Recommended resources
The freely available resources this lesson will direct you to.
Hello! Welcome back to our capstone module on applying analytic methods.
In our last lesson, we focused on the essential first step of philosophical analysis: deconstructing an argument to identify its premises, conclusion, and underlying logical form. We saw how formalization, a technique familiar from your mathematics background, can reveal structural weaknesses that are hidden in natural language.
Today, we take the crucial next step. It's not enough to know an argument's structure; we must also judge its quality. This lesson addresses the learning outcome: Evaluate the soundness of a philosophical argument by assessing its premises and inferential strength. We will develop a two-part test for any deductive argument, allowing you to determine whether it provides good reason to accept its conclusion.
1. The Two Pillars of a Good Argument: Validity and Truth
When we evaluate a deductive argument, we need to ask two distinct questions:
- Does the conclusion logically follow from the premises? (This is a question about the argument's form or inferential strength).
- Are the premises actually true? (This is a question about the argument's content).
A good deductive argument must pass both tests. An argument can fail by having faulty reasoning, by being based on false information, or both. The following video provides an excellent visual flowchart for these concepts.
Deductive vs Inductive Reasoning FLOW CHART | Valid, Sound, Strong, & Cogent
This short video, 'Deductive vs Inductive Reasoning FLOW CHART', offers a clear map of the key terms we'll be using. It brilliantly separates the evaluation of an argument's reasoning from the evaluation of its premises.
Please watch from the beginning to 03:04, and then from 04:34 to 08:01. Focus on the distinction between the 'reasoning' level (valid/invalid) and the 'truth' level (sound/unsound).
As the video illustrates, the first step is to analyze the argument's internal logic, temporarily setting aside the question of whether the premises are true. This brings us to the concept of validity.
2. Assessing Inferential Strength: Validity
In logic, validity has a precise, technical meaning. An argument is deductively valid if and only if it is structured such that if the premises are true, then the conclusion must be true. In other words, it's impossible for a valid argument to have all true premises and a false conclusion.
Validity is a property of the argument's logical form, not its content. An argument can be valid even if its premises and conclusion are factually absurd.
To delve deeper into this crucial concept, let's turn to a foundational text on philosophical arguments by Jim Pryor.
The article 'Philosophical Arguments' provides a rigorous but clear explanation of the core concepts of argument analysis. It will solidify the definitions we'll be working with.
Please read the sections 'Different Flavors of Argument', 'What Makes a Deductive Argument Good?', and 'Valid Arguments'. Pay close attention to the examples of valid arguments with false premises, like the 'Bugs Bunny is a reptile' argument. This drives home the point that validity is about structure alone.
As Pryor explains, one way to test for invalidity is to find another argument with the same logical form that has true premises and a false conclusion. For example:
| Argument to Test | Logical Form | Counterexample |
|---|---|---|
| 1. If Socrates was a philosopher, then he wasn’t a historian. 2. Socrates wasn’t a historian. 3. So, Socrates was a philosopher. |
If P then Q. Q. So, P. |
1. If Socrates was a horse, then he was warm-blooded. (True) 2. Socrates was warm-blooded. (True) 3. So, Socrates was a horse. (False) |
Since the form If P then Q. Q. So P. can lead from true premises to a false conclusion, it is an invalid form, known as the Fallacy of Affirming the Consequent. The original argument about Socrates is therefore invalid, even though its conclusion happens to be true.
Test your understanding!
Using the definitions from the resources, determine if the following argument is valid or invalid. Explain your reasoning.
- If the moon is made of green cheese, then cows jump over it.
- The moon is not made of green cheese.
- Therefore, cows do not jump over the moon.
Show answer
The argument is invalid. Its logical form is: If P then Q. Not-P. Therefore, not-Q. This is a common formal fallacy known as the Fallacy of Denying the Antecedent. Just because the "if" part (the antecedent) is false, it doesn't guarantee the "then" part (the consequent) is also false. We can create a counterexample with this form that has true premises and a false conclusion:
- If Socrates was a horse (P), then Socrates was mortal (Q). (True, since the premise P is false)
- Socrates was not a horse (Not-P). (True)
- Therefore, Socrates was not mortal (Not-Q). (False)
Since the form can lead from true premises to a false conclusion, it is invalid.
3. Assessing the Content: The Truth of the Premises
Once we've confirmed an argument is valid, we move to the second question: are the premises actually true?
This step moves from formal logic to critical thinking about the world. Assessing premises involves:
- Checking empirical facts.
- Questioning definitions.
- Uncovering hidden or implicit premises.
- Evaluating the plausibility of moral or metaphysical claims.
Often, the most contentious part of a philosophical argument isn't its logical form, but the truth of one of its premises.
This video gives practical examples of how to critically probe the premises of an argument.
Analyzing the argument - Part 1 of 2
Let's watch 'Analyzing the argument' to see how this process works in practice. The video uses everyday examples to show how to question the evidence and assumptions that make up an argument's premises.
Watch from 00:41 to the end (04:59). Notice how the speaker questions the premises in the Hawaii and cell phone examples. They ask about subjective terms ('beautiful'), implied causal links ('correlation'), and the strength of evidence ('possible cause').
4. Putting It Together: Soundness
We can now define the gold standard for a deductive argument. An argument is sound if and only if it meets two conditions:
- It is valid.
- All of its premises are true.
Because a valid argument with true premises cannot have a false conclusion, a sound argument always has a true conclusion. This is the power of a sound argument.
Let's return to the Pryor reading to solidify this final concept.
This section of Pryor's 'Philosophical Arguments' ties everything together.
Please read the sections 'Implicit or Hidden Premises' and 'Sound Arguments'. The key takeaway is this: if you disagree with the conclusion of a deductive argument, you are committed to claiming it is unsound. You must either show that its reasoning is invalid or that at least one of its premises is false.
This principle is the engine of philosophical debate. It's not enough to simply reject a conclusion; you must diagnose the flaw in the argument presented for it.
Test your understanding!
Evaluate the following argument for soundness. Is it sound or unsound? If it's unsound, what is the flaw?
- All engineers are human.
- All humans are mortal.
- Therefore, all engineers are mortal.
Show answer
This argument is sound.
- Validity: It has a valid logical form known as a Hypothetical Syllogism (or Transitive Reasoning):
All A are B. All B are C. Therefore, all A are C.The conclusion logically follows from the premises. - Truth of Premises: Premise 1 ("All engineers are human") is true. Premise 2 ("All humans are mortal") is true.
Since the argument is both valid and has all true premises, it is sound. Therefore, its conclusion must be true.
5. Practice Applying the Concepts
Your mathematics background gives you an advantage in quickly identifying logical forms. The following resource provides a set of exercises designed to test this skill.
PART 2 MODULE 5 ANALYZING PREMISES, FORMING ...
This PDF, 'ANALYZING PREMISES, FORMING CONCLUSIONS', offers a number of short arguments for analysis. It is a great way to practice rapidly assessing inferential strength.
Look at the 'PRACTICE EXERCISES' section. Try problems 1, 2, 4, and 6. For each, determine if a valid conclusion is warranted. You can check your answers in the 'ANSWERS TO PRACTICE EXERCISES' section at the end. This will help sharpen your ability to distinguish valid forms (like #1, Contrapositive Reasoning) from invalid ones (like #2, Fallacy of the Inverse).
Conclusion
Today we have built a complete toolkit for evaluating deductive arguments. This two-step process—assessing validity and then assessing the truth of the premises—is fundamental to the entire discipline of analytic philosophy.
Key Takeaways:
- Validity vs. Soundness: Validity concerns only the argument's logical structure, while soundness requires both validity and true premises.
- The Two-Step Evaluation: To evaluate an argument, first check its validity (is the inference logical?). If it is, then proceed to check the truth of its premises.
- Soundness Guarantees Truth: A sound argument forces acceptance of its conclusion.
- The Burden of Disagreement: To reject a conclusion supported by a deductive argument, you must identify a flaw in the argument—either it is invalid, or at least one premise is false.
In our next lesson, we will move from analyzing and evaluating other people's arguments to creating our own. You will learn how to construct a formal argument for a given philosophical thesis, anticipating and addressing potential objections, putting the skills from the entire course into practice.