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
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
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.
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-
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>
2 : relating to, characteristic of, or constituting the case of words that follow prepositions or
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>,
- ob·jec·tive·ly adverb
- 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
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.