1. Assessing arguments vs. assessing conclusions: The question of whether an argument is good is different to the question of whether you agree with the conclusion. For example: Gaunilo agreed with the conclusion of Anselm’s argument — he, like Anselm, thought that God existed. But Gaunilo did not think Anselm’s argument was a good argument. He thought Anselm’s argument doesn’t give you a good reason to believe that God exists.
When assessing arguments, make sure to keep your assessment of the argument separate from your opinion about the conclusion.
2. Technical definition of validity vs ‘logical chain’: several of you found the definition of validity hard to wrap your minds around.
(Let me remind you: an argument is valid if and only if it is impossible that (the premises be true and the conclusion false)).
You found it especially difficult when dealing with some of the tricky cases — the valid arguments with inconsistent premises that seemed to have nothing to do with the conclusion. Let me start by saying that you shouldn’t worry too much about this. All valid arguments with inconsistent premises are bad arguments, because they are all unsound, and obviously so. We will not be looking at any more such arguments in this course.
Anyway; several of you thought we were getting something wrong, because you had an alternative definition of validity in mind: one that has something to do with a `logical chain’ from premises to conclusion.
It is completely right that when people talk of the conclusion of an argument ‘following’ from the premises, they often have something like ‘the premises and conclusion forming a logical chain’ in mind. But, when we philosophers define validity, our immediate project is not to try to capture exactly the idea of the conclusion of an argument following from its premises.
(It is actually very difficult to capture exactly the idea of the conclusion of an argument following from its premises. To do it in an accurate way we would need to do what logicians call ‘model theory’. But that is by the by.)
Our project instead is this: We are looking for a feature of arguments, such that, when you see an argument has this feature, and you see that the premises of the argument are true, then you must accept the conclusion. The simplest such feature is validity the way we have defined it.
It has turned out to be very fruitful for philosophers (and logicians, and computer scientists, and others) to concentrate on this feature. The point of the exercises on validity was to try to get you to concentrate on it. We wanted you to apply the technical definition strictly and literally, without relying on your feelings about what follows from what.
3. Truth and falsehood vs possibility and impossibility: The definition of validity involves both the notion of truth and the notion of possibility. This can be a little confusing. Let us try to make things clearer.
Imagine you have all of the possible ways the world could be lying in front of you, like grains of sand. At one special grain, things are exactly the way they really are — you are reading these words at this time, Manmohan Singh is Prime Minister of India in 2013, the Pacific Ocean is the largest Ocean in the world, and so on. But at other grains of sand, things are different. At some grains, you aren’t reading these words now; you are riding a bike instead. At some grains, Sushma Swaraj is Prime Minister of India in 2013 instead of Manmohan Singh. At some grains, the tectonic plates moved differently, and the Atlantic is the biggest ocean in the world.
Every single way things could have been is out there somewhere, in one of those grains of sand.
Now, for something to be true is for things to be that way at the special grain of sand — the one that corresponds to how things really are. What is going on at the other grains of sand has nothing to do with what is true. Similarly, for something to be false depends only on that special grain of sand.
However, for something to be impossible is for there to no grains of sand at all where the thing is true. You need to look at all the grains of sand to know if something is impossible or not.
Now let’s get back to our definition of validity. It contains the following phrase:
it impossible that (the premises be true and the conclusion false)
What does that mean? It means there is no single grain of sand where the premises are true and the conclusion is false. That’s what it takes for an argument to be valid. And that is all it takes. As long as there are no grains where the premises are true and the conclusion is false, the argument is valid.
4. On Definitions: Sometimes we define a notion and see whether there is anything that conforms to that definition. For example, Anselm defines God as ‘something than which nothing greater can be thought’.
As some people have pointed out, there are different ways to define God. However, our goal is not to capture every notion of God; rather, our definition only seeks to identify a very specific conception of God. The question is whether God as Anselm defines Her exists. The conclusion of the argument is that ‘something than which nothing greater can be thought’ exists.
It is an interesting question how that thing, if it exists, relates to what people traditionally call God. Has that thing spoken to prophets throughout history? Can that thing speak at all? Did it create the universe? Unclear; we’d need more arguments to know.
This means that Anselm’s argument might be less interesting than you hoped. Even if the argument works, it does not establish everything you might like to establish. But it is still pretty interesting. It would be pretty amazing if something than which nothing greater can be thought really existed.
In a course that was exclusively about God, we would think about all the different conceptions of God and see whether there were good or bad arguments for each one. Since this is a survey course, however, we must constrain our investigations. In any particular argument, we will try to find both a relatively clear and relatively interesting conception of God, and see if that argument works for that conception.
When you are assessing an argument for the existence of God, try to keep two things separate. First, try to think about whether the argument works for the definition of God being used in the argument. When you have sorted that out, then think about what the conclusion of the argument entails for other conceptions of God.