Catalog

Topics in Mathematics is for those students at Pima Community College to use while taking MAT 142 or MAT 142RQ. The material covered in the book includes applications of probability, statistics, finance, proportional reasoning, geometry, and growth models.

Open ELA is a complete course in Reading and Language Arts for instructors and self-directed learners in Adult Basic Education settings. These materials are designed to aid students in completing the GED exam and to support college and career pathways. This course includes resources for the Reading and Language Arts, Social Studies, and Science portions of the GED exam. It also includes GED Study Guides and lessons contextualized to college and career exploration and readiness. Open ELA covers six units of study: Understanding Literature, Intro to Communications, Metacognitive Reading, Film & Television Studies, Reading for Science & Social Studies, and Journalism.

This course introduces the main types of logical reasoning. Studying logic provides brain fitness and awareness training to support life as a responsible citizen and consumer in a world where misinformation and enticing arguments are widespread. Throughout the book, interactive exercises are included for learners to check their understanding with immediate feedback. Selected topics offer non-interactive practice assignments for applying skills.

Logic Fundamentals are covered in the two initial learning modules.

• Module 1: The Basics of Logical Analysis – Arguments are the fundamental unit of logical reasoning. In this module, we learn about the components and basic structure of arguments, how to recognize arguments in ordinary language and distinguish arguments from explanations. The essential features of deductive and inductive reasoning are introduced, along with the concepts of validity, soundness, and logical strength.
• Module 2: Language and Informal Fallacies – Language is messy. In this module, we start by exploring some frailties and imprecision of ordinary language that contribute to faulty reasoning. Then we work with fallacies – arguments with defects. The distinction is made between formal and informal fallacies, with detailed focus on informal fallacies that make arguments and claims incorrect but often, nevertheless, persuasive.

Deductive Logic is the topic of the next two modules, each of which involves a unique approach for evaluating deductive arguments. In effect, we will see two different “deductive logics”. Each will have its own method for accomplishing the same goal — evaluating deductive arguments to determine whether they are valid or invalid.

• Module 3: Aristotelian Logic – Aristotelian Logic is the first of two “deductive logics” to be addressed. The four categorical proposition types are explored in depth, and Venn diagrams are used to demonstrate relationships between categories, or classes of things. The Square of Opposition and operations that can be performed on categorical propositions demonstrate how inferences can be drawn when the truth value of a particular type of categorical proposition is known. Problems that arise from categories with no members (empty classes) are explored. And finally, Venn diagrams are used to demonstrate the validity of standard-form categorical syllogisms.
• Module 4: Sentential Logic – Sentential Logic presents a second deductive logic that can be applied to a wider range of argument forms than Aristotelian logic. We learn to translate natural-language sentences and arguments to a symbolic language and use truth tables to determine the validity status of the symbolic-language argument forms.

Inductive Reasoning is covered in the final three modules, each of which examines a specific type of inductive reasoning that has its own useful applications. These reasoning patterns are common ways of thinking that many of us use routinely.

• Module 5: Analogical Reasoning – Analogies are similarities between a known set of circumstances and others that we’re seeking to understand more fully. We apply a standard pattern to ordinary-language argument-from-analogy to identify analogical components. Criteria for assessing strength and weakness of analogical arguments are presented, and the use of analogical arguments is demonstrated as a strategy for refuting bad arguments we hear. And finally, the analogical mechanisms that support legal decisions are explored.
• Module 6: Causal Reasoning – Causal arguments make claims about causes and effects. The distinction between sufficient causes and necessary causes is explored. Patterns of reasoning identified and cataloged by John Stuart Mill are presented as methods for discovering the causes of natural phenomena, and some cautionary limits are identified for using certain methods.
• Module 7: Hypothetical Reasoning and Science – Hypothetical reasoning is an essential strategy in scientific discovery. This general method is compared to the inductive method delineated by Sir Francis Bacon. We focus on the basic steps of the hypothetical method. Conditional (hypothetical) statements are used as the logical building block of hypothetical reasoning, and we refer back to both correct and fallacious deductive argument forms that are integral to the hypothetical method for testing scientific hypotheses. We consider the possibility and criteria for acceptance of hypotheses as working theories, despite lack of certainty (in the deductive sense) that is available with hypothetical (inductive!) reasoning.

This survey course on Western Philosophy includes primary explanatory text, short original-source readings, videos, and occasional linked external readings. Further links provide supplementary reading/viewing for learners seeking deeper insight on specific topics.

Eight areas of Western philosophic thought are addressed, each in its own unit, along with interactive exercises for reviewing key concepts. Selected sections offer “thought projects” to stimulate awareness of connections between key philosophic concepts and present-day affairs.

Unit 1: Logic involves the study of the human activity of reasoning. Topics include:

• Basic structure and components of arguments
• The role of arguments in “doing” philosophy
• The distinction between and features of deductive reasoning and inductive reasoning
• Features of “good” arguments
• Fallacious arguments and claims, with emphasis on informal fallacies encountered in everyday discourse

Unit 2: Epistemology seeks answers to questions about the possibility and nature of human knowledge. How do we know, and what can we know? Topics include:

• Distinctions between a priori and a posteriori knowledge and analytic and synthetic claims
• How reasoning and experience characterize rationalism and empiricism, respectively, as main schools of epistemological thought
• Epistemological positions of specific philosophers including Rene Descartes, Gottfried Leibniz, and John Locke
• David Hume’s skepticism and how Immanuel Kant attempts to resolve it with synthetic a priori judgments

Unit 3: Philosophy of Science, like the unit on epistemology, concerns how can we know about the natural world, with focus on scientific models, methods, and theories. Topics include:

• Aristotle’s use of causes to explain the natural world, as a precursor to the modern focus on causal relationships in science
• Comparison of Sir Francis Bacon’s scientific method of induction and generalization with the hypothetical-deductive method
• Karl Popper’s recognition of the nature and importance of falsifiability in confirming theories
• Thomas Kuhn’s work on shifting paradigms that lead to scientific revolutions and the irregular pace of scientific progress

Unit 4: Metaphysics zooms in on the specific subset of the broad field of Metaphysics — the Philosophy of Mind. The focus is on theories and their implications about the nature of a person’s reality, as a physical body with a mental life. Topics includes:

• How Rene Descartes’s method of doubt led him to dualism
• The nature of materialism (including eliminative materialism)
• The problem of free will
• Baron D’Holbach’s determinism, William James’s libertarian indeterminism, and Daniel Dennett’s compatibilism

Unit 5: Ethics introduces moral concepts and distinctions that are central to ethical studies and presents major ethical theories for how human actions are to be evaluated as good or bad, right or wrong. Topics include:

• The moral relativism-vs-objectivism debate
• Views of Immanuel Kant and David Hume on moral epistemology – how we can know right from wrong
• Distinction between intrinsic and instrumental good
• The deontology of Immanuel Kant
• Utilitarianism from the perspectives of Jeremy Bentham, John Stuart Mill, and Peter Singer
• Aristotelian virtue ethics and some modern virtue ethicists who find deontology and utilitarianism inadequate
• The ethics of care as proposed by Nel Noddings.

Unit 6: Social and Political Philosophy considers the relationship between an individual and the government, and what makes a society good, given issues such as distribution of resources, fairness, justice, human rights, and the responsibilities of government. Topics include:

• The impact of a philosopher’s view of human nature on proposals made about social order
• Aristotle’s “good life”
• “Social contract” from diverging viewpoints of Thomas Hobbes, John Locke, Jean-Jacques Rousseau, and John Rawls
• Contrasting the values underlying liberalism and socialism
• Influences of John Locke and John Stuart Mill on present-day liberalism and democracy

Unit 7: Philosophy of Religion looks first at views on the nature of religion held by both late 19th-century and contemporary philosophers. Topics include:

• Religion as personal/private experience exemplified by William James’s experience of the divine and by Karen Armstrong’s personal summons to action serving others
• Emile Durkheim’s characterization of religion as a group/communal experience related to sacred objects
• Kwame Anthony Appiah’s view that generalizations about religion are risky

Then historical arguments and objections to them for the existence of God are examined along with the problem of evil. Topics include:

• Ontological argument of Saint Anselm, Cosmological argument of Saint Thomas Aquinas, and Teleological argument as renewed by William Paley
• Moral arguments for the existence of God from Saint Thomas Aquinas and Immanuel Kant
• The nature of God and the problem of evil
• John Hick’s theodicy whereby evil functions as a means for spiritual development

Unit 8: Aesthetics presents some dominant theories on the nature of beauty and art, the character of the aesthetic experience, and aesthetic judgement in art criticism. Topics include:

• The distinction between objectivism and subjectivism in theories of beauty
• The problem for Beauty as an ideal with pure subjectivism
• Denis Dutton’s evolutionary theory of beauty
• Representationalism, formalism, functionalism, or emotionalism as an essential characteristic of art
• Family-resemblance (cluster) theory for denying any specific common property for art
• Immanuel Kant’s “disinterested interest” as a central principle of contemporary aesthetics and attitudes for art criticism
• Representationalism, formalism, functionalism, and emotionalism as tools for judging art