Introduction


Course Outline: This course is designed as an introduction to problem solving. It is intended to teach students how to successfully solve problems using practical reasoning. This course will use the scientific method as its pattern for effective thinking. Within these parameters we will investigate both formal and informal aspects of sound thinking.

The goals of this course are: 1) Improving thinking skills required for successful problem solving 2) Increasing the students sensitivity to subjective factors which influence decision making strategies 3) Integrating these techniques into the individual's decision making process.

Syllabus - A few comments concerning the necessity of attendance and homework assignments

This course is entitled critical thinking in the university's handbook. "106-3 CRITICAL THINKING.

[SKILLS] [IAI Course No. H4 906] Study and practice of critical thinking and correct problem-solving methods.

Organizing information, analyzing meaning, developing correct arguments, detecting fallacies, using effective methods of investigation. Graduation credit may be earned for either PHIL 106 or MATH 106, but not for both." This course is taught by the Philosophy department. Traditionally this subject matter was called Logic.


What is Logic? Logos >Gr. - word, speech (thought) Logic is the theory of inquiry . On the surface the study

of logic appears to have some connection to our thinking process as it relates to our ability to successfully solve

problems. Discussions focusing on thinking generally invoke the use of the word "mind" in one context or another.

For the purpose of this class I will use an instrumental, functional definition of mind. Mindful behavior. The mind

emerges in conduct as behavior - attempting to solve a problem We don't always use our mind to solve

problems. I.e. Instinct, reflex(driving a car, applying the breaks) Thinking a process like digestion. Not

always present. Cf. - handout - Dewey's "How we think" This Class - Thinking about thinking


Brief history of logic: Effective problem solving techniques


Early history of human kind, at least to the extent we understand prehistoric life through the archeological records, -

brutish and unpredictable - animalistic - to the extent that animals "solve" problems are they exercising logical

behavior??? - reflective thought - their ability to control and predict - canine behavior today is identical to canine

behavior. The manner in which dogs solve problems today is the same as 5000 years ago. However, there is

something characteristically different about human problem solving techniques. People solve problems although

often not too effectively.


I'm not going to attempt a complete history of logic here - must too energetic of an undertaking. However there are

some significant developments that I will point out. I'll give some references for future study. These may form the

basis for extra credit work.


The early Greeks began formulating sets of rules for effective thinking. This culminated in the works of Aristotle.

(The Organon ) Aristotle wasn't the first to use the term "logic" Xenocrates of the Academy was probably the first

to consider this as an independent area of investigation. Other Greek thinkers which we'll consider - Socrates

(Plato), Heraclitus(The Logos or reason - regulates all processes and is the source of all human law, The Stoics -

harmony - the world a living unity - emphasis on harmony-In Christian philosophy the Logos becomes the second

person of the trinity We'll study some of this when we study categorical reasoning. This is a form of reasoning that

we will refer to later as deductive reasoning - deductive reasoning does not go beyond the evidence provided. The

point to be made is that scientific thinking, the formulation of a logic, up to this point based on observation of

nature. In this discussion Aristotle becomes even more significant. Aristotle's father was personal physician to the

Macedonian king, Amyntas II. Aristotle became the tutor of Amyntas II's grandson, Alexander (Alexander the

Great). Before Alexander died in 323 BC , he and Aristotle maintained their friendly relationship. Many elements

and items of Alexander's conquests were returned to Athens where Aristotle began an exhaustive classification of

these strange and unique items gathered from distant conquests. We will discuss Aristotle's method of definition

later this semester. Classification by genus and species . Aristotle's definition of man as a rational animal takes on

greater significance when examined in the light of that animal which can compare and contrast - form ratios. The

emphasis in this early formulation of logic was on understanding. The question "what do we know" was primary in

Aristotle's logic. More will be said about this in our discussions concerning deduction. The focus of the enterprise

of Logic was understanding. Understanding was achieved through classification of the world


St. Augustine - The emperor Constantine converted to Christianity in 312 AD. Under Theodosius (379-395)

Christianity became the official state religion. To be a citizen you had to adopt the Christian faith. This led to some

distressing consequences since most of the population was non-Christian. St. Augustine's book, City of God

(413-426) was written when the empire was under attack by the infidels of the times. Many of Augustine's

writings were attempts to incorporate within the Christian faith those articles of belief held dearly by the non-

Christian population. Plato's writings can be seen reflected in the writings of Augustine.


Arabic Logic - Before the revival of logic in 12th century Europe Aribic logic was thriving. Around 850, at

least Porphyry's Isagoge and Aristotle's Categories, De interpretatione, and Prior Analytics had been translated

via Syriac into Arabic. The Muslim al- Farabi(c. 873-950) wrote important commentaries and other logical works

there that influenced all later Arabic logicians. (Encyclopedia Britannica) Avicenna and Averroes were probably the

best of the Arabic logicians. We should also consider the mathematics of the great Persian poet, mathematician

and astronomer Omar Khayyam. His scientific studies certainly laid the basis for future endeavors in the scientific

community.


St.Thomas Aquinas - Aristotle's writings provided for St. Thomas (1224-1274) the basis on which he

developed his philosophy of Scholasticism. Aquinas emphasized Reason as the principle that leads the Mind to

God. Aquinas developed 5 proofs for the existence of God. Again the emphasis is on understanding - understand

the creation you understand the creator.


Roger Bacon - 1214-1294 - Franciscan monk -- recognized the significance of the deductive application of

principles and the need for experimental verification of the results of the reasoning. Keenly interested in

mathematics. Important aside - the church was very supportive of this form of logic - proofs for the existence of

God.


William Ockham - Controversial 14th century Scholastic philosopher (1280-1349) Born - in the village of

Ockham in Surrey England The Law of Parsimony - Ockham's Razor -"Entia non sunt multiplicanda sine

necessitate". = Plurality should not be posited without necessity. Simplicity in reasoning. Also lead to a brand of

skepticism. Ockham had a distrust of the human ability to reach any level of absolute certainty


Francis Bacon - (1561-1626)- Inspired by the renaissance. In revolt against the Aristotelian (Scholastic)logic

Proposed an inductive method of discovering truth - This method was founded on empirical observation, analysis

of observed data, inference which results in hypothesis and the verification of these hypothesis through continued

observation and experiment. This was a major shift from preceding attempts to explain the universe in which we

live. The methodology prescribed by the Greeks and medievalists shifted from observation, enumeration and

understanding nature to the manipulation of the events found in nature. The use of the inductive method prescribes

the extraction of the essentials from the non essential and discovering the underlying form of the phenomena. Use

of comparison of instances, study of concomitant variation, and exclusion of negative instances. We'll discuss these

issues at a later date. The inductive method advocated by Francis Bacon was to enable man to attain mastery over

nature in order to exploit it for his own purposes. Apocryphal claim -"we must twist nature's arm to make her yield

her secrets" The mind should pass from particular facts to more general knowledge of forms. Generalized physical

properties. These are laws according to which phenomena actually proceed. Demanded an exhaustive enumeration

of possible instances of occurrences of phenomena, the recording of these comparative instances, and the

additional registration of negative occurrences. Experiments must be performed to test the observations. More

about this later. Science proceeded by leaps and bounds with this new method - the scientific revolution.


The Personal Point of View (World View)


Every phase of decision making is strongly affected by the fact that we see ourselves and the world from our own unique

point of view. Discuss the black board problem. What color is the black board. Reality of human perspective. Questions

about time - Reality vs actuality-Time on stove vs time at a party James -New born children thrust into a world of

blooming buzzing confusion - How we carve the world up - Anna the wolf girl vs Einstein


Three headings under the personal point of view.


1. Frame of Reference - The organized body of knowledge, belief and experience with which we interpret and understand

new experiences. Includes all that one believes or knows to be true of the world. How we sort the world out. No one's

frame of reference is totally complete of accurate - vast gaps in our fund of knowledge. We all make mistakes. Frame of

reference limits us in many ways 1) Frame of reference limits perception. Problem of being tone deaf. My daughter

hears things in a Bach concerto that I don't because she has been trained 2) limits our ability to recognize problems. I.e.

noises in a car when driving down the road. 3)Limits the ability to interpret or use evidence in solving any kind of

problem. Sherlock Holmes 4)Limits the acquisition of new knowledge. Knowledge is required in order to gain new

knowledge - advanced courses and prerequisites. False information can be worse than no information. Medicine -

example. Bloodletting, ascribing influenza to meteorological events etc. Essential that we develop good frame of reference

- wide not narrow - sound education - liberal education does not refer to political party.


2. Values - system of values - value judgments affect our decisions - interplay of emotions - questions of lying and

stealing. For example - our views concerning Clinton's affair, Bush's policies in Iraq, etc.


3. Self concept - the mental picture that each of us has of the kind of person we believe ourselves to be. Our self-concept

includes our beliefs about our abilities, special talents, strengths and weaknesses, and our notion of the role we play in the

world. At times this can be helpful but other times it can interfere with objectivity


The elements that comprise our personal point of view are limiting factors. These factors limit our abilities to solve

problems. We generally only approach the solution of a problem from our limited perspective. Discuss the "reality

(actuality) of human perspective. Question - what color is the board I'm now facing? (depends on at what angel I am

viewing it) How fast am I moving. (This is a trick question - depends on the location of the person viewing me - to my

students I'm standing still - The circumference of the Earth at the equator is 25,000 miles. The Earth rotates in about 24

hours. If the person viewing you were to hang above the surface of the Earth at the equator without moving, s(he)would

see 25,000 miles pass by in 24 hours, at a speed of 25000/24 or just over 1000 miles per hour. The viewer would see me

moving at about 1000 mph. Earth is also moving around the Sun at about 67,000 miles per hour. So depending on the

location of the viewer my speed would be change In any case it is the limitations imposed by our personal points of view

that often cause problems when we attempt to solve a problem.

<http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970401c.html> There is a methodology that will help reduce if not

eliminate these limitations imposed by our frame of reference. A question of objectivity.


Objectivity


What does it mean to be objective? This question has many different answers. If you don't believe this

go ahead and type "objectivity" into one of your search engines and you could spend the rest of your life studying this

question (over ½ million entries) However, this study of "objectivity" will not be nearly so rigorous. According to

Encyclopedia Britannica - objectivity Main Entry: 1ob·jec·tive

Pronunciation: &b-'jek-tiv, äb-

Function: adjective

1 a : relating to or existing as an object of thought without consideration of independent existence --

used chiefly in medieval philosophy b : of, relating to, or being an object, phenomenon, or condition

in the realm of sensible experience independent of individual thought and perceptible by all

observers : having reality independent of the mind <objective reality> <our reveries... are

significantly and repeatedly shaped by our transactions with the objective world -- Marvin Reznikoff>

-- compare SUBJECTIVE <http://www.britannica.com/dictionary?book=Dictionary&va=subjective+>3a c of a symptom of disease : perceptible to persons other than the affected individual -- compare SUBJECTIVE

<http://www.britannica.com/dictionary?book=Dictionary&va=subjective+>4c d : involving or deriving from sense

perception or experience with actual objects, conditions, or phenomena <objective awareness>

<objective data>

2 : relating to, characteristic of, or constituting the case of words that follow prepositions or

transitive verbs

3 a : expressing or dealing with facts or conditions as perceived without distortion by personal

feelings, prejudices, or interpretations <objective art> <an objective history of the war> <an

objective judgment> b of a test : limited to choices of fixed alternatives and reducing subjective

factors to a minimum

synonym see MATERIAL <http://www.britannica.com/dictionary?book=Dictionary&va=material>,

FAIR <http://www.britannica.com/dictionary?book=Dictionary&va=fair>

- ob·jec·tive·ly adverb


ob·jec·tive·ness noun

- ob·jec·tiv·i·ty /"äb-"jek-'ti-v&-tE, &b-/ noun


It is the 3a entry for the definition that we will consider and hold as our definition. More simply put -objectivity = viewing

the world without distortion How is this to be accomplished? What is our methodology? We shall begin with a

discussion of the scientific method - the 5 phases of problem solving (I add a 6th phase - I will explain why in this lecture)


Two kinds of thinking: The procedures described in this text require two distinctly different types of thinking.


A. Creative Thinking: defined as the formation of possible explanations of a phenomena or possible solutions to a

problem

B. Critical Thinking: defined as testing and evaluation of these proposed solutions


In class exercise - What are activities or personalities generally associated with critical thinking? What are activities or

personalities generally associated with creative thinking?


Effective thinking is a combination of both of these aspects of thinking. The methods of modern science are

both creative and critical. Create and Criticize are the twin watch words. I will discuss how these two types of

thinking are integrated in the lecture on the scientific method.