> this is by ABSTRACTION ABSTRACTION => drawing of something from some source

=> act of the mind that draws out from the individual things and their phantasm the essential nature and other universal reasons that they embody

3. The intellect now strips the individuals of their non essentials qualities,

retains the essential attributes only and forms them into one INTELLECTUAL IMAGE

4. The intellect now makes its own image or representation Idea Phantasm

1. exist in the intellect Exists in the imagination

2. universal Individual

3. constant Changeable

4. possible of immaterial and complex things

Not possible of immaterial and complex things

PROPERTIES OF IDEA

COMPREHENSION the sum-total of the intelligible elements of the quiddity (essence of an object ) signified by the term or concept

EXTENSION - the sum-total of the individuals and classes or groups to which an idea can be applied

NOTE: comprehension of an idea always remain the same. Extension of an idea may change continually

Classifications of Ideas

According to Comprehension

a. Simple expresses only one conceptual features or formal reason Ex. Objective, existence

Compound expresses several constituent conceptual elements or integral features Ex. Man, animal, human being

b. One expresses 1 thing, nature, or formal features Multiple expresses in an explicit manner a thing, nature, or formal features as a modified by another thing, nature or formal features in an cessionary manner Ex. Poor philosopher, tall girl

c. Concrete expresses a subject that is qualified by a nature or formal feature

Ex. Student, beautiful dress Abstract- expresses only a nature, or a formal feature w/out a subject Ex. Religiosity, tallness, whiteness

d. Absolute expresses a thing, nature, or formal feature, w/out any relation to some other thing

Ex. Minerals, living beings, modesty

Relative expresses a thing, nature, or formal feature bearing a relation to something else Ex. Husband, motherboard

e. Complete expresses all the conceptual reasons or formal features that correspond to the comprehension or to the nature of an object

Ex. Man is a rational animal Incomplete express only some of the conceptual reasons or formal features that correspond to the comprehension or to the nature of an object Ex. Man is a rational being

CONCEPT

product of simple apprehension Concrete the subject of the logic Abstract - the way the concept is presented

Ex. Man concrete Honesty - abstract

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THE TERM

TERM = Terminus = Latin

= the last element to which a proposition may be resolved = in relation to inference or argument, TERM is a word or arrangement of words that can serve as the subject or predicate of a proposition which is a statement of denial or affirmation about something.

EX. A cat is an animal Cat and animals are TERM Cat serves as the subject and animal serves as the predicate

1. This means the TERM is the most basic element o fan INFERENCE because w/out it no Inference can be made

CLASSIFICATION OF TERMS A. According to Components or Comprehension

1. Simple - it expresses only one conceptual note. Examples: Truth - conformity between the intellect and the thing being - an existential thing

2. Compound- it expresses more than one conceptual note. Examples: Man may be expressed as - rational animal

human being 3. Concrete - it expresses something which has attributes that are capable of

being perceived through the senses. Examples: ball, can, desk, shirty stone table

4. Abstract- it expresses something as separated from any single object. It denotes the general attributes of many objects. Examples: fear, happiness, heights, knowledge, perfection

B. According to Extension

1. Singular -it represents a single object only. Examples: United States of America, Bishop TeodoroBacani, this book

2. Universal - it represents not only a class as a whole but also each member of the class. . Examples: table, chair, stone, plant, glass, pen, girl

3. Particular -it represents only a part of the universal whether it is definite or indefinite. Examples: many books, few guests, three kings, several trees

4. Collective - represents a number of things constituting a unit-group or whole. Examples: family, choir, band, fleet, team

C. According to Origin

1. Immediate - (intuitive) it is formed from the direct perception of things. Examples: chair, cars, chirping of birds, falling rain, hot water, etc.

2. Mediate - (abstractive) it is formed through the mediation of other ideas. Examples: God, human soul, philosophy

D. According to Meaning

1. Univocal - a term that carries the same meaning in its several uses. Examples: Animal when predicated of "dog" and "cat" has exactly the same meaning.

2. Equivocal - a term that carries a different meaning in its different .uses.

The term may be equivocal: a. only in pronunciation

sweet and suite, sun and son, dear and deer b. in pronunciation and spelling

weak and week, queue and cue, trunk of a tree, of a car

3. Analogous a term that carries a meaning in some ways different, and in some ways the same. . Examples: "Good" does not have the same meaning in good cement, good Job, good medicine, good food.

E. According lo Qualify 1. Positive inform, positive in meaning

Examples: Life, justice, truth 2. Positive inform, negative in meaning

Examples: death, evil, error, misery, cruelty 3. Negative inform, negative in meaning

Examples: illegal, impolite, incompetent, dishonest 4. Negative in form, positive in meaning

Examples: immortal, infinite, blameless

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Definitions and its Laws

- means the statement w/c explains what a thing is. - Latin definire to enclose w/in limits

o To put fences around, to mark boundaries or limits o The act of stating the meaning of a term o The logical or verbal manifestation of the conceptual features

of an idea Kinds of Definition

1. Nominal definition nominis or definition of a name - purpose is to give meaning of a term Types of Nominal

a. Etymology or word derivation, e.g., definition from the word, "definire"', martyr from the word "witness,"

b. By description, e.g., defining sugar from its qualities that include sweetness, granulatedness, etc.

c. By synonym, e.g., an thropos means "man" and to confect means "to put together."

d. By example of the thing being defined, e.g., sorghum varieties, rice varieties, etc.

2. Real Definition - from the word definition rei, "definition of a thing," real definition does not only indicate what thing is signified by a term but also declares the very nature of that object or thing. Sub-types of real definitions

1. Essential (quidditative) definition. - explains the essence or nature of a thing, e.g., the statement that man is a rational animal.

2. Descriptive - explains what a thing is in itself by enumerating the positive, but non-essential, elements of its nature, e.g., when saying "man is an erect vertebrate."

3. Distinctive - explains a thing by its unique properties, e.g., the statement that "a chemist defines oxygen as a colorless, odorless, tasteless gas, 1.105 times as heavy' as air."

4. Genetic - explains a thing by its process of origin or production, e.g., the statement that "the genetics of certain drug is specifically prescribed by the Generic Law."

5. Causal - gives the explanation of a thing by means of its efficient or final cause. Efficient causes are those which produce a things final causes are the end, the purpose, on account of which a thing is produced or comes into being. For example, painting is a picture in colors produced by an artist. (Efficient cause). Or, that "watch" is a mechanical device which indicates the hours of the day. (Final cause).

6. Accidental - gives an explanation of a thing based on characteristics which are neither essential nor necessarily connected with the essence of a thing. For example. Prof. David Libatique, alias macho man; age, 38 years; height, 5 ft. 4 inches; weight, 61 kilos;

History of Syllogisms

Aristotle (384-322 BC) can be seen as the founder of todays form of logical reasoning e.g. syllogisms. He was the first in his time to divert with the correctness and validity of logical reasoning. A lot of his work from those days unfortunately has gone lost. The few remains however of his work were bundled in books called The Organon. These books, consisting out of 6 parts, contain a lot of his works and documents concerning logical reasoning and as a part of that syllogisms. Aristotles was interested among others in syllogisms, a form of logical reasoning.

A syllogism always consists out of 3 parts;

1. The subject = the word already indicates, the central theme in the syllogism. This is the keyword of the syllogism.

2. Predicate = connects to the subject. 3. Middle term = which consists out of all the remaining information

in a syllogism.

Solving Syllogisms

Venn diagrams = show all possible and hypothetically logical relations between a collection of finite and infinite statements

English Mathematician and logician = John Venn Using 2 or 3 overlapping circles= shows relationship between subject and

predicate. Syllogism Example: a. All Canadians are right handed b. All right handed are opticians c. Conclusion: Some opticians are Canadian Subject =Optician Predicate =Canadian Middle term =Right handed Since the two premises (a and b) from the example are valid, the conclusion must be valid two, since it is not possible for the premises to be true and the conclusion to be false.

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Syllogism Example 2: a. All mortals die b. All men are mortals c. Conclusion: All men die To check the validity of this statement first the different terms are appointed. Subject =Men Predicate =Die Middle term =Mortal Again it can be concluded that the two premises (a and b) are valid and so is the conclusion. This is in general always the case with syllogisms, which is a form of logical reasoning of the deductive reasoning type. For more information about different types of syllogisms, you can take a look at our related pages shown below. Example 1: a. All Canadians are right handed b. All right handed are opticians c. Conclusion: Some opticians are Canadian To check the validity of this statement first the different terms are appointed. Subject: Canadian Predicate: Optician Middle term: Right handed We will start with the first out of the two given statements from above. The first thing to do is draw two circles and write the terms Canadian and Right handed in

them. The circle with the word Canadian without the overlap

represents only Canadian people, while the part within the overlap with the right

handed circle represents all Right handed Canadian people. Everything outside

these two circles represents everything not connected to these two terms. With this one can think of plants, animals, cars but even you and me. 1st Statement Next, the 1st statement claims: all Canadians are right handed. Thus this means

that all Canadian

people outside the overlap of the two circles are not involved in this statement,

since they are not connected to the term right handed. As a conclusion of that this part of the circle is being shaded. 2nd Statement Subsequently the 2nd statement is reviewed. According to this statement all right handed are opticians. This statement can be solved by drawing two circles and again shading everything except the overlap in the right handed circle, just as was done with the first statement. Linking Statements Linking the two statements and the circles together results in the Venn Diagram of figure 2. Here both the first (red) as well as the second (green) statement are displayed. The overlap between Right handed and Optician is clearly shown, even as the absence of one between Canadian and Opticians. Further it can be noticed that there is a small area where all three term are overlapping, a part which is still present. Now that the Venn diagram is completed, the validity of the conclusion can be checked. The conclusion states: some Opticians are Canadian. The Venn diagram clearly shows the correctness of this conclusion. Although the overlap area between both orange and green circle is shaded, there is still a small area in the middle where all three terms are present which it not shaded. It is this area that results in the correctness of the conclusion. This case is characterized as a valid reasoning, since the conclusion can be drawn directly using the Venn diagram. It is however also possible that additional information is needed in order to check the validity of the conclusion. In that case the reasoning is invalid.

Example 2. a. All hamburgers are meals b. Some cows are hamburgers Possible answers:

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1. All meals are cows 2. At least some meals are cows 3. No cows are meals 4. Some cows are no meal It is possible to assign a subject, predicate and middle term for all the statements. However, this would take lot of unnecessary time. Choosing between four statements when solving syllogisms can be handled best by making a Venn diagram straight away. In that way the possible answers from the statements can be checked on their validity piece by piece, resulting in the correct statement. 1st Statement First statement 2a will be examined. The method behind drawing this part of the Venn diagram is exactly the same as the one explained in example 1, resulting in figure 3. In this way the first part of the Venn diagram displays that all hamburgers are meals, since the part with only hamburgers is shaded to result in the overlap area between the two terms; hamburgers and meals. 2nd Statement Next statement 2b is examined. This statement needs a different approach since the statement claims the following: some cows are hamburgers. This means that it is not possible to just shade a whole area as was done before. In order to do that the statement should contain words like all or none. In this case the statement contains the word some and in that case a cross is used to represent that part of the statement in the Venn Diagram. Therefore a cross is put in the overlap between cows and hamburgers, representing the statement that some cows are hamburgers.

Linking Statements Linking the two statements and the circles together results in the Venn Diagram of figure 5. With the help of this Venn diagram the 4 statements can be checked for their validity. Checking Statements: 1. All meals are cows.

However it can be seen that the term meals has an overlap with both hamburgers as well as cows, meaning that both are possible en thus resulting in an invalid statement.

2. Some meals are cows. This is correct, since the Venn diagram clearly shows a link between hamburgers and meals (a) and Cows and hamburgers (b). This automatically generates a link between meals and cows (be aware of the fact that there is no link between cows and meals). The Venn diagram clearly shows that this area is not shaded and thus a possible correct answer.

3. No cows are meals. It can easily be concluded that this statement is incorrect, since an overlap is present between these two terms.

4. Some cows are no meals. Be aware of the rank of the terms. It was already suggested that some cows are hamburgers, but nothing is stated between the relation of cows and meals. In statement 2 the rank was different so conclusions could be made, which in this situation is not the case.

In this example the correct answer is statement 2. Most syllogisms can be solved by using the above manner. The trick by solving syllogisms is oftencorrect reading and

interpreting of the statements and conclusions for obtaining a valid reasoning.

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Syllogisms Examples and Types

Syllogisms are todays most commonly accepted form of logical reasoning, however they are closer related to mathematical reasoning. Within the syllogisms three different types can be distinguished:

Conditional syllogisms

Conditional syllogisms are better known as hypothetical syllogisms, because the arguments used here are not always valid. The basic of this syllogism type is: if A is true then B is true as well. An example will follow to elucidate the former.

Major premise: If Johnny is eating sweets every day, he is placing himself at risk for diabetes.

Minor premise: Johnny does not eat sweats everyday Conclusion: Therefore Johnny is not placing himself at risk for diabetes This conclusion is invalid because it is possible that Johnny does not eat sweats every day but does eats cake every day what also puts him at risk for diabetes.

Disjunctive syllogisms

These syllogism types do not actually state that a certain premise (major or minor) is correct, but is does states that one of the premises is correct. The basic type for this syllogism is: Either A or B is true, but they cant be true at the same time. Example:

Major premise: Either the meeting is at school or at home. Minor premise: The meeting is not at home. Conclusion: Therefore the meeting is at school. The conclusion of the syllogism type may be given, however most of the times the conclusion can be drawn based up on own conclusions.

Categorical syllogisms

The third and most commonly used type of syllogisms are the categorical syllogisms. The basic for this syllogism type is: if A is a part of C, then B is a part of C (A and B are members of C). An example of this syllogism type will clarify the above:

Major premise: All men are mortal. Minor premise: Socrates is a man. Conclusion: Socrates is mortal. Both premises are known to be valid, by observation or historical facts. Because the two premises are valid, the conclusion must be valid as well. Be aware that this conclusion is based on logical reasoning and thus it doesnt have to represent the truth always.

Next, these categorical syllogisms can be divided into 4 kinds of categorical propositions which will be explained separately:

Propositions

1. A: Universal Affirmative This is a syllogism of the form: All X are Y, like the example: all woman are shopaholic.

2. E: Universal Negative This is the negative form of universal affirmative, which is a syllogism of the form: No X is Y, or as example: No humans are perfect. This syllogism type is exactly the opposite of proposition A explained above.

3. I: Particular Affimitive Another syllogism type is the particular form which only influences some people and not the whole population. This syllogism is of the form: Some X are Y.

4. O: Particular Negative The opposite of proposition I is proposition O which is of the form: Some X are not Y. an example of this would be: some cars are not green.

By explaining these 4 kinds of categorical syllogism types each syllogism can be identified, which is also called stating the mood of an argument. We know syllogisms always consist out of a major and minor premise and a conclusion. In standard form, as shown on this page, the major premise is always shown first, after which the minor premise and the conclusion follow. An example of a mood of a categorical syllogism could be: AEO. We now know that the major premise is of type A (all A are B), the minor premise is of type E (No A is B) and the conclusion is of type O (some S is no P).

Logic Lesson page12

1st figure 2nd figure 3rd figure 4th figure

Major premise M P P M M P P M

Minor premise S M S M M S M S

Conclusion S P S P S P S P

THE CATEGORICAL SYLLOGISM

STRUCTURE OF SYLLOGISM

MAJOR PREMISE Predicate of the conclusion

+ Middle Term

Every man is mortal Mortal = major term PREDICATE OF THE

CONCLUSION

Man = middle term CONNECTOR OF THE

PREMISES

Philip = minor term SUBJECT OF THE

CONCLUSION

Minor Premise Subject of the Conclusion

+ Middle Term

Philip is a man

Conclusion Subject of Minor Premise

+ Predicate of the Major

Premise

Philip is mortal

10 Rules in Categorical Syllogism

1. Must contain Major, minor and Middle term 2. Middle Term should not be in Conclusion 3. Quantity of Major and Minor Term should not be extended in the conclusion if

they are in PARTICULAR. 4. Quantity of the Middle Term must be universal at least once 5. Conclusion must be affirmative if both premise are AFFIRMATIVE 6. Conclusion must be negative if one premise is NEGATIVE 7. Two premises must not be both negative 8. One premise must be universal 9. Conclusion should be particular if One premise is. 10. The subject term of the premise must be ASSERTED IN THE CONCLUSION 11.