Naturalism and First Philosophy: Logic & Rationality

I pointed out in an earlier post that the naturalist can still deny the necessity of first philosophy by claiming that the principle of non-contradiction is a component of something else (such as rational thought). This something else would then be justified on the basis of pragmatic value or experience. This is the final move available to the naturalist. This forces the naturalist to ground rationality by design, accident or necessity.

The idea that the principle of non-contradiction is a component of rational thought is surely true. In fact, to the extent that one denies the principle in practice one is no longer thinking rationally. So the principle of non-contradiction is a necessary condition of rationality - both practically and theoretically. However, one would not want to claim that the principle is a sufficient condition. The belief that the President is an alien because the voices told me is irrational. Yet is not contradictory.

Once again one can note that rationality can be justified pragmatically in one of two ways. Either one can claim that one's experience grounds one's belief in one's rationality or that one's rationality is grounded in the circumstances of its origin. Since rationality is a practice, it cannot be grounded unless it works correctly. I am assuming that one is rational if and only if one's thinking processes that are aimed at the truth function in a way consistent with their aim, and that at least some of one's thinking processes do aim at the truth. Now our rationality can be grounded in historical circumstances only if these circumstances caused our rationality to be truth aimed. One's experience cannot ground rationality itself, it can only justify beliefs in one's own rationality. Since that is a different claim, I will focus on the actual ground of rationality rather than our belief that we are rational.

To point out the grounding problem in a different way, consider it as the question of why it is that our thinking processes that are aimed at the truth function in a consistent manner, and why we have such processes. These are two different ways of looking at the same problem. Since the naturalist believes that science (or empirical investigation) must provide the answer to this question. Therefore, if naturalism is true then empirical investigation will be able to discover both why we have thinking processes that are aimed at the truth and why these processes are consistent. Since empirical investigation is done using rational methods, the results obtained are meaningful only if they were obtained by a rational method. That means that empirical investigation cannot ground rationality. It can only tell us (at most) what occurred in order to give us the rational processes we do have.

Since no empirical investigation has been done on the matter, one must proceed hypothetically. There are several different ways that rationality could be grounded. It could be grounded as the aim of a particular process. In that case, rationality would be designed as such. It could be grounded as the product of particular process in which rationality was an accidental by-product. This would be the case in which rationality was not designed but was made. It could also be grounded in necessity. This is the case in which rationality is eternal and so are our processes. These separate options must each be addressed before naturalism gives way to first philosophy.

Kant and the Logic of Morality

There are some people, such as my professor, who do not believe that intuition is useful for philosophy. I am not completely sure what he believes about it, but I do believe that one cannot avoid the use of some sort of intuition in morality. If I have to use it, then I might as well use it right. So why shouldn't philosophers deal with intuition? As I understand it, the only way to avoid this line of reasoning is to adopt the belief that intuition can be avoided. Now one may not be able to completely avoid it, but perhaps a certain area - such as ethics - can be done without it. If this is possible then one is left with the idea facts and logical reasoning are sufficient to know what the right thing to do is. Kant tried to do this and failed.

Kant believed that some act was morally permissible only if it could be successfully universalized. We start off with a maxim. I do something in order to achieve some result. For example, I lie about my identity because I wish to deceive someone. One takes this maxim and pretends that everyone does it. So everyone lies about their identity in order to deceive someone. Now we ask whether or not I could succeed with my action if everyone was doing it. Well, if everyone lied about their identity, then no one would believe anyone's claim about their own identity. So I would not succeed (in such a world) in my aim. Therefore, lying about my identity is immoral.

Now this procedure does get the right answer quite a bit of the time. The problem come from the fact that no limit is placed on how general a maxim is allowed to be. Consider this new maxim: I become a philosophy professor in order to fulfill a desire of mine. Can such a maxim be universalized? Imagine a world in which everyone is a philosophy professor. This would not work - we need to eat after all. So according to Kant, it is immoral to be a philosophy professor. Since this can be extended to absolutely every vocation, it is immoral to have any vocation at all! This is absurd.* Without some kind of restriction of what maxims are appropriate, this procedure does not determine what is right or wrong.

Kant could say (but I am not sure whether he does or not), that the maxim has to be as general as possible. Here is the most generally possible statement: I act because I choose to. On Kant's criteria, this is morally permissible. Nonetheless, not every kind of act is morally permissible - we all know this. So at the most general level, Kant's method fails to give unconditional permission to do something. So Kant cannot be as general as possible with his maxims.

When one looks at the philosophy professor example, one believes that it is perfectly permissible to be a philosophy professor, all other things being equal. However, it is not permissible to be in an immoral vocation such as the drug dealer or assassin. So Kant's moral view would have to say that being an assassin was wrong, but being a philosopher is not. If we use his method without restricting this maxims, this does not happen. If we do restrict his maxims in some particular fashion, then Kant has a different problem.

Kant wishes to say that one only needs the facts and reason to arrive at moral prohibitions. However, the facts do not determine how to restrict the maxims. They only determine whether a universalized maxim is successful. So reason must do so if Kant's method is to succeed. But it is far from clear how one would do this. Kant already has reason supporting the method of universalization. He claims that the usage of morality in our speech shows that all moral claims have that property. In other words, universalization is a part of moral judgments just by being moral judgments. Unless he were to make a similar - and quite implausible - claim about a particular restriction of maxims, then Kant's method fails to give us moral claims.

There is a lesson in all of this. First, one should start with what was right about what Kant said. Surely there is something to the universal character of morality. It is supposed to apply everywhere and to everyone under every possible circumstance. However, it is quite doubtful that one can get moral claims without starting with some kind of moral principles, beliefs or characters. Kant's attempt to show otherwise only illustrates this.

* This illustration and its point were taken from a lecture with the above mentioned philosophy professor.

Looking at Morality: Discovering the Boundaries

I suggested that the best way to discover the exact domain of moral statements is to distinguish them from law, etiquette, art, skills and other disciplines. So now the question is which disciplines to compare morality with? The best strategy is probably to look at each of the allegedly common characteristics of morality and ask which other areas of discourse also have these common characteristics. Working from these areas of discourse,

One of the first areas I noticed was the prescriptive. Morality gives us commands. So do the areas of law and etiquette. As far as I can think of, no other domain of discourse gives us commands. A second area I noticed was that of action-guiding. Morality guides our behavior. Law and etiquette also guide our behavior. A third area is that of rationality and descriptiveness. These are very large areas to look at, as they contain science, some law and etiquette, ordinary beliefs and practices, etc. So by looking at the general characteristics of these domains of discourse one finds that three areas share them: morality, law and etiquette.

The next thing to do is to ask what these domains all have in common apart from what has already been mentioned. One of the things one notices is certain kinds of language such as "should", "ought", "good", "bad" and other evaluative and normative terms. Another thing that one notices is that failure to abide by the rules has consequences ranging from bodily harm to societal disapproval. One also notices that breaking the rules is usually comes with some negative feelings such as guilt or regret, and one is apt to try and hide one's behavior or justify it to others. As far as I know, these are the common areas between these three areas of discourse.

Not all of our behavior is found to fall under an area of discourse. Looking generally, do any other practices show these features? I think that the answer is yes. Normative language is used in skills (such as construction, art and technological innovation). It is also used in discourses and arguments (ie. that is a bad argument, you ought to use this inference rather than that one, etc). These areas also have consequences ranging from bodily harm to societal disapproval from breaking their norms. Consider what happens when you build a bad bridge (but assume that you are not morally at fault), or what happens when you advance a bad argument. These situations can even cause the same kind of emotions and reactions as moral or legal situations can.

These four areas: three domains of discourse and two general areas are the only ones in which these general features occur. Rational oughts such as an ought to believe or practical one can both be treated as as discourse oughts. Self-interest can be treated as an issue of practical rationality either actually or hypothetically. I am not aware of any other examples.

A Look at Morality

I have spent some time thinking about morality. I am just about finished a class on metaethics (the study of what morality is), and I am familiar with other areas of ethics as well. One problem that has jumped out at me is that everyone assumes that what they mean when they talk about morality is the same as what everyone else means. Since that is rarely true, some disagreements are hidden by verbal agreement. However, these thinker do tend to agree that certain statements are definitely moral ones. (Such as "lying is wrong", "we ought to keep our promises" and so on.) So how do we decide what morality is about?

First I think that it would be good to point out common features of moral thinking that are commonly agreed to be there. First, moral thinking tends to be prescriptive. Moral commands are not descriptions. They are imperatives. Morality tends to guide our actions. This action-guiding of morality is not just in exceptional circumstances but often. Morality is usually considered to override our wants and preferences. We are not allowed to steal simply because it would be fun or because we would like to have the new toys without buying them. Finally, morality is both rational and descriptive. We disagree about moral claims, reason about moral claims and these claims include descriptions - that is right or he is bad.

Once we have these basic features, we can look at the problem. Nearly every point above has been disputed by some philosopher. The majority (near majority?) of current work in metaethics assumes that there are no true moral descriptions. Also, some disagree over whether other non-moral areas have some of these properties. Examples include etiquette, art, self interest, law, etc. Others insist that these areas only have moral properties because they are based to some degree in moral thought. Finally, it is not as if there is any agreement on what sort of moral theory is right or what methods are the right ones to find the right theory.

It seems that we must start somewhere. I suggest that we start with a few guidelines. First, we should say that ordinary moral decisions and practices are usually rational. All other things being equal, if one theory says that people are less rational than another theory, the first theory is less likely to be true. Second, we should preserve as much common sense morality as possible. All other things being equal, a theory that preserves our common sense is better than one that does not. Third, we should explain why morality includes the things that it does and excludes others. Fourth, our theory should explain what morality is and why it has the properties that it does. Finally, our theory should explain why rival theories exist and why they believe what they do.

Given these sort of principles, I think that we must start with what absolutely everyone agrees with. This is the idea that ethics is not the same thing as etiquette, art, law or any other area. The proper question is why it is a different area. Once that question is answered, one is well on the way to answering what the domain of morality is.

Naturalism and First Philosophy: Logic As Practice

The last post pointed out that naturalism (of the epistemic variety) assumes that first philosophy is unnecessary. I used the example of the principle of non-contradiction as a counter-example to this claim. I pointed out that naturalists have at least three responses to this claim, and refuted the first response. At this point the naturalist could claim that the principle of non-contradiction is not a belief. If this response is successful, then the naturalist has successfully defended her theory from my attack.

The naturalist might believe that the principle of non-contradiction is a proposition describing the behavior of human being when believing. No one believes contradictions. She could extend this even farther. Quine describes his two principles as pragmatic principles, not beliefs or rationally based principles. If the principle is not a belief, then she could explain adherence to it in pragmatic terms. We behave in this way because believing contradictory things decreases survival value. Since it is not a belief, there is no need to provide a justification for it.

The question to ask is this: do people ever believe that the principle of non-contradiction is true? If anyone does, then the question of justification enters again, and naturalism is defeated. So someone who believes that principle is not a belief must also believe that the principle is neither true nor false. Anyone who claims to believe the principle is either mistaken (because they actually do not believe it) or ignorant.

There are implications for that kind of belief. First, not all instances of P & not-P can be false. If they were, then the principle of non-contradiction would be true. So there is a severe problem. It gets worse, for there is no rational reason to object to any instance of P & not-P. If I claim that the moon is both white and not-white, how could you object apart from claiming the truth of the principle of non-contradiction? All of this demonstrates that if we are to accept the idea that the principle of non-contradiction is neither true nor false, then all of our rational thinking would vanish. Therefore, the principle of non-contradiction must be true. Since the principle is either true or false, one can believe it. Therefore, the second strategy against accepting an example of first philosophy has been refuted.

There is a final strategy available to the naturalist. She could claim that the principle of non-contradiction is a component of something (such as rational thought) that has pragmatic value, or that is not a belief, or is in some way is justified by experience. That possibility is for later.

Naturalism and First Philosophy: Logic & Usefulness

From what I can currently understand, naturalism is dominant among current philosophers. Naturalism excludes any consideration of first philosophy. First philosophy is the philosophy that we engage in prior to any scientific or generally empirical understanding. It is sometimes, perhaps usually, associated with justifying the scientific method or science in general. My first reaction to this is that there is nothing wrong with first philosophy, and it looks to be necessary. A consideration of the logical principle of non-contradiction and it justification by usefulness contributes towards showing that this is true.

Consider the realm of logic. Aside from various formal logics, and the standard treatment of fallacies, there are basic principles of logic. One of these is the principle of non-contradiction: it is not the case that P & not-P. For example, it is not the case that I exist and I do not exist. This principle was first formalized by Aristotle. It is part of first philosophy for two reasons: no empirical evidence supports this, and no empirical evidence can defeat it (contra Quine). Therefore, there is a first philosophy because certain logical principles are a part of it. Since these logical principles are also necessary for any kind of thinking, first philosophy is also necessary.

The naturalist could claim that our belief in logic is justified by its usefulness. Without it, we would be unable to think correctly or behave well. This principle was useful in our survival. Let's suppose that we grant this. We can understand the usefulness claim in two ways. One is a justifiying way: I am justified in believing the principle of non-contradiction because it is justified by my experiences of the world. The other is historical: I came to believe in the principle because of its survival value. The historical reading does not justify my belief. All it does is explain why I have it. So I can still ask what justifies my belief in it. If we use the justifying reading, then we are left with a question: just how are my experiences of the world supposed to justify the principle of non-contradiction?

When I come to the world I do not take any experience as being a possible defeater for the principle of non-contradiction. If went outside and saw that the moon was bright green, I would not conclude that the moon is both white and not-white (green). I would conclude that the appearance of the moon is now green, but was previously white. Those who believe in the doctrines of the Trinity or Incarnation do not believe that there is no sense to be had in the doctrine. They believe that they do not understand all of it, and cannot. Neither case is a violation of the law of non-contradiction. Therefore, as far as I know, there is no experience that either defeats or supports my belief in the principle. I am highly attached to the claim and would give up anything else to preserve it.

Now we move into the territory of Quine. He claimed that our web of beliefs were all revisable in principle - including our logical beliefs. However, we must revise as little as possible, and make the changes as simple as possible in order to preserve coherence. It is fairly easy to point out given Quine's principles of belief revision, the principle of non-contradiction is not revisable. First, the very principles he gives assume that the principle is true. What determines how much revision and how many changes are necessary is found by determining what set of beliefs can be held without contradiction. Second, no possible change could ever be sufficient to alter this principle. Let's suppose that you denied the principle. By doing this, you are adding the contradictory of every belief in your web to your web. You also add every other belief and its contradictory to your web. So now your web of belief contains every possible belief and its contradictory. It is as large as possible. But that violates Quine's first principle - make as little revision as possible. Any other set of beliefs would be smaller, therefore, one should never reject this belief. Therefore, the principle of non-contradiction is not revisable - even in principle - on Quine's system. Since Quine's system is the only one to provide a way to revise our logical beliefs, there are no systems that successfully show that belief in the principle of non-contradiction is revisable by anything at all.

These considerations defeat the naturalist who attempts justify the principle of non-contradiction using its usefulness as the reason. The naturalist does have other options. She could attempt to justify it by rationality, or could deny that the principle is a belief. I will examine these options some other time. Apart from the success of those other options, the naturalist will be unable to reject at least some of the traditional first philosophy.

Four Errors of (Modern) Philosophers

When we read philosophical writings, we aim to learn from what we read. Sometimes these writers point out errors in the work of other philosophers. These errors often tend to be the opposite of the errors that the particular philosopher falls into. As I think about it now, there are four errors that modern philosophers tend to fall into. These errors come in pairs, just like Aristotle's vices.

One of these errors is commonly found in 'scientific' philosophers. These are the philosophers who think of philosophy as a building block, defense or conceptual analysis of science itself. They often try to avoid metaphysics, deeper epistemology, and anything that carries the least scent of religion. Science is understood to be the ultimate human inquiry. The methods of science are the methods of knowledge. Science, as well as any discipline informed by its methods, are capable of discovering all knowledge in the universe given enough time. Nothing is hidden from human beings. We really can know everything! This is the error. No formal method can tell us everything, and some knowledge really is out of the reach of human beings.

The error opposite to this one is well recognized by 'scientific' philosophers themselves. It is commonly presented by mystical, ideological and religious philosophers for various reasons. These philosophers reject human reason(ing) because of various circumstances in the world. Perhaps reason is a human construct, it does not apply in the divine realm, it is irredeemably biased by power, or it does not address human concerns. Whatever the reason may be, human reason is rejected in favor of action. Yet these various philosophers attempt to use reason to support their own ideas! If it had such problems, then their reasoning shows that they should not use reason to justify their position. Their devaluing of reason is their error.

Sometimes, the discussion in academic philosophy can become so focussed and detailed that it is difficult to relate to the central issues of philosophy or the concerns of human beings. Many philosophers engage in minor disputes that eat up all of their time, while spending no time relating such disputes to the wider philosophical picture. This creates a divide between various philosophical areas. Connections between the philosophy of mind and the philosophy of religion are not explored. Neither are connections between other areas of philosophy. There is no systematic picture of philosophical thought. This error is the most common and therefore the one least likely to be recognized.

The opposite of that error is a focus on the central issues of philosophy and the concerns of human beings to the exclusion of those matters of detail necessary to them. The few philosophers who fall into this error recognize the current error in philosophy. The best solution is for the central matters to receive our time, and side issues are simply irrelevant. This position sounds quite silly. Matters of detail are necessary to solve any important matter. What we must avoid is turning a major issue into a minor one, or a minor one into a major one!

I do not mean to suggest that these are the only errors of modern philosophy, or even the most important ones. But I do think that they are common and important. The answer to these errors lies in recognizing them when they appear and seeking a middle ground between two extremes - just like the virtues of Aristotle.

The Trinitarian Doctrine

My series of posts related to paradox have been using the trinity as an example of a paradox. So this is a good point to clarify what this doctrine is. It is also a good point to distinguish between two different sets of claims regarding the trinity. One set of claims is the actual propositions that make up the trinitarian doctrine. The other set is those claims that enable us to both recognize trinitarian doctrine and indirectly believe it.

One first starts with what trinitarians actually believe about the doctrine of the trinity. First off, all trinitarians are monotheists. They all believe in exactly one God. Therefore they deny any form of polytheism. Second, all trinitarians believe that the historical person of Jesus is God, and that he is God is the same sense that the Holy Spirit and the Father are God. This means that all three are equally God. Therefore they deny any diminishing of the divine status of Jesus or the Holy Spirit. Third, all trinitarians believe that the Father, Son and Holy Spirit are distinct. Each one has a property that the other does not have, and each one is a person. (Both terms were defined by the trinitarian controversies.) These three points define the center of trinitarian doctrine. (I am ignoring the doctrine of procession because some trinitarians reject it.)

Any doctrine of the trinity will be a set of propositions that is the truth-maker of the above positions while not entailing any contradiction. Yet the three points above are not the actual doctrine of the trinity. Consider the Father, Jesus and God. According to the first point, there is one God. According to the second point, the Father and Jesus are both equally God. According to the final point, the Father and Jesus are distinct and have different properties. So the simplest reading of these points generates a contradiction. That means that the three points are not first-order propositions. They must be second-order propositions about unmentioned first-order propositions instead. One does not discuss the meaning of propositions, only whether they are true or false. One discusses the meaning of sentences.

So what are those three points? They are the way to recognize the actual doctrine of the trinity. Since these three points are true of the trinitarian doctrine, they are necessary to recognize that doctrine. Any doctrine these points are true of would be trinitarian, so these points are also sufficient. Therefore, these points are both sufficient and required to recognize trinitarian doctrine and to believe it indirectly.

Sentences and Propositions

At this point, clarity on the nature of both sentences and propositions is required. One cannot speak with clarity on matters of belief (direct or otherwise) while the concepts used to explain it are vague!

The first thing to become aware of is the nature of signs. I am using this word generally to refer to any mark, image, sound or other feature perceived through the senses that represents something. So traffic lights, pictures and words are all signs. Morse code, binary digits, bumps on a CD, and smoke signals are also signs. Signs may represent another sensory feature. This occurs in the case of pictures and recordings of various kinds. Signs may also represent a command: street signs and lights. They may also represent ideas. It is these last kind of signs that we are interested in, for they are the ones that are also known as sentences.

Sentences may be in any language, may be in any medium, and may be written, spoken, demonstrated (sign language) and so on. The unifying feature of sentences is that they express thoughts or ideas. But not every idea is one that can be either true or false. Some sentences are questions, others are commands and still others are declarative sentences. Those sentences that can meaningfully be called either true or false are the bearers of propositions.

A propositions is any thought that can meaningfully be called either true or false. Many sentences may express the same proposition. For example "Snow is white" and "La neige est blanche" (French) both express the proposition that snow is white.

These points apply to belief in a very simple way. One believes propositions, and only propositions. One cannot believe sentences, nor can one believe signs in general. These is because the object of belief is a thought, and belief comes down to whether the thought is thought to be either true or false.

Appearing to Contradict?

In a previous post, I have made use of the idea that some propositions appear to contradict one another. In another post I implied that any appearance of contradiction is identical to an actual contradiction. These two ideas can be explained by explaining what an apparent contradiction is and how it is different from an actual contradiction.

An actual contradiction is simple. A and not-A is a contradiction. Any set of propositions that generate that are also contradictory. So is any set of propositions conjoined with a logically necessary truth, or a conceptually necessary truth. For example, the propositions this square is red all over and this square is green all over form a contradictory set because it is a conceptually necessary truth that no square can be red all and green all over at the same time.

An apparent contradiction cannot be any set of first-order propositions. Any such set would either be contradictory, or it would be consistent. The appearance of contradiction in such a set would be the same as the reality.

Because of this, an apparent contradiction must contain second-order propositions. Not only this, but at least some of them must be about which proposition a certain sentence expresses. Let's consider the example of the doctrine of the Trinity. Any such doctrine states the sentence that "God is one". It also states that "God is three". Any first analysis of these sentences takes them to be stating the propositions God is one unit and God is three units. These propositions form a contradictory set along with the logically necessary truth if something is one unit then it is not three units. So if the doctrine of the Trinity is not a contradiction, then those sentences cannot express the propositions that they appear at first to express. Yet this is a second-order proposition about what propositions are actually expressed by a sentence! In fact, any Trinitarian believer believes that the "is" of the first sentence, and the "is" of the second are not the same relation. This does not tell us what the Trinitarian doctrine is, but what it is not. It is also the second-order proposition used in order to avoid having two sentences express contradictory propositions.

An apparent contradiction is not a contradiction at all. It is a set of sentences that appear to express a set of contradictory propositions, but are believed to express a different set of propositions instead. Without the second-order belief, one would be believing in a contradiction.

On Contradictions, Direct Belief and Tillian Paradoxes

In my previous post I laid out a brief case that Tillian paradoxes cannot be believed directly. In the midst of that argument, I made the assertion that one cannot directly believe a contradiction. Although true as a simple summary, there are some distinctions that need to be made. Under some circumstances it is possible to directly believe a contradiction, and under others it is not. The key difference is immediate awareness of the conflicting propositions.

Let's imagine a situation in which a person believes these four propositions: my computer was not operating at noon, there are only two computers in the house, a computer was in use at noon in the house and the other computer was not at use at noon. The conjunction of these four propositions generates a contradiction. Since these are all propositions, this is a case of direct belief. So all that remains is to imagine a situation in which someone would have all of these beliefs at the same time. Let's suppose that I know that my computer is off and the other computer is only used by others while they are there. I know that there are only two computers in the house because that is all that I see, and I know that the others in the house were away at noon. I later receive an e-mail that indicates that it was sent from an address used by the others in the house. As I think about it, I realize that it could not have been sent unless someone was at home. But until I think about it, I am directly believing a set of contradictory propositions.

Now try to imagine believing a simple contradiction of any kind, such as the sky is blue and the sky is not blue. I can't. I imagine something else: some of the sky is blue and some is not, or the sky is blue at one time and not at another, or I first believe one and then the other. None of these count as believing a simple contradiction. Neither can one believe a set of contradictory propositions while being immediate aware of all of them. Consider the previous example. Once I became aware that the e-mail was sent and focus my awareness on this fact, I believe that someone was home using the other computer. Focusing my awareness on that proposition leads to the belief that the other computer was in use at noon. Yet that is the contradictory of the belief I previously held!

These examples show that immediate awareness is sufficient to dispel any direct belief in contradictory propositions. They also show that lacking such awareness allows for the possibility of such beliefs existing directly. So precision requires that I restate my earlier point on Tillian paradoxes. They cannot be believed directly while bringing such propositions into the immediate awareness. One can believe them directly without doing so.

Believing in the Trinity vs. 'Paradoxing' the Trinity

Is a paradoxical doctrine of the trinity compatible with believing that same doctrine? The answer to that question is the same as the answer to paradox in general. It depends on what one means by paradox.

First off, there are two different ways that one can believe a doctrine. One way is to believe in it directly, by believing a proposition or series of propositions that express that doctrine. Another is to believe indirectly. This way of believing does so not by believing a proposition, but a person or group of people. We believe that the doctrine of the trinity, that those people believe, is true. We trust that these people believe some set of propositions or believe some others who do.

Secondly, there are at least three different senses of the word paradox. One sense is that of contradiction. I am going to ignore that one because it is not compatible with belief in the trinity. The other two senses are different ways of understanding merely apparent contradiction. In one sense, there can be no demonstration that the set of propositions that appear to contradict do not actually contradict one another. In practice, this position is the same as the one I rejected. I am calling this kind of paradox the Tillian paradox. In the other sense, there can be a demonstration that the set of propositions do not contradict one another. I am calling this kind of paradox the Thomist paradox.

Combining these points shows that any Tillian paradox cannot be directly believed, and any such paradox refers to nothing. In the realm of belief, the Tillian paradox is identical to a contradiction. Since one cannot directly believe any contradictions, one cannot directly believe a Tillian paradox. But this creates a problem. For the only way to believe a Tillian paradox is to believe it indirectly. Let's suppose that such a paradox is called X. So I believe X because I believe the doctrine that these other people believe. But then why do these other people believe? They must believe indirectly as well. Since this is an infinite regress, X does not refer to any propositions at all! But in that case, Tillian paradoxes do not successfully reference any paradox of belief at all.

So what does this mean in the end? It means that any attempt to understand theology in a Tillian sense of paradox is doomed to fall into an epistemological abyss. And that includes the doctrine of the trinity.

Links and Reading

Just recently I have begun a serious reading of Newman's work Idea of a University. It is a serious reflection of what a university is and how various disciplines are related to one another. It was written in the 1850's, so a lot of his starting points are quite different from ours. It clearly shows how different modern thought is now from the thought of his time.

William Lane Craig also has his own website. He is a Christian philosopher who works in the areas of time, uniqueness of Christ and Molinism. He also does apologetics work related to the Christian faith.

There are also a few links that I have found to be particularly good recently. One is on three different ways of professing a creedal claim. Another is on the claim that evil people are annihilated instead of being eternally punished. There is a good post on the knowability paradox.