Deductive logic. Has a nice ring to it. Mathy. Maybe you're already intimately familiar with it. But in case you aren't, or you want a refresher, or whatever, I thought I'd try my best to summarize how someone can use deductive logic in a kind of everyday way. The Everyperson's Logic, as it were.

The idea is simple: let's say you have a point you want to make, but not everyone agrees. To convince them, you craft an argument. You have your final point---your conclusion---and to convince people, you have a bunch of other points---premises---that support your conclusion. The idea behind deductive logic is this: strong arguments have conclusions that

**cannot**be false if the premises are true.

Let's look at the following (very simple) argument:

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P1. All carrots are root vegetables.

P2. All root vegetables grow in the ground.

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C. All carrots grow in the ground.

Where P1 and P2 are premises and C is the conclusion. Note that it is impossible for the conclusion to be false if we agree that the premises are true. Logicians have different words for this---we'll call it "logically coherent" or "valid."

P2. All root vegetables grow in the ground.

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C. All carrots grow in the ground.

Where P1 and P2 are premises and C is the conclusion. Note that it is impossible for the conclusion to be false if we agree that the premises are true. Logicians have different words for this---we'll call it "logically coherent" or "valid."

Let's look at another example:

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P1. All dogs love meat.

P2. My cat loves meat.

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C. My cat is a dog.

This argument is

P2. My cat loves meat.

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C. My cat is a dog.

This argument is

*not*logically coherent. That is, both premises can be true, but the conclusion may not be true. We can easily conceive of a counterexample---a cat that loves meat but is not a dog.Let's look at one more:

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P1. Basketball is a team game.

P2. All team games are made of chocolate.

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C. Basketball is made of chocolate.

Is this argument logically consistent?

Yes.

It is logically consistent because

The problem with this argument is not about its consistency---it's about something else. We could call this it's "soundness," or its "actual truth value," or whatever. In other words, the argument is logically consistent, but we believe one of the premises is false. Let's call a "sound" or "actually true" argument one that is a) logically consistent/valid and b) one in which all premises are indeed true.

P2. All team games are made of chocolate.

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C. Basketball is made of chocolate.

Is this argument logically consistent?

Yes.

It is logically consistent because

*if*the premises*were*true, the conclusion would have to be true.The problem with this argument is not about its consistency---it's about something else. We could call this it's "soundness," or its "actual truth value," or whatever. In other words, the argument is logically consistent, but we believe one of the premises is false. Let's call a "sound" or "actually true" argument one that is a) logically consistent/valid and b) one in which all premises are indeed true.

In deductive logic, the concern is not with the actual truth value of premises---the concern is with validity/consistency. We can model validity in the same way we model algebraic equations:

P1. If x then y

P2. x

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C. y

Plug any statement into x and y and the argument will be logically consistent.

If you want to learn more about the theory behind deductive logic, then you'll be looking more at this kind of stuff. But even without knowing how to prove that if x then y is equivalent to not(x and not y), knowing how to break arguments down into their premises and calculate logical consistency is helpful. Why? Because if you can break down an argument into its premises, then one of three things will happen:

a) you will notice a hole in the argument's logic---that is, maybe the argument is not logically consistent. Someone could oppose the argument by presenting a counterexample in which all premises are still true but the conclusion is false.

b) you will notice that the argument is consistent, but that one of the premises is actually false. Someone could oppose the argument by providing a counterexample to that premise.

c) you will notice that the argument is consistent

*and*that all of its premises are plausible. There is no clear way to oppose this argument unless one of the premises is discovered to be false.

So how do you guarantee that your argument is logically consistent?

Well, that's not always easy. But the basic test is this:

Step 1: Write out your premises. Use consistent language (always refer to something the same way, don't use superfluous words, avoid pronouns). Write conditional statements as "if/then." + Show Spoiler [why?] +

Conditional statements are tricky. I made a mistake with one myself when I posted this. Take the statement "If it rains, then the ground will be wet." Let's assume we agree that this statement is true. Now, say we look outside and see that the ground is wet. Does this mean logically that it rained?

No. Just because the ground is wet does not mean it rained.

All this conditional statement tells us is that these two facts will never occur simultaneously: it will never be the case that a) it rains and b) the ground is

**not**wet. But if it doesn't rain then the ground could be wet or dry, and if the ground is wet then it may not have rained.

If you don't write out your conditionals like this, it can be very easy to make a mistake with this, and think that your conditional statement makes your argument logically valid when in fact it does not.

Step 2: Write out your conclusion. Use the same language as your premises.

Step 3: See if you can write out a counterexample---that is, an example in which all the premises are true but the conclusion is false.

If you want, you can model your premises with some basic variables. Like this somewhat unwieldy argument:

P1: An esports game is enjoyable to watch if and only if that esports game lasts at least 25 minutes.

P2: All Starcraft games are Esports games.

P3: 75% of Starcraft games last 25 minutes.

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C. 75% of Starcraft games are enjoyable to watch.

Modeled as:

P1. An E is W if and only if E is C.

P2. All S are E.

P3. 75% of S are C.

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C. 75% of S are W.

The language in this argument isn't even as refined as a logician might prefer, but it can still reduce to some simple variables that make the consistency much easier to see.

Have fun with logic!