In this assignment, you will apply truth-functional logic to analyze and evaluate the validity of arguments in a real-world example. Here are the details:
(Book is critical thinking by Moore& Parker 2024 edition. Chapter 10)
Identify and Translate
Select a short argument from a credible source, such as a news article, editorial, or speech, that includes multiple statements and at least one connective (e.g., and, or, not, if…then). Rewrite the argument in standard form, identifying the premises and conclusion. Then, translate each statement into symbols, using letters (e.g., P, Q, R) to represent each statement and appropriate symbols to indicate connectives.
Construct a Truth Table
Using the symbolic version of the argument, create a truth table that shows all possible truth values for each statement and the overall argument. Make sure to clearly indicate the rows where the premises are all true and evaluate whether the conclusion is also true in those cases.
Evaluate Validity
Based on your truth table, determine whether the argument is valid or invalid. Explain your reasoning in detail, showing how the truth values support your conclusion about the argument’s validity.
Reflection
Reflect on your findings. Was your initial intuition about the argument’s validity confirmed by the truth table analysis, or did it surprise you? Discuss any challenges you encountered in translating the argument into symbolic form or constructing the truth table.
Be precise in your symbolic translation, careful in constructing your truth table, and thoughtful in your reflection. Below, you’ll find an example of what I’d like to see:
Original Argument:
If it is raining, then the ground will be wet. It is raining. Therefore, the ground will be wet.
Standard Form:
Premise 1: If it is raining, then the ground will be wet.
Premise 2: It is raining.
Conclusion: The ground will be wet.
Symbolic Translation:
Let P = “It is raining”
Let Q = “The ground will be wet”
The argument in symbolic form is:
Premise 1: P—–>QUnknown node type: br
Premise 2: PUnknown node type: br
Conclusion: Unknown node type: brQ
Here is the truth table:
P (It is raining) Q (The ground will be wet) P—>QUnknown node type: br P Conclusion Unknown node type: brQ
T T T T T
T F F T F
F T T F T
F F T F F
Evaluation:
Because in every instance where the premises are true, the conclusion Q is also true, this argument is valid. The truth table confirms that when P and P→Q are both true, Q is true, which satisfies the conditions of a valid argument.
Reflection:
Reflecting on this exercise, my initial intuition was that the argument seemed valid because it followed a structure I recognized as modus ponens. The truth table confirmed this, showing that the conclusion must be true whenever the premises are true. This analysis was straightforward because of the simplicity of the argument. However, if there had been more connectives or multiple statements, constructing the truth table would have been more challenging and would require careful attention to detail.