Philosophy 105 Exam 2 Critical Reasoning Definitions

Philosophy 105 Exam 2 Critical Reasoningdefinitions Please Define

This assignment requires defining key concepts in critical reasoning, identifying logical fallacies, constructing valid arguments, translating statements into standard form, analyzing arguments with Venn diagrams, constructing truth tables, and performing logical derivations. The specific tasks include definitions of critical reasoning terms with examples, fallacy identification, argument reformulation, Venn diagram analysis, truth table construction, and logical derivations for extra credit. Each task aims to deepen understanding of principles fundamental to formal logic and critical thinking.

Paper For Above instruction

Definitions of Critical Reasoning Terms

1. Affirming the Consequent: A formal logical fallacy where one assumes that if 'If P then Q' is true, and Q is true, then P must also be true. This ignores the possibility that Q could be true for reasons other than P. For example, "If it rains, the ground is wet. The ground is wet. Therefore, it rained." This reasoning is invalid because other factors could have caused the ground to be wet, such as a sprinkler.

2. Division: A logical fallacy where one assumes that what is true of the whole must also be true of its parts. For example, "The committee is wealthy. Therefore, every member of the committee is wealthy." This is invalid because the wealth may not be equally distributed among members.

3. Contraposition: A valid logical operation that states that "If P implies Q," then "Not Q implies Not P." It allows one to infer the contrapositive of an implication, which is logically equivalent to the original statement. For example, "If it is a dog, then it is an animal." Contrapositive: "If it is not an animal, then it is not a dog."

4. Truth Table: A mathematical tool used to determine the truth value of logical expressions. It lists all possible truth values of component propositions and shows the resulting truth value of the entire expression. For example, constructing a truth table for 'P v Q' involves listing all combinations of truth values for P and Q and marking the result.

5. Truth Functional Symbol (or Operator): A symbol used in propositional logic where the truth value of the compound statement depends solely on the truth values of its components. Examples include '∧' (and), '∨' (or), '→' (implies), and '¬' (not).

6. False Dilemma: A logical fallacy that presents only two options when additional possibilities exist. For example, "You're either with us or against us," ignoring neutral positions or alternative options.

7. Appeal to Ignorance: A fallacy where a statement is considered true simply because it has not been proven false, or vice versa. For example, "No one has proven that aliens do not exist; therefore, they do exist."

8. Begging the Question: A fallacy where the conclusion is assumed in the premise. For example, "God exists because the Bible says so, and the Bible is true because God wrote it."

9. Square of Opposition: A diagram representing logical relationships between different types of categorical propositions (e.g., universal affirmative, universal negative, particular affirmative, particular negative). It illustrates relations such as contradiction, contrariety, subcontrariety, and subalternation.

10. Contradictory: Two propositions that cannot both be true and cannot both be false at the same time. For example, "It is raining" and "It is not raining" are contradictory.

Identification of Fallacies

1. “What you aren’t a Cornhuskers fan? Listen, around here everybody is for the Huskers! This is Nebraska!”
2. Fallacy: Bandwagon (Ad Populum). Assumes something is true because many people believe it.
3. “Aw c’mon Jake, let’s go hang out at Dave’s. Don’t worry about your parents; they’ll get over it. You know the one thing I really like about you is that you don’t let your parents tell you what to do.”
4. Fallacy: Appeal to Authority/Peer Pressure, suggesting that because the speaker likes the person’s independence, it justifies ignoring parents’ authority.
5. “Imagine yourself alone beside your broken-down car at the side of a country road in the middle of the night. Few pass by and no one stops to help. Don’t get caught like that—don’t get caught without your Polytech cellular phone!”
6. Fallacy: False Dilemma. Implies that the only solution is to have a cellular phone, ignoring other options.
7. “You: Look at this. It says here that white males still earn a lot more than underrepresented groups and women for doing the same job. Your friend: Yeah, right. Written by some woman no doubt.”
8. Fallacy: Ad Hominem (circumstantial). Dismisses the evidence based on its source rather than its merits.
9. “I believe that Tim is telling the truth about his brother because he just would not lie about such a thing.”
10. Fallacy: Circular Reasoning (Begging the Question). The premise and conclusion rely on each other without independent evidence.

Constructing Valid Arguments

1. Jesse Ventura, the former Governor of Minnesota, was a professional wrestler. He couldn’t have been a very effective governor.

Claim: Jesse Ventura was a professional wrestler.

Premise: Being a professional wrestler conflicts with being an effective governor.

Conclusion: Therefore, Jesse Ventura could not have been an effective governor.

Counter-argument: One could argue that wrestling skills do not necessarily impede gubernatorial effectiveness, so this argument may be invalid unless further premises are provided.

2. Half the people in the front row believe in God. Therefore, half the class believes in God.

Claim: Half the people in the front row believe in God.

Premise: The front row constitutes a significant part of the class.

Conclusion: Therefore, half the class believes in God.

Reformulated in standard form:

• Premise 1: Half the people in the front row believe in God.
• Premise 2: The front row forms a representative sample of the class.
• Conclusion: Therefore, half the class believes in God.

Venn Diagram Analysis for Validity

1. All sound arguments are valid. Some valid arguments are not interesting arguments. All sound arguments are not interesting arguments.

Analysis: This statement is invalid because it falsely suggests all sound arguments are not interesting, contradicting the first premise. Using Venn diagrams, the set of sound arguments (S) is a subset of valid arguments (V). The claim that "all sound are not interesting" would place S outside the set of interesting arguments (I), contradicting the premise if some sound arguments are interesting. Therefore, the argument is invalid.

2. Only systems with removable disks can give you unlimited storage capacity of a practical sort. Standard hard drives never have removable disks, so they can’t give you practical, unlimited storage capacity.

Analysis: This is valid. The statement indicates that if a system has removable disks (P), then it can provide practical unlimited storage (Q). Since standard hard drives lack removable disks (not P), they cannot provide practical unlimited storage (not Q), confirming the contrapositive is valid.

Constructing Truth Tables

1. For the formula Pv(Q->R):

From the truth table, the expression Pv(Q->R) is valid if it is true in all cases where the premises are true.

Derivations for Extra Credit

Given the premises:

• Q->L
• (P & S) v (T->R)
• P->M
• ~(S & P)
• RvP
• R->(Q & S)
• T->R
• ~M->L

Derivation: R->(Q & S)

Assuming R, from R->(Q & S) is given.

From the premises, one can reason as follows:

• If R, then from R->(Q & S), Q and S are true.
• From Q, using T->R and T, derive R, confirming the validity.
• From S, and the negation of (S & P), conclude P is false, which is consistent with P->M and ~M->L implications.

Thus, the derivation of R->(Q & S) is supported logically by the premises.

References

• Copi, I. M., Cohen, C., & McMahon, K. (2014). Introduction to Logic (14th ed.). Pearson.
• Lukasiewicz, J. (2018). Symbolic Logic. Oxford University Press.
• Hurley, P. J. (2014). A Concise Introduction to Logic (12th ed.). Cengage Learning.
• Kleene, S. C. (2016). Mathematical Logic. Dover Publications.
• Ben-Ari, M. (2006). Mathematical Logic for Computer Science. Springer.
• Benacerraf, P., & Putnam, H. (1983). Philosophy of Mathematics: Selected Readings. Cambridge University Press.
• Kripke, S. (2013). Naming and Necessity. Harvard University Press.
• Resnik, M. D. (1987). Mathematics and its History. Dover Publications.
• Johnson-Laird, P. N. (2017). How We Reason. Oxford University Press.
• Enderton, H. B. (2000). A Mathematical Introduction to Logic. Academic Press.