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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.
If you need any logic or ways to win an argument, come talk to me.
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
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
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?
4) Then, from fact 1, there are no life forms in the universe as the total mass of all life forms is zero.
In a way this is similar to the inequations:
3 > 2 ( 3 higher than 2)
2 > 1 ( 2 higher than 1)
3 > 1 ( 3 higher than 1)
and i understand validity but not sound and how is valid and sound an argument where nothing is related?
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.
Actually, I kinda left out some steps here- perhaps this will make it easier to follow my "logic":
3) Then, the density (mass per volume) of living things in the universe is 0, since the volume of the universe is infinite.
and i understand validity but not sound and how is valid and sound an argument where nothing is related?
and i understand validity but not sound and how is valid and sound an argument where nothing is related?
4) Then, on average every finite subsection of the universe contains exactly zero life. (A "finite subjection" here is like a bounded region of the universe)
But your fact (1) talks about the mass of life, not its density over some area. Thus (4) is an unsupported subconclusion.
Your reductio makes perfect sense to me. But then again, one could use a reductio against a variety of arguments that incorporate claims about infinity. But this doesn't mean that there is an actual contradiction in the premises.
I suppose we could try to formalise the argument, but I'm thinking that this will be beyond my limited abilities as a logician. Trying to formalise the notion of an infinite universe, for example, is going to be very problematic. I'm not even sure how it would be done. We would need something more than a mere property statement (it would seem), but I'm just not sure what that 'something more' would amount to. At any rate, it's something fun to think about!
But this doesn't mean that there is an actual contradiction in the premises.
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.
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