Philosopher's Toolkit

Validity and Soundness

• Validity

  • First, we need to know whether an argument is valid. Validity refers to the logical part of an argument - it asks whether what has been presented logically follows. It assumes, for the sake of the argument, that what is being said is actually true.
  • Therefore, an argument is valid where, if the premises are true, it logically follows that the conclusion is true.
  • A really simple example would be is Aquinas’ cosmological argument for the existence of God —
    • Premise 1: Everything that exists has a cause.
    • Premise 2: Infinite regress is impossible (that is, the chain of causes has to stop somewhere — it can’t go on for infinity).
    • Conclusion: Therefore, there has to be a first causer. We call that being “God.”
  • This argument is valid because if we assume, for the sake of argument, that Premise 1 & 2 are true, it logically follows that the conclusion is true. If the argument isn’t valid, it’s incoherent and doesn’t logically follow — so you should just reject it. But if it is valid, then to determine the argument’s truth; you must go on to assess whether it is sound.

• Soundness

  • Soundness focuses on each of the premises and evaluates their truth.
  • Therefore, an argument is sound  if and only if, the argument is valid, and the premises are in fact true.
  • This is often difficult to establish, of course. In the cosmological case, to determine whether the argument is sound you have to run through each premise, and ask:
    • Does everything really require a cause?
    • Is infinite regress really impossible?
  • As this is a discussion on the existence of God, Philosophers are happy to admit the cosmological argument is valid — but whether the premises are true is widely debated.
  • If you conclude that the argument is sound, then the conclusion is true. In this case, if the cosmological argument is sound — God really does exist.

• Modus Ponens

  • This valid form of argument focuses on a conditional, (if..then…,) along with positive affirmation.
  • It holds the form —
    • Premise 1: If P, then Q
    • Premise 2: P
    • Conclusion: Therefore, Q
  • This is clearly valid. If “every time it’s raining I use an umbrella,” is true, and it is in fact raining — then it follows that I will be using an umbrella.
  • This valid shouldn’t be confused with affirming the consequent. This being an invalid (and false) argument that takes the form —
    • Premise 1: If P, then Q
    • Premise 2:** **Q
    • Conclusion:** **Therefore, P
  • This is obviously incoherent. Assuming “every time it’s raining I use an umbrella” is true, it doesn’t follow that every time I use an umbrella it is raining.

• Modus Tollens

  • This similarly focuses on a conditional but assumes a negation is true to derive truth.
  • It holds the form —
    • Premise 1: If P, then Q
    • _Premise 2: _Not Q
    • _Conclusion: _Therefore, not P.
  • Again, this is clearly valid. If “every time it’s raining, I take an umbrella,” and it’s not raining — I obviously won’t be using an umbrella.
  • This shouldn’t be confused with rejecting the antecedent —
    • _Premise 1: _If P, then Q
    • Premise 2:** **Not P
    • _Conclusion: _Therefore, not Q.
  • Again, it’s clear this doesn’t logically follow. I’ll leave it up to you to think of the reason why.

Inductive & Deductive

• Deductive arguments: If the premises are true, then the conclusion is as a matter of fact, true.
• Inductive arguments: When the premises don't serve to guarantee the conclusion is true. Instead, the premises being true make it probably that the conclusion is true.
  • A common example refers to premises using experience.
  • For example: this swan is white. In fact, every swan I have ever seen is white, therefore — it’s probable that all swan’s in existence are white.
  • Inductive arguments can be persuasive, and make it likely the case that something is true. But they need not guarantee its truth.

• Counterexamples

  • To prove that an inductive argument is false, we need to think up a counterexample that disproves the conclusion. A counterexample is an example that contradicts, and therefore disproves.
  • Some counterexamples might not be so obvious — after all, inductive arguments are persuasive; and seem true at face value. Because of that, we might have to think outside the box if we are going to be successful in thinking some up.
  • If you can’t think of one, then the inductive argument stands — and the conclusion remains probably true.

Fallacies

• Arguments are persuasive even when they're incoherent and false - they have a valid form, but aren't actually valid. Fallacies trick us, leading us to believe a false conclusion.

• False Dichotomy

  • These occur when the person arguing for their conclusion presents you with an ultimatum or dichotomy.
  • They give you two choices and claim that these are the only available options; it has to be one, or the other. They then insist it’s not one of them — and so must be the other.
  • This is a fallacy, because there’s really more than just 2 options – so even if one of them is false, it doesn’t entail that their conclusion is true.
  • Socrates fell down here when giving his Argument of Opposites.
    • He gave an example: “either something is hot, or cold, and cannot be both.”
    • He claimed when something ceases to be hot, it must, therefore, be cold — because it must be either one or the other, and cannot be both.
    • He concluded that “opposites come from opposites: hot comes from cold, and life comes from death.”
  • It looks persuasive, but it's not really true. If that’s the case, the conclusion fails — hot doesn’t necessarily come from cold. And so, opposites don’t come from opposites, and life might not come from death.

• Straw Man

  • These sorts of arguments typically occur as a response or rebuttal of someone else’s ideas.
  • Let’s suppose I present an argument for the Existence of God. Instead of attacking my actual argument, a straw man proposal, will downplay my argument, adapt it, and present it in an evidently false form.
  • It will then attack that weaker argument, rather than my actual one, and conclude by claiming my original claim was false.
  • Of course, this conclusion is misled and unfounded — so watch out for people claiming your wrong and using this method to back it up.

• Ad Hominem

  • This means "attacking the person".
  • Rather than disproving any argument you’ve made, someone committing this fallacy will just attack you in a desperate attempt to discredit you by showing you as unreliable.
  • They’ll call you stupid, point out you’ve lied in the past, or illustrate that you’re typically wrong about these sorts of things.
  • Of course, despite all this — you could still be right.
  • “All the fallacies of human reason had to be exhausted, before the light of a high truth could meet with ready acceptance.” ― Friedrich Max Müller

• These fallacies are all too common. It's important that we don't fall prey to them while assessing the truth of an argument. After all, we wouldn't want to dismiss something that is in-fact valid, true or legitimate.
• To avoid this, we need to be charitable during our Philosophical analysis.
• Rather than assessing or attacking what the author or arguer actually said — you should really present, and assess, their argument in the best light.
• All this means is that, rather than assessing or attacking what the author or arguer actually said — you should really present, and assess, their argument in the best light.
• This is because some people struggle to articulate and present their arguments. But, just because they haven’t made it clear, doesn’t mean there’s no truth there.
• Therefore, in order to avoid falling prey to the straw man fallacy — listen to what’s been said, and ask yourself what the intended argument was. Present it in the best light, and assess that — even if it wasn’t exactly what was said.