ForumsWEPRAn Introduction to Logic

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Moegreche
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Moegreche
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Part 1: ARGUMENTS

The entire purpose of the logic we're looking at is assessing arguments. So it'll be helpful to understand exactly what an argument is. Here's a working definition:

ARGUMENT: A series of propositions consisting of premises which are purported to support a conclusion.

Of course, to understand this definition, we need to know what a proposition, premise, and conclusion are.
A proposition is a special kind of statement - it's one that can be true or false. Obviously, questions like 'What time is it?' can't be true or false. And neither can commands like 'Shut the door.'
A proposition says something about the world. Here are some examples of propositions:

1) It is sunny outside.
2) Mercury is the closest planet to the sun.
3) All mammals lay eggs.

Notice that 3 is false. But that's okay, it's still a proposition. Remember, these are statements that can be true OR false. As it turns out, there are some philosophers who have some strong arguments about what is and isn't a meaningful proposition. But that discussion is for an Analytic Philosophy class. We don't really care about these things in logic. If it's something to make sense to say it's true or false, then it's a proposition.

So an argument consists of premises and a conclusion. The premises are propositions that give you a reason to accept the conclusion, which is also a proposition. The conclusion is what you're supposed to, well, conclude! Here's as example:

1) All men are mortal.
2) Socrates is a man.
3) Therefore, Socrates is mortal.

In this argument, 1 and 2 are the premises which support 3, the conclusion. You can usually tell the conclusion by keywords like 'therefore' 'so' and 'thus.'
Look back at the definition of an argument - notice it says that the premises are PURPORTED to support the conclusion. That just means that they are intended to give support - but they may fail miserably. The result would be a bad argument, but it's still an argument. Here's an example:

1) Monkeys like bananas.
2) I like bananas.
3) Therefore, I'm a monkey.

In this argument, the premises lend very little support to the conclusion. You may even have an argument where the premises have nothing at all to do with the conclusion. But these are still arguments - just really bad ones!

So now you know what an argument is. Up next, we'll go over the basics of how to assess an argument. This, remember, is the central goal of logic (at least, the logic we're talking about).
It's worth noting here that the kind of logic we'll be talking about is called PROPOSITIONAL LOGIC. This logic deals with, you guessed it, propositions. Overall, it's very weak - there are many arguments it can't assess.
More powerful logical systems like predicate logic and modal logic can handle more arguments. But you have to walk before you can run, and this kind of logic is a very good place to start. If you can understand this, you'll have a much easier time learning more powerful logical systems.

These are the basics, so if there are any questions, please post them. It's vital that you understand these definitions so that the next part will make sense.

  • 114 Replies
calemango
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calemango
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Balls are bouncy
Bowling Balls are balls.
Bowling Balls are probably bouncy

Everyone knows a bowling ball cant bounce so it probably shouldn't b called a ball but it is because it has the same characteristics but not (ex.) weight.

snowguy13
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Wait a second! You're problem is in the statement "Balls are bouncy", I think. All balls (all objects in general) have an amount of elasticity, but some items have less than others. "Ball" refers to a round object (in simple terms), but has nothing to do with how elastic an object it. So, I believe that would mean that your conclusion is logically true, but that your first statement "Balls are bouncy" may not necessarily true, since all balls are obviously not bouncy. Phew! :O

I'm not even sure if everything I said about logic is right. Was it right, Moegreche?

Moegreche
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Moegreche
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I'm not even sure if everything I said about logic is right. Was it right, Moegreche?


Seems right to me. Since calemango's first premise is false, the argument is valid, but not sound. Although his conclusion makes the argument seem like an inductive, rather than deductive one. If that's the case, then the following would be a good argument:

1) Most balls are bouncy.
2) Bowling balls are balls.
3) Therefore, bowling balls are probably bouncy.

This is a sound and cogent inductive argument (assuming that most balls are bouncy - I'm not sure this is true, but it seems reasonable.
With inductive arguments, you can have a false conclusion. These kinds of arguments don't guarantee the truth of the conclusion, but only make it more likely. I never really went over inductive arguments, even though these are the most common kind of argument you see in everyday life. The reason is that the analysis of these arguments is highly problematic and complicated. Trying to get an argument like this into a logical form turns into quite a mess. For starters, even capturing what is meant by 'most' is logical terms is very tricky.
EmperorPalpatine
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EmperorPalpatine
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Everyone knows a bowling ball cant bounce

I rolled one badly earlier today and it bounced a good 2 feet.
snowguy13
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@Moegreche

Okay! Thank you very much for explaining that!

When you say inductive and deductive, I'm not completely sure what you mean.

This is what I think I know:
Deductive conclusions are those that are undeniably true based on the premises.
Inductive conclusions are conclusions that may be true based on the premises, but may be determined by other information as well.

^Is this understanding correct?

Moegreche
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Moegreche
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Yeah, pretty much. Just to fill in any holes (if there are any) here are some definitions that you might find in a textbook.

Deductive Argument: an argument in which the premises purport to guarantee the truth of the conclusion.

Inductive Argument: an argument in which the premises purport to make probable the truth of the conclusion.

Some important things to note. First, notice the definitions say that the premises 'purport to guarantee' or 'purport to make probable'. This just means that they are intended to do that.
Here are 2 examples:

All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.

All dogs have 4 legs.
This animal has 4 legs.
Therefore this animal is a dog.

Both of these are classified as deductive arguments because the premises are intended to guarantee the conclusion's truth. But notice the Socrates argument does this quite well while the Dog argument does not. So, the first argument is deductively valid while the second is deductively invalid. Hopefully you can see where the flaw in the Dog argument is and how we might go about fixing it.

Here's an inductive argument:

Most mammals give live birth.
This animal is a mammal.
Therefore this animal probably gives live birth.

In this case, it's possible for the premises to be true and the conclusion false, so it's not deductive. But if the premises are true then the conclusion is supposed be quite probably true. Typically this means the probability of the conclusion being true is greater than 0.5. A successful inductive argument can further be classified as moderate or strong. An unsuccessful inductive argument would be classified as weak. Here's an example:

Some football players are left-footed.
Wayne Rooney is a footballer.
Therefore Wayne Rooney is probably left-footed.

This would be a weak inductive argument even if Rooney was left-footed because the premises don't break that 0.5 threshold.
Hope this helps!

snowguy13
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So, if both premises are indisputable (all men are mortal), the argument is deductive, whether the conclusion is valid or invalid?

And, for the dog one:

All dogs have 4 legs.
This animal has 4 legs.
Therefore this animal is a dog.

Would this be a better phrasing?
"All dogs have four legs.
This animal is a dog.
Therefore, this animal has four legs."
Moegreche
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Moegreche
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Remember, validity is a property of arguments, not conclusions. You can look back in the first few pages for a full discussion of validity. If an argument is deductively valid and sound, then the conclusion must be true, necessarily.
But your reworking of the dog argument is spot on, well done. This is a good example of a deductively valid argument. If the premises are true, then the conclusion must be true. Of course, I'm sure you realize that the argument is not sound because one of the premises is false: not all dogs have four legs. But for validity, all we care about is what the argument would be like if the premises were all true.

snowguy13
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snowguy13
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So validity has to do with the relationship between the premises and the conclusion. If a conclusion can be reached reasonably via the premises, then the argument is valid, whether or not the premises are true (whether or not the argument is sound)?

About the dog example, would this be a more realistic and life-like argument?
"Most dogs have four legs.
This animal is a dog.
Therefore, it probably has four legs."

^To me, that's almost exactly what goes on in my head (almost subconsciously). When someone mentions a dog, I imagine a four-legged animal, but also acknowledge the fact that it may have fewer than four legs.

thepunisher93
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thepunisher93
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this is a thread
i aay it is lame
so
it is lame

Darkroot
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Darkroot
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this is a thread
i aay it is lame
so
it is lame


Hardly, basic philosophical logic is the same as discrete mathematical one. Computer are built with the same rules by the way of logic gates. So if you like using computers then you must admit that this stuff is not lame at all.
BigP08
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this is a thread
i aay it is lame
so
it is lame


I think you mean:
What I say is always true.
I say this thread is lame.
Therefore, it is lame.

I disagree, but your argument would be deductively valid. It would just be unsound because you would have to demonstrate a confirmer for the first premise, which would be near impossible.
zeakers
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zeakers
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Bob is is sponge who lives under the sea, and my name is bob, therefore i live in a pineapple under the sea and am square
?

darkengy
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darkengy
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Does anyone know the Box of Contradiction?

jeol
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jeol
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I disagree, but your argument would be deductively valid. It would just be unsound because you would have to demonstrate a confirmer for the first premise, which would be near impossible.

Most of that is based on opinion, though. Logic is about the facts, at least the facts presentable.
Bob is is sponge who lives under the sea, and my name is bob, therefore i live in a pineapple under the sea and am square
?

Let's sort this out: (I'm new at this, so if I mess up, sorry 'bout that)

Bob is a sponge who lives under the sea.
My name is Bob.
Therefore, I live in a pineapple under the sea and am square.

I'm not exactly sure where the living in a pineapple and being square came from. The argument itself is an invalid deductive argument, am I right? If the facts presented were to cross-connect:

Bob is a sponge who lives under the sea.
My name is Bob.
Thus, I am a sponge who lives under the sea.

The reason it is invalid is because it is a weak analogy - While the premises may be true, the conclusion might be false. It isn't sound because it isn't valid and the two premises might be false (though they are presumably true. Is your name really Bob? Is there really someone named Bob who is a sponge who lives under the sea? Maybe there is a sponge dubbed 'Bob' who lives under the sea. I don't know that, though). Since it gives a definite conclusion, it is deductive.
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