Sumários

Discussion on God's existence

11 Outubro 2024, 13:30 • David Yates

This session was a discussion of the two ontological arguments for the existence of God and the problem of evil as an argument against God's existence. Main points of discussion:

The two ontological arguments depend on conceptions of God that can be resisted (rejecting for example the idea that God is a necessary being, if He exists).
The two ontological arguments also depend on a controversial claim about the role of imagination in modal epistemology, simply: if we can imagine something, then it is possible. Both arguments depend on the idea that the concept of God, as a maximally great being, is self-consistent, and both rely on imagination to establish this.
The problem of evil can be resisted in at least two ways: (i) by claiming that a certain amount of "evil" is necessary for God to create the best of all possible worlds. This is what the freewill defence effectively says; other defences along these lines suggest either that God allows us to suffer so that we can show virtues such as courage, without which the world would be morally less good than it is; or simply that what look to be evils to us need not look that way to God, who sees the entire cosmos at once. One problem for these responses is that it seems very difficult to imagine why e.g. child abuse or animal suffering could possibly be part of God's plan, or could possibly make the world a better place. The problem of natural evil is perhaps the hardest one to deal with: why are there earthquakes, floods and hurricanes?
Alternatively, (ii): we can revise our conception of God so that he is no longer all of omniscient, omnipotent, and benevolent. On this view, God may lack the desire to prevent suffering because he is not morally perfect; or he may lack the power to prevent all suffering, because he is not omnipotent. If we do this, however, we can no longer argue for God's existence based on our conception of Him as maximally great, because according to this response to the problem of evil, God is not maximally great!

Ontological Arguments vs. the Problem of Evil

9 Outubro 2024, 13:30 • David Yates

This week we will examine two versions of the infamous ontological argument for the existence of God. We will begin with Anselm's classic version and consider how an atheist might respond. We will then consider Plantinga's modal version of the ontological argument, and again consider how an atheist might respond. We will then study the problem of evil for theists, and consider how theists might respond. The purpose of these classes is to see how philosophers with opposing views not only offer arguments for their own position, but also need to respond to their opponents' arguments. When you defend a position using an argument, you must respond not only to your opponent's objections to your argument, but also to their arguments for their own position, which you are committed to denying!

Suppose you argue for the existence of God and your opponent argues that there is no God. You can't both be right!
If your argument for the existence of God is sound, then your opponent's argument against God's existence is not sound.
Just because your conclusions are opposite, that doesn't mean either of you has an invalid argument! It's possible that both of you is arguing correctly from a logical point of view, but it's not possible that both arguments are sound.
Your opponent will not only offer a positive argument for the non-existence of God, they will also offer additional arguments either that: (i) your argument is invalid, or (ii) your argument contains at least one false premise.
You will also target your opponent's argument in this way! It all gets very complicated, very quickly. If nothing else, learning the philosophical method will teach you to be humble: are you really that sure of your own beliefs? If so, on what grounds?

Anselm's Ontological Argument

"Thus even the fool is convinced that something than which nothing greater can be conceived is in the understanding, since when he hears this, he understands it; and whatever is understood is in the understanding. And certainly that than which a greater cannot be conceived cannot be in the understanding alone. For if it is even in the understanding alone, it can be conceived to exist in reality also, which is greater. Thus if that than which a greater cannot be conceived is in the understanding alone, then that than which a greater cannot be conceived is itself that than which a greater can be conceived. But surely this cannot be. Thus without doubt something than which a greater cannot be conceived exists, both in the understanding and in reality." Proslogion II (tr. William Mann [1972: 260–1].

Here is one interpretation of this passage, adapted from the Internet Encyclopaedia of Philosophy Entry on Anselm and the Stanford Encyclopaedia Entry on Ontological Arguments (sections 6 and 11):

We can understand the idea of God as a being greater than which no greater being can be imagined (that is, we understand the idea that God is by definition the greatest possible being that can be imagined).
What we can understand exists as an idea in the mind.
Therefore, God exists as an idea in the mind.
A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).
But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)
Therefore, God exists.

This argument attempts to establish the existence of God from the very concept of God. If God is by definition that greater than which nothing can be conceived, then God exists by definition, since if He did not, we could conceive of an even greater being. What, if anything, is wrong with this argument?

Plantinga's Modal Argument

This argument is inspired by Anselm's and is very influential. Instead of arguing that God exists by definition, Plantinga argues that if it is possible that God exists, then it is necessary that God exists. In possible worlds speak, this means: If God exists at any possible world, then He exists at all possible worlds. But the actual world is one of the possible worlds, so if it is possible for God to exist, then God actually exists. Plantinga first defines maximal excellence and maximal greatness:

A being is maximally excellent in a world W if and only if it is omnipotent, omniscient, and morally perfect in W; and
A being is maximally great in a world W if and only if it is maximally excellent in every possible world.

He then argues as follows:

The concept of a maximally great being is self-consistent.
If 1, then there is at least one logically possible world in which a maximally great being exists.
Therefore, there is at least one logically possible world in which a maximally great being exists.
If a maximally great being exists in one logically possible world, it exists in every logically possible world.
Therefore, a maximally great being (that is, God) exists in every logically possible world.

What, if anything is wrong with this argument? How should an atheist respond to it?

The Problem of Evil

Atheists often argue as follows (from Stanford Encyclopaedia of Philosophy):

If God exists, then God is omnipotent, omniscient, and morally perfect.
If God is omnipotent, then God has the power to eliminate all evil.
If God is omniscient, then God knows when evil exists.
If God is morally perfect, then God has the desire to eliminate all evil.
Evil exists.
If evil exists and God exists, then either God doesn’t have the power to eliminate all evil, or doesn’t know when evil exists, or doesn’t have the desire to eliminate all evil.
Therefore, God doesn’t exist.

What, if anything, is wrong with this argument? How should a theist respond to it?

Discussion - The causal argument for physicalism

4 Outubro 2024, 13:30 • David Yates

Now, we will see an example of a real philosophical argument and apply the recipe described in the previous class to generate the alternatives. In this case, it is not at all obvious which of the arguments is the sound one!

Example 2 - The Causal Argument for Physicalism

This argument is more complex and has three premises rather than two. It is not entirely clear that the argument is deductively valid, but we will assume for the purposes of this class that it is valid. If you want to challenge its validity, tell me about that in Friday's class!

P1 Mental events cause physical effects ("efficacy of the mental")
P2 All physical effects have sufficient physical causes ("causal closure of the physical")
P3 In general, effects do not have more than one sufficient cause ("no-overdetermination rule"
C Therefore, mental events are identical with physical events

Pick a mental event such as a conscious pain, and suppose that this events causes you to say "ouch", which is a physical event. This is an instance of P1. By P2, yousaying "ouch" had a sufficient physical cause - it was caused by some complex brain event B. But by P3, you saying "ouch" did not have more than one sufficient cause. It follows (or at least it seems to follow) that your conscious pain must be identical with the brain event that caused you to say "ouch". If the pain is not identical to B, then you saying "ouch" had two sufficient causes, but that is ruled out by P3.

Try to apply the recipe above to generate the alternative arguments! It works in exactly the same way, but here the alternatives are far more interesting, and every one has a conclusion that has at some point been defended by some philosopher. It is therefore not obvious at all which of the resulting arguments (how many are there?) is the one that is sound.

In the lecture slides titled "Discussion" you will find the four arguments that can be based on the logical form of the causal argument for physicalism. One important thing to bear in mind is the following question, which may have occurred to you:

How can we say that an argument is logically equivalent to an inconsistent set of propositions, but then say that an inconsistent set of propositions can be used to generate more than one argument?
The answer is that the logical form of an argument is not all that it has! All four arguments that can be constructed using the logical form of the causal argument for physicalism have exactly the same logical form. However, each one involves defending a different set of 3 propositions in order to reject the 4th.
It is when you decide which set of 3 propositions to defend, and hence what your conclusion will be, that you turn an inconsistent set of propositions into an argument.

In the discussion slides (Moodle) you will also find the 4 arguments that can be constructed using the Cartesian sceptical argument. Previously we had seen 2 of these: the original sceptical argument and Moore's repsonse. Now you will see that there are two more: an argument against epistemic closure, and an argument against the apparently obvious truth that if I am a brain-in-a-vat, then I do not have two hands.

For more on the possibility that we still have hands, cars, homes, children, partners, food, etc. even if we are brains-in-a-vat, see David Chalmers The Matrix as Metaphysics. In Chalmers' view, sceptical scenarios (at least, most of them) are really just alternative hypotheses about the fundamental metaphysical nature of our world. In these scenarios, he claims, almost all of our ordinary beliefs about the world are still true - but they are made true by a different kind of fundamental reality.

The logical form of a valid argument

2 Outubro 2024, 13:30 • David Yates

The Logical Form of a Valid Argument

We concluded last week with some material that some of you found confusing. But don't worry, we will clarify everything this week with some further examples. Here are the central points, please read this carefully (several times, if necessary):

Any valid argument is (fromthe definition of validity) such that the premises P1, P2, P3,…, guarantee the truth of the conclusion C. In other words, the premises cannot be true and the conclusion false
Thus, any valid argument with e.g. 3 premises can be written as follows: it is not possible that {P1 & P2 & P3 & not-C}. That is just what validity means: it's not possible for the conclusion to be false if the premises are true.

Notice that "not-C" here is the negation of the conclusion. If the conclusion of the original argument was that we can never be justified in believing that we have two hands, then not-C will be the proposition that we can (at least sometimes) be justified in believing that we have two hands. If the conclusion of the original argument was "David is mortal", not-C will be the propopsition "David is not mortal"; and so on.

Now if an argument is valid, we know that the following set of propositions is inconsistent, i.e. they cannot all be true:
{P1, P2, P3, not-C}
Super-important (and perhaps why some of you were confused on Friday): when we say that P1, P2, P3 and not-C cannot all be true, we are referring to "not-C" as a single proposition (see examples above). If you say that "not-C" is false, you are saying that C is true. This is because two negations cancel out: not(not-C) is equivalent to just C.
Logically, to say that the propositions in the set {P1, P2, P3, not-C} cannot all be true, we are saying that at least one of them must be false. But which one? What you have now is a recipe for constructing 4 possible arguments. If you choose any 3 of the propositions in the set and say that they are all true, you must reject the fourth proposition.
Any valid argument with N premises and a conclusion is in fact logically equivalent to N+1 arguments, each one with a different conclusion, and each one valid. Don't worry if you do not see this immediately! We will go over it with examples next week.

Now we will give several worked examples of this logical form so that students will at the very least learn a recipe for constructing the alternative possible arguments from any particular case, and hopefully also why this recipe works!

Example 1 - Aristotelian Syllogisms

P1 David is a man
P2 All men are mortal
C David is mortal

In this example argument, we have divided the three propositions into two premises (P1 and P2) and a conclusion (C). The argument is clearly valid. Now, for any valid argument with N premises and a conclusion, we can construct N+1 valid arguments, each with a different conclusion. Recall the definition of logical validity:

An argument A is valid if, and only if, it is not possible for A's premises to be true and A's conclusion false.

That is, validity is necessary truth preservation: necessarily, if the premises of a valid argument are true, then the conclusion is also true. That is what it means for an argument to be valid! Why is validity important? The main reason is that if you use a valid argument form, then if you also start with true premises, you are guaranteed to reach a true conclusion. In other words, if you reason logically from true premises, you will end up with a true conclusion. That is why e.g. deductive mathematical proofs are important - if we have a proof of some theorem in maths, and we know that its premises are true, then we can know the theorem is true as well.

Recipe for Constructing Alternative Arguments - Example 1

Step 1 Write down the two premises and the negation of the conclusion as three propositions, i.e. not separated into premises and conclusion. The negation of the conclusion is its opposite: take whatever the conclusion says, deny it, and you get another proposition. In Example 1, the negation of "David is mortal" is obviously "David is not mortal". Following step 1, here are the three propositions we get:

P1 David is a man
P2 All men are mortal
P3 David is not mortal

Step 2 Write down the argument as an inconsistent set of propositions. Now, we know that the original argument was valid, which means that P1 and P2, if they are true, guarantee the truth of "David is mortal". But what that means is that it is not possible for the above three propositions to be true. This is pretty simple when you think about it: there is no way it can be true, all at the same time, that I am a man, that all men are mortal, and that I am not mortal. Thus we can rewrite the original argument form, assuming it is valid, as follows:

Not possibly (P1 & P2 & P3)

This just says that it is not possible for all three propositions P1, P2 and p3 to be simultaneously true. But now we can see that there are three possible arguments here, all with the same logical form, and all valid. If we know that it is not possible for all three of P1, P2 and P3 to be true, then we know that at least one of them must be false. But that means that if you defend any two of them, you must reject the other one!

Step 3 Write down the logical forms of the possible arguments. The original argument went like this:

P1 is true (David is a man)
P2 is true (all men are mortal)
Therefore, P3 must be false - it is not true that David is not mortal. In other words, I am mortal.

But we can also reason as follows:

P3 is true - David is not mortal
P1 is true - David is a man
Therefore, P2 must be false: it is not true that all men are mortal, i.e. at least one man is not mortal.

And finally:

P3 is true - David is not mortal
P2 is true - all men are mortal
Therefore, P1 must be false: David is not a man!

Thingts to note: (1) all three arguments presented here are valid, (2) only one of these arguments can possibly be sound, (3) in this case, it is very obvious which of the arguments is the sound one - it is the one whose premises are true (sadly, the original argument that concludes that I am mortal).

Moore's reply to the sceptic

27 Setembro 2024, 13:30 • David Yates

Here we covered Moore's "refutation of scepticism". Slides available on Moodle. Main points covered:

Does Moore beg the question against the sceptic? We read Moore's paper "Certainty" in class to assess this question and to try to assess where the burden of proof lies. We also covered some important material on the logical structure of argument.

Any valid argument is (fromthe definition of validity) such that the premises P1, P2, P3,…, guarantee the truth of the conclusion C. In other words, the premises cannot be true and the conclusion false
Thus, any valid argument with e.g. 3 premises can be written as follows: it is not possible that {P1 & P2 & P3 & not-C}. That is just what validity means: it's not possible for the conclusion to be false if the premises are true.

Now if an argument is valid, we know that the following set of propositions is inconsistent, i.e. they cannot all be true:
{P1, P2, P3, not-C}
Super-important (and perhaps why some of you were confused on Friday): when we say that P1, P2, P3 and not-C cannot all be true, we are referring to "not-C" as a single proposition (see examples above). If you say that "not-C" is false, you are saying that C is true. This is because two negations cancel out: not(not-C) is equivalent to just C.
Logically, to say that the propositions in the set {P1, P2, P3, not-C} cannot all be true, we are saying that at least one of them must be false. But which one? What you have now is a recipe for constructing 4 possible arguments. If you choose any 3 of the propositions in the set and say that they are all true, you must reject the fourth proposition.
Any valid argument with N premises and a conclusion is in fact logically equivalent to N+1 arguments, each one with a different conclusion, and each one valid. Don't worry if you do not see this immediately! We will go over it with examples next week.