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An Introduction to Logic

Posted Nov 23, '12 at 2:49pm

Moegreche

Moegreche

2,853 posts

Moderator

Fruits are edible.
Vegetables are edible.
Therefore, fruits are vegetables.

There! That should solve all those conspiracies about, "Is pumpkin a fruit or a vegetable?"

So here we have a prime example of a logical fallacy. This fallacy is knows as 'affirming the consequent'. I haven't looked through the 'lecture' pages in quite some time, but I would hope that this fallacy should be evident through those discussions.
So clearly the above argument isn't right. In other words, the conclusion is clearly false. So when we go about assessing an argument with an obviously false conclusion, we need to figure whether 1) the argument is invalid, or 2) the argument is unsound.
For the most part, people will give argument that are unsound - that is, you can reject one of the premises as being false. But the argument we have on hand in invalid - i.e. not valid. Can you see why?
Remember that validity is a feature of an argument's structure. It doesn't matter whether the premises are true - this is a matter of whether the argument has a valid structure or not. You can use logic to show that an argument is invalid (although the logic that is presented in this thread is not powerful enough to do this). But you can also use a more intuitive method. All you need to do is present an argument with the same structure that is clearly invalid.

So, here's the structure of the above argument:

All X are Z.
All Y are Z.
Therefore, all X are Y.

Now all you have to do is plug in terms to show that the above argument is clearly invalid (although the fact that the premises are true and the conclusion false should give this away immediately). But try this on:

All dogs are mammals.
All cats are mammals.
Therefore, all dogs are cats.

Again, we've just plugged different terms into the structure of the argument, and clearly this argument has a false conclusion. This is because the argument structure is invalid. As I mentioned before, this is the fallacy of affirming the consequent, and we can see now why this is a fallacy. It takes more sophisticated logic to prove this (compared to what's been presented in this thread) but it should be intuitively clear that this argument is invalid.a

 

Posted Dec 9, '12 at 3:39pm

theEPICgameKING

theEPICgameKING

458 posts

After reading this, I feel as though I will win any debate/argument/court case.
In the case of:
All dogs are mammals.
All cats are mammals.
Therefore, all dogs are cats
And assuming you dont know the conclusion is false, we must also assess the validity of the Subjects in each line. IE: Dogs, Cats, and mammals. By working each Subject down to atomic level and finding at least ONE difference between dogs and cats, we therefore prove that the conclusion is false. IE: counterexample.
Wow, with logic, you really dont need to know anything in order to learn everything.

 

Posted Dec 24, '12 at 4:34pm

SaifurRahman

SaifurRahman

73 posts

If you need any logic or ways to win an argument, come talk to me.

 

Posted Dec 25, '12 at 12:23am

pangtongshu

pangtongshu

8,704 posts

If you need any logic or ways to win an argument, come talk to me.

i think I'll stick to this guide...but if I really need to talk to someone I'd much rather talk to Kasic

 

Posted Dec 25, '12 at 12:24am

pangtongshu

pangtongshu

8,704 posts

Sorry didn't get to finish

MGW, nich, Von, or partydevil

 

Posted Sep 27, '13 at 12:37pm

mbbs112

mbbs112

174 posts

This was an excellent guide Moegreche ^_^.

 

Posted Nov 29, '13 at 9:24pm

jorgedbp96

jorgedbp96

4 posts

There is not life in the universe
The Earth is in the universo
Therefore there is not life in Earth

There is life in the Earth
Earth is a planet
Therefore there is life in other planets

 

Posted Nov 30, '13 at 10:15am

Moegreche

Moegreche

2,853 posts

Moderator

There is not life in the universe
The Earth is in the universo
Therefore there is not life in Earth

A valid argument, but it's not sound (notice premise 1 is false). But there's an interesting sort of argument that hinges on the ambiguity of the 'in' relation. Consider the following:

1) There is a pain in my finger.
2) My finger is in my mouth.
C) Therefore, there is a pain in my mouth.

We might say there's a fallacy of equivocation going on here. Notice that the use of the word 'in' in (1) is subtly different from (2).

There is life in the Earth
Earth is a planet
Therefore there is life in other planets

An invalid argument, though close to being valid and sound. If we changed 'in other planets' in the conclusion to 'on a planet', we'd have a valid and sound argument :)

 

Posted Dec 1, '13 at 5:57pm

aknerd

aknerd

1,276 posts

Hmm... I'm going to try to be tricky here.

Suppose (Ie, assume these statements are true):
1) The universe is infinite in size, and
2) All non-earth locations do not contain life.

Facts:
1) Life forms must have mass, that is, all living things must be made of matter
2) Matter has a finite, maximum density

Therefore:
1) The maximum volume of all living things cannot exceed the volume of Earth, since we are assuming that there are no living things not on Earth.

2) Then the mass of all living things must be at most finite, since they occupy a finite volume (from fact 2)

3) Then, the density (mass per volume) of living things in the universe is 0, since the volume of the universe is infinite.

4) Then, from fact 1, there are no life forms in the universe as the total mass of all life forms is zero.

I know where I went wrong, do you?

 

Posted Dec 1, '13 at 6:29pm

pangtongshu

pangtongshu

8,704 posts

4) Then, from fact 1, there are no life forms in the universe as the total mass of all life forms is zero.

This seems to be contradictory to one of your first statements
2) All non-earth locations do not contain life.
But, then I would be assuming the converse is correct, which you never established.

 
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