Logic

Using Arguments to Arrive at Understanding

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As I suggested in the previous post, we come to understand something better through a number of arguments rather than through a single argument.

Suppose you prove your position through a single argument that seems strong to you. In this case there is a second-order consideration which significantly weakens your argument. Namely, if you already suspected or held a position, or if you wanted it to be true or to believe it, how likely is it that you would manage to find at least one argument in favor of that position which seemed strong to you, given that the position was false? It is probably not much less likely than the same thing given that the position is true, and so the strong argument should not increase your belief in that position by very much. This of course does not imply that you should ignore the content of the argument, but it does mean that you should take it with a bit of caution. Approaching the matter with many arguments weakens this second-order consideration and gives you more reason to accept the implications of the arguments.

Using a number of arguments also helps you to refine your view, making it more precise, giving you a better ability to resolve objections, and so on. This is certainly one of Aristotle’s reasons for proposing the use of dialectic in coming to understand, and a reason for the use of many arguments in disputed questions, as I said in the previous post.

On the other hand, even if you come up with multiple arguments for your position, this may not be very helpful if you ignore opposing evidence, and so it is necessary to construct arguments against your position as well. This is the reason that a disputed question has arguments on both sides.

If you manage to construct a large number of arguments on both sides of a position, this will often give you a very strong basis for judging the truth of the position. It is difficult to assign numerical probabilities, and consequently to determine the exact strength of the evidence or of an argument for a position. But it is often comparatively easy to see the relative strength of two pieces of opposing evidence, or two opposing arguments. Consequently once such a list of opposing arguments has been constructed, it is possible to look at one side and see how the arguments compare to those for the other side.

As I have said earlier, there is evidence for any position, whether it is true or not. However, the evidence for a false position generally tends to be weaker than the evidence for a true position. So for example if nearly all the arguments for one side of a position are fairly weak, while many of the arguments for the other side seem significantly stronger, we can get a pretty good sense of which position is true and which is not.

On another note, there is a good post against the Equality Dogma here.

Whether the Structure of a Disputed Question in the Summa Be Most Perfect?

entirelyuseless Logic, Theology

It seems that the structure of a disputed question in the Summa is most perfect.

1. For St. Thomas was the greatest of theologians. Consequently his work, namely the Summa, was constructed in the most perfect manner.

2. Again, Aristotle says that in order to come to know a certain matter, one should consider the opinions of others on the issue and the difficulties that can arise concerning it. This is done by considering the objections before proceeding to resolve the issue with the body of the article, and then finishing by resolving all of the difficulties in the answers to the objections. Therefore the structure of a Summa article is a perfect structure for coming to know.

3. Again, it belongs to the teacher to explain a matter in full, and then to use this explanation to resolve all of the difficulties. Thus the objections correspond to the questions of the students, while the rest of the article corresponds to the explanation of the teacher. Thus the structure of a Summa article seems to be perfect.

But against this are the words of St. Thomas introducing the Summa, “We intend in this book to treat of whatever belongs to the Christian religion, in such a way as may tend to the instruction of beginners.” Thus the articles are formulated for beginners and not for the sake of a perfect understanding which can be achieved by those who more advanced.

I respond, it should be said that the structure of a disputed question in the Summa is not most perfect, but is abbreviated for the sake of beginners, as St. Thomas implies in the words quoted above. It is true that in order to come to know, one must understand the difficulties of an issue, but it is not sufficient to understand the difficulties that are opposed to the truth. It is also necessary to understand the various indications by which the truth is made known, and therefore the more perfect structure is that found in the disputed questions of the schools, where arguments are made not only against the position of the teacher, but also in favor of that position. The reply to the first is evident from this.

To the second it should be said that the structure of a Summa article does indeed model the dialectical process in general, but it does not include the whole of the process, since the arguments in favor of the truth are omitted.

To the third it should be said that the students may also have some thoughts that correspond to the truth, and also that even the teacher actually comes to a knowledge of the truth not only through a principal argument, as in the body of the article, but through many arguments.

The Evidence Does Not Change Sides

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Suppose someone holds the following position:

(1) Mormonism is the true religion.

Then he discovers this fact:

(2) Joseph Smith claimed to have translated the Book of Abraham from an Egyptian manuscript, but in reality the Egyptian manuscript was about something completely different.

Now this doesn’t look good. In fact, it looks exactly as though the Book of Abraham is a complete fraud, which seems to imply that position (1) is false. In other words, (2) is strong evidence against (1).

So our protagonist modifies his position like this:

3) Mormonism is the true religion, and Smith interpreted the Egyptian manuscript by divine inspiration, revealing its spiritual sense.

Now he notices something. After the discovery of fact (2), position (3) becomes more probable than it originally was, since part of position (3) is now verified to be definitely true, namely the fact that the book of Abraham is a not a literal translation of the Egyptian manuscript. Thus, the original disturbing fact which seemed to be evidence against his position, is now evidence in favor of his new position! And the new position includes position (1), so there is no need to change a thing!

This reasoning is technically valid, of course, but our protagonist is overlooking a few things.

First of all, (1) is in itself more probable than (3), since (3) requires the truth of (1) and something else in addition.

Second, after the discovery of (2), (1) becomes less probable, likely significantly less probable, than it was before. This fact remains unchanged by the rest of the process.

Third, (3) does indeed become more probable than it originally was, after the discovery of (2). However, (3) was less probable than (1) in the first place, and even after it becomes more probable, it remains less probable than (1) originally was, and it also remains less probable than (1) became after the discovery of (2). This is necessary because (3) is nothing but a particular way that (1) could be true. So by adopting the new position, our protagonist has not benefited by (2) in the way that he believes. Rather, he ends up holding a position that is even less probable than claiming that Mormonism is true, admitting that the Book of Abraham is not a valid translation of the Egyptian manuscript, admitting that this makes his original position regarding Mormonism less probable, and making no other changes.

In other words, the evidence does not change sides.

The Evidence is Not Automatically on Your Side

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One thing is evidence for a second thing if the second thing is more probable given the first, than the second without considering the first. Thus the fact that you are reading this blog post is evidence that you are a native English speaker, since someone reading the post is more likely to be a native English speaker than a random person is.

One common mistake is to think that there cannot be evidence for something false; but my position is true and the opposite is false; therefore there cannot be any evidence against my position. Thus people say things like, “Evolutionary belief is a remarkable and largely unexplained phenomenon. It is a belief held by most intellectuals all over the world, despite the fact that there is no real scientific evidence for it at all.” Again, someone holding another position says, “Critics of evolution claim that it is just a theory for which there is no proof. It is true there is no definitive proof, and nor is there likely to be, but there is a vast amount of evidence in its favour. Whether you choose to believe it is sufficient is up to you, but it is there. By contrast, there is no scientific evidence for creationism.”

The claim that your opponent’s position has no evidence for it is always false, without exception. For the very fact that your opponent holds the position is evidence for it, since a position that someone holds is more likely to be true than a random position that no one holds. But even apart from this, given any particular position that real people hold, we can expect to be able to find any number of facts that make more it more likely than it would be without those facts, even if the thing is absolutely false. Thus if you buy a lottery ticket, it is evidence that you will win the lottery, since it becomes more likely that you will win, having a ticket, than not having one. But ordinarily you won’t win anyway, despite your evidence for it.

The Order of the World

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Aristotle gives five meanings of before and after:

1. Before in time. 2:00 PM is before 3:00 PM.

2. Before by nature. The existence of man implies the existence of animal, but the existence of animal does not imply the existence of man, so animal comes first.

3. Before in understanding. The premises of an argument come before the conclusion.

4. Before in goodness. The better thing is first.

5. Before in causality. The cause is before the effect.

The world is ordered in all of these ways, and the various orders have certain relationships. The order of time lines up with the order of nature to some extent, since if a thing implies the existence of something else, it cannot exist temporally before the thing the existence of which it implies. Thus animals existed before human beings, but not human beings before animals. This order is never reversed, but sometimes the order of nature does not also include an order of time. Thus the first bodies must also have been some particular kind of body; there was no temporal sequence there.

For material, formal, and efficient causes, the cause is always simultaneous in time with the effect. However, on account of its causal priority, that which constitutes the cause sometimes comes temporally before that which constitutes the effect, and never the other way around. Thus in this sense the order of the things which are causes to some extent shares in the temporal order in the same way that the order of nature does.

The final cause is sometimes taken as that which is loved, and in this sense it has no definite temporal relation to its effect. Thus sometimes it comes after, as the money which is loved makes a man work for it, and sometimes it comes before, as the wife who is loved makes a man praise her even after her death.

But when the final cause is taken as that which is desired but not yet possessed, it always comes after its effect, assuming that it comes to be at all. This results in a temporal order which is reversed according to final causality, but which corresponds to the order of goodness. What possesses the good is better than what does not possess it, and comes after in time, unless something fails such that the efficient cause which sought the final cause does not succeed in attaining the good it desired.

Thus a successful world is one in which the order of time basically corresponds with the order of causality and the order of goodness. This is what St. Thomas means when he says that the good of the world consists in its order, and that its order consists principally in the fact that one thing is the cause of another, and that one thing is better than another.