Exam One Philosophy 1101: Introduction To Philosophy

Exam One Philosophy 1101: Introduction to Philosophy print Name

Identify examples of explicit and implicit contradictions, state the logical rule for negating categorical propositions, perform logical negations of given propositions, define branches of philosophy, explicate differences between concepts, match Greek/Latin roots to English meanings, analyze the truth of compound propositions, state the Principle of Excluded Middle, explain Aristotle's principles regarding non-contradiction and metaphysics, and apply Reductio ad Absurdum to demonstrate the non-existence of universal exception rules.

Paper For Above instruction

The foundational task in understanding philosophy involves grasping the nature of contradictions, logical negations, and the essential principles that underpin rational discourse. Examples of explicit contradictions occur when a statement directly opposes itself in a single assertion, such as claiming "It is raining and it is not raining" simultaneously in the same context. Implicit contradictions, however, are less overt and involve contradictory implications, as in asserting "All swans are white" while presenting evidence of black swans, thereby undermining the universality of the statement indirectly.

Logic dictates that negating a categorical proposition involves changing its quantity or quality based on specific rules. For universal affirmative propositions ("All S are P"), negation entails asserting "Some S are not P." Conversely, negating a universal negative ("No S are P") results in an existential affirmative ("Some S are P"). For particular propositions ("Some S are P"), the negation is "No S are P," and vice versa. These rules ensure clarity and precision in logical reasoning about categorical statements.

Applying negations to the provided propositions, we find that "All dogs are non-lizards" negates to "Some dogs are lizards." "Some cats are bipeds" negates to "No cats are bipeds." "All horses are not brown" is more complex; its negation is "Some horses are brown," assuming that "not brown" is a negative predicate. The negation of "Some lies are not immoral" becomes "All lies are immoral," which is often a stronger statement requiring justification.

Branches of philosophy clarify the scope of inquiry: axiology deals with values, ethics, and aesthetics; epistemology investigates knowledge, belief, and truth; semeiotics examines signs, symbols, and meaning. These subdivisions allow philosophers to specialize in fundamental questions about human experiences, morality, and communication.

Distinguishing concepts such as "knowledge that" (propositional knowledge) and "knowledge why" (know-how or causal understanding) highlights different epistemic states: the former pertains to facts known to be true, the latter to understanding reasons or explanations behind phenomena. Similarly, physical impossibility refers to situations impossible within the laws of nature, while logical impossibility pertains to contradictions within the principles of logic, such as asserting "A and not-A" simultaneously, which is impossible regardless of physical constraints.

The Greek/Latin matching exercise includes items such as: "episteme" (knowledge, systematic knowledge), "sophia" (wisdom, knowledge of first cause), and "axioma" (self-evident principles). "Praxis" refers to doing or action; "phusis" to nature or change; "semeion" to sign; "logos" to word or reason; "theoria" as meditation or contemplation; "analytica" related to analysis; "genus" as a broad class; and "reductio ad absurdum" an argument demonstrating falsehood through absurd consequences.

Analyzing composite propositions, the statement "Both all S are P and some S are not P" explores the tension between universal and particular claims. Such a combination can be true only if one part is false; typically, if all S are P, then "some S are not P" must be false, making the conjunction false in classical logic. Conversely, if "some S are not P" is true, then "All S are P" must be false, preventing the conjunction from being true simultaneously.

The statement "Some trees are plants" is true, as all trees are indeed a subset of plants. The Principle of Excluded Middle states that for any proposition, either that proposition is true or its negation is true—there exists no middle ground.

Aristotle’s emphasis on the Principle of Non-Contradiction as "the principle of all principles" underscores that logical consistency is foundational; contradictions undermine any rational system. He also asserts that metaphysics presupposes logic because understanding being and existence relies on clear, non-contradictory reasoning. Without logical principles, metaphysical claims collapse into ambiguity or contradiction, making logical coherence indispensable for metaphysical inquiry.

Using Reductio ad Absurdum, one can demonstrate that not every rule has an exception by assuming the contrary (that all rules have exceptions) and deriving a contradiction or absurdity from this assumption. For example, assuming that "every rule has an exception" leads to the contradiction of having a rule with no exception, thereby proving that some rules are exceptionless, such as logical laws themselves.

References

• Copi, I. M., Cohen, C., & McMahon, K. (2018). Introduction to Logic. Routledge.
• Ayer, A. J. (1952). Language, Truth, and Logic. Dover Publications.
• Aristotle. (1984). Metaphysics. Hackett Publishing.
• Descartes, R. (1985). Rules for the Direction of the Mind. Cambridge University Press.
• Peirce, C. S. (1931). Collected Papers of Charles Sanders Peirce. Harvard University Press.
• Baron, S., & Quine, W. V. (2004). Logic and Philosophy. MIT Press.
• Russell, B. (1912). The Problems of Philosophy. Oxford University Press.
• Foucault, M. (1981). Writing The History of Thought. Routledge.
• Heidegger, M. (1962). Being and Time. Harper & Row.
• Kant, I. (1998). . Cambridge University Press.