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An Introduction to Logic

Posted Aug 5, '11 at 12:43pm

snowguy13

snowguy13

2,172 posts

@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?

 

Posted Aug 10, '11 at 10:24am

Moegreche

Moegreche

3,391 posts

Moderator

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!

 

Posted Aug 12, '11 at 11:37am

snowguy13

snowguy13

2,172 posts

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."
 

Posted Aug 13, '11 at 2:21am

Moegreche

Moegreche

3,391 posts

Moderator

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.

 

Posted Aug 16, '11 at 11:06pm

snowguy13

snowguy13

2,172 posts

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.

 

Posted Sep 1, '11 at 1:51am

thepunisher93

thepunisher93

1,863 posts

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

 

Posted Sep 21, '11 at 10:50pm

Darkroot

Darkroot

2,879 posts

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.
 

Posted Sep 24, '11 at 11:50pm

BigP08

BigP08

1,469 posts

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.
 

Posted Sep 29, '11 at 9:18pm

zeakers

zeakers

3 posts

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
?

 

Posted Oct 24, '11 at 11:24pm

darkengy

darkengy

207 posts

Does anyone know the Box of Contradiction?

 
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