The Logic of Vampires

Let’s say we’re trying to prove the vampire rule below.

VAMPIRE RULE: If someone is a vampire, then they drink blood everyday a noon.

Question: Does observing someone drink blood at noon prove this rule?

Answer: No

Why? – We have only observed them on one day (and perhaps on previous days). We have not observed their future behavior.

Note, however, that we may be able to falsify the vampire rule.


Discussion


FMB

Case1: Affirming the antecedent (Correct inference)

Let’s say you think this rule about vampires is true in our world, but you are not sure:

VAMPIRE RULE: If someone is a vampire, then they drink blood everyday a noon.

In our world, knowing that someone is a vampire is a sufficient reason to infer that this individual will drink blood at noon.

This is using the rule correctly. You are affirming the antecedent.

However, it may be that our rule is wrong. In other words, we don’t really know that the rule is true.

Just because we have observed someone’s past behavior doesn’t prove that their behavior will continue in the future. It may be that our putative vampire will not drink blood at noon at some point in the future. Therefore, we may have overgeneralized. Perhaps vampires only drink blood when they feel like doing so. But, they don’t drink blood every day at noon.

On the other hand, we may be able to falsify the vampire rule, even if we cannot prove it. (See Case2 below.)

Consider the case of an ancient society that has always lived near the equator. It may be that they have an empirical rule that one cannot walk on water. In their world, they have never seen frozen water. So, they know nothing of frozen lakes and rivers. But, one day someone may venture out and observe people walking on frozen water. When they return to their society, they may tell others of their new empirical observations. If these observations are confirmed by other travelers, then the society may decide to revise their cannot-walk-on-water rule.


FMB

Case 2: Denying the consequent (Correct inference)

Again, let’s say you think this rule about vampires is true in our world, but you are not sure:

VAMPIRE RULE: If someone is a vampire, then they drink blood everyday a noon.

If we are considering someone who is supposedly not a vampire, then we could test that hypothesis by observing them at noon.

Suppose that we observe that they do not drink blood at noon.

In our world, knowing that someone does not drink blood at noon is a sufficient reason to infer that this individual is not a vampire.

As for the rule itself – our empirical observation that our putative vampire did not drink blood at noon has shown that our rule has resisted falsification in this one instance.

Philosophers have argued about the nature of empirical laws. Can they ever be proven if we don’t know what will happen in the future?

One philosopher, Karl Popper, argued that empirical rules should be judged by there ability to resist falsification.

In Popper’s view, however, empirical rules are always tentative.


FMB

Case 3: Denying the Antecedent (an invalid inference)
Case 4: Affirming the Consequent (an invalid inference)

These are two ways you can go wrong with a rule like this:

VAMPIRE RULE: If someone is a vampire, then they drink blood everyday a noon.

For more on why these two cases are invalid, check out my blog post:

Four Lessons in Simple Logic
https://memeinnovation.wordpress.com/2021/06/03/four-lessons-in-simple-logic/

2 thoughts on “The Logic of Vampires

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