This document attempts to make clear that there are several forms of atheism, of varying 'strength' in their opposition to theism, and that there are several types of theism to which each type of atheism can be opposed. This means that instead of atheism being just a single viewpoint it covers a multitude of cases, each definable by a type of theism and a type of objection to that form of theism.

A slightly curious consequence of this is that a person who accepts one type of theism and is an atheist about another type of theism can be both a theist and an atheist. This is no more inconsistent than admiring some novelists and not others.

I first present some background to this discussion note: an exchange that occurred on the PHILOS-L email forum. I then mention a web site on intelligent design in which I described myself as an atheist, and then present the analysis of types of atheism. This helps me to be clearer about the type of atheist I am. Perhaps it will help others also.

I responded making three points:

   1. As a D.Phil student in Oxford in the 1960s, I had met and
   interacted with the individuals named, and had generally not found
   that their catholicism had interfered with their quality as
   analytical philosophers.

   2. I did not think the proportion of catholics amongst prominent
   analytic philosophers was particularly high.

   3. My impression was that most of the well known analytic
   philosophers were atheists.

    I was then and remain an atheist (of the kind who doesn't claim
    that God does not exist, but that the usual concept when
    analysed closely is incoherent, so that existence of an instance
    makes no sense -- is there a standard name for that sort of
    atheism?).

After a few comments had been posted, the moderator of PHILOS-L requested that further discussion be transferred to the Chora list, available here:

    http://listserv.liv.ac.uk/cgi-bin/wa?A1=ind0804&L=chora

    http://www.cs.bham.ac.uk/research/projects/cogaff/misc/teaching-intelligent-design.html

In order to make my own position clear I stated in that document:

    The universe is moving in a north-easterly direction at three
    miles per hour, but the motion cannot be detected because all
    measuring devices take part in the same motion.

(a) the notion of 'the universe' includes everything that exists,
    including everything that can move and space itself,

(b) the notion of something moving (in any direction at any speed)
    presupposes some fixed entities relative to which the motion
    can be measured.

Atheism as a claim about incoherence

    This table is made entirely of rubber and this table is
    not made entirely of rubber

    This table is made entirely of days of the week.

In the remainder of this paper I shall try to make more precise what the thesis is that I refer to as "analytical atheism" and what the alternatives to it are. Producing and evaluating all the best arguments for and against the thesis and showing that this atheistic thesis is correct, or at least better supported by arguments and evidence than any of its rivals, would require a much longer document.

Readers who are tempted by that view need to be aware that it can take a complex and unobvious argument to show that some set of propositions is logically inconsistent even if there are people who believe they are all true. Showing that a collection of propositions that appear to make sense cannot form a coherent whole, because some of them undermine the presuppositions of others, can also take a complex and unobvious argument. The existence of such a proof of incoherence is perfectly compatible with many people feeling they understand something coherent by that set of propositions.

Compare the five year old child who was asked where a fast racing car and a slow moving van would meet if they simultaneously started moving towards each other after starting some distance apart. His answer was to point at a location nearer the starting position of the racing car. When asked why he sincerely answered: "it is moving faster so it will get there sooner".

He was not ready to understand his own confusions. Adults can be in the same state. Training in analytical philosophy can help them to recognize and get over some of their own confusions.

Being able to discover that some of one's thoughts are nonsensical requires a kind of intellectual development, which for many people can be very difficult if they have not studied analytical philosophy.

The specific kind depends not only on the kind of rejection, but also on what is being rejected. There are different sorts of theism and to each one of them there can correspond several varieties of atheism. Not all varieties of theism are incoherent in the way I shall attempt to define.

For example, Einstein sometimes claimed to be religious and to accept a kind of God, but, in saying that, he was not referring to the usual kind of Judeo-Christian type of God, but to some deep features of the natural world that make it awe-inspiring even to a hard-headed scientist. He was not endorsing more common kinds of theism, or religious belief. For more on Einstein's views and how they are sometimes distorted by theists, see
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/einstein-religion.html

In order to define various kinds of atheism we need to specify various kinds of theistic thesis. Different subsets of those theses are accepted by different theists (and different religions).

It should be obvious therefore that there will be different atheistic (or anti-theistic) positions, denying the truth of different combinations of theistic claims.

For each theistic position, TS, defined by the conjunction of a set S of theistic propositions, we can define the following six anti-theistic views more or less strongly opposed to TS:

• A1. Agnosticism about TS
  This can have different forms, e.g.:

  1. An individual claims he does not know whether TS is true or false
  2. An individual claims he (or humans) will never be in a position to know whether TS is true or false.
  3. An individual claims that it is completely impossible, for humans or anything else, to know whether TS is true or false

• A2. Mild atheism about TS:
  The claim that the evidence/arguments against TS are stronger than the evidence/arguments supporting TS.
• A3. Weak atheism about TS:
  The claim that TS is probably false, or almost certainly false, e.g. because there is far more convincing evidence against TS than evidence for TS.
• A4. Strong atheism about TS:
  The claim that TS is definitely false, based on assessment of empirical evidence and philosophical or scientific arguments about the best available explanations of phenomena some version of theism attempts to explain.
• A5. Logical atheism about TS:
  This is the claim that the propositions in TS form a logically inconsistent set so that their conjunction must be false. A typical example of this would be the claim that these three propositions are mutually contradictory:

  1. Evil exists
  2. God is omniscient
  3. God is omnipotent
  4. God is perfectly good
• A6. Analytical atheism about TS:
  The claim that TS is incoherent and incapable of being either true or false in any possible universe, e.g. because some of the content of the theistic claims undermine requirements for the claims to be meaningful.

I am not claiming that there are always sharp distinctions between these cases -- there may be atheists whose views straddle two or more of these cases.

It should be clear from this that for every different set of theistic propositions, TS, there will be (at least) six different atheistic (or anti-theistic) positions that can be held, according to the schemata presented above,

    A1(TS)
    A2(TS)
    A3(TS)
    A4(TS)
    A5(TS)
    A6(TS)

I am an analytical atheist, in the sense of A6, about various sets of theistic propositions, discussed below.

This should not be read as a claim that I am dogmatically or irrevocably committed to A6.

Unlike most theists I always accept the possibility that I shall later find that my views are mistaken -- as has happened in the past, when I have changed my mind on some philosophical or scientific question.

E.g. I may one day find that theism can have additional flaws not listed above. Or I may learn that there is some variety of theism that I have never encountered (or have encountered but failed to understand) that comes very close to the types of theism I have summarised here but is neither self-contradictory nor incoherent.

This is one of the main differences between scientific or philosophical atheists and religious theists: the latter typically will not even admit that it is possible that they are mistaken, and in some cases try to make a virtue of having faith that is not backed up by evidence or reason.

Educating children to have closed minds of that sort is thoroughly unethical and can be compared with foot-binding. I have called it mind-minding, since it constrains intellectual development, leaving minds permanently immature -- stunted mental growth. This is a cause of much harm that people do to one another in the name of religion. It is for that reason that state-funding should never be used to support faith-schools.

    being Aware of ...   being Unaware of ....
    AW(A1(TS))           UW(A1(TS))
    AW(A2(TS))           UW(A2(TS))
    AW(A3(TS))           UW(A3(TS))
    AW(A4(TS))           UW(A4(TS))
    AW(A5(TS))           UW(A5(TS))
    AW(A6(TS))           UW(A6(TS))

It is also possible to distinguish differences between the reasons why people hold a position or whether they have reasons. I am fully aware of being an analytical atheist in relation to some common varieties of theism AW(A6(TS)), and I have reasons for that, indicated elsewhere in this paper.

The important point is that for each type of theism there is some set of propositions all of which or some subset of which are accepted as true by the adherents. For any such subset there will be six corresponding varieties of atheism represented by replacing TS with a label for that set of theistic propositions in each schema above.

What follows illustrates the sorts of theistic theses, various subsets of which, at least in the communities I have encountered, are commonly regarded as characterising religious beliefs.

There is something or someone, often referred to as God,

• who created everything that exists, including himself
• who is a person with personal capabilities such as caring, wanting, suffering, intending, loving, listening, understanding,
• who is all knowing (there is nothing he does not know)
• who loves all humans
• who loves all animals
• who is perfectly good
• who is the source of all goodness
• who is not responsible for the evil in the universe
• who was responsible for the words in the bible, or the Koran, or ....
• who listens to the prayers of those who believe in him and takes action to make their prayers come true (well, in some cases at least).
• who chooses certain representatives to tell others what they are supposed to believe or do
• who came to earth in human form
• who alone can provide the salvation that all humans required
• whose nature is incomprehensible to humans
• without whose existence the universe would have no purpose
• belief in whom is a requirement for finding life worth living
• for whom everyone has a deep need, whether acknowledged or not (sometimes referred to as "a God-shaped hole" in every human)
• whom humans will encounter directly in an after life (or at least some humans at least)
• who wants humans to kill people who deny his existence, or who do not act according to his will, or who offend those who believe in him, (etc.)
• who will inflict eternal and terrible torment on sinners

Different theists will accept different subsets of those assertions. Some may accept none of them: there are many kinds of religion and many kinds of theism. I suspect there are mystical kinds of theism for which all the above statements are far too simple and definite.

The main point here is that for each kind of theism, as long as its adherents put forward some set of statements TS that they regard as true, there will be in principle (at least) the six possible forms of atheism about TS.

If a theistic doctrine says nothing true or false, but merely consists of exhortations to act in certain ways, or to take up certain attitudes of awe or reverence or respect to the universe, or some portion of it (which is how R.M.Hare characterised his religious belief in the 1960s), then none of the above forms of atheism is relevant. Of course, other forms, opposing the exhortations, are possible.

(I shall extend the list of theistic propositions, and possibly the list of types of atheism, from time to time. Suggestions welcome.)

Originally there were only five types of atheism on my list, until searching literature on atheism made it clear that types 5 and 6 needed to be distinguished. Many people seem to have noticed type 5, without noticing type 6.

Different subsets of that list can be taken to define different sets of theistic propositions,

    TS1, TS2, TS3, .....

For each subset, TS, there will be different kinds of Atheism, e.g.

    A1(TS)
    A2(TS)
    A3(TS)
    A4(TS)
    A5(TS)
    A6(TS)

The other theists make more or less vague statements about their attitudes to life, or their sense of mystery or awe about the universe, or they utter prescriptions about how people should live. But they don't claim to be saying something that is true. Sometimes they don't even try to convince others that they should believe or accept anything: i.e. they are not evangelical at all. We could call them 'non-assertive' theists. Nothing written here implies that what non-assertive theists say is incoherent. (It may, in some cases, be perfectly coherent, but ethically objectionable.)

My 'personal' tutor while I was a student at Balliol College in Oxford working for a DPhil on philosophy of mathematics was Richard Hare, who was a non-assertive theist.

I am not an analytical atheist about non-assertive theists. I just don't care to join them, in their claims, prescriptions, rituals, etc.

Unfortunately a normal school syllabus will not, as far as I know, teach students to do conceptual analysis, even though it is a most important skill. Usually, learning to do it requires a degree in philosophy, with a strong component of analytical philosophy.

However it is possible for people to teach themselves. In 1978 I published a tutorial on conceptual analysis in Chapter 4 of The Computer Revolution in Philosophy, now available online here. However, many readers will find that quite heavy going. Clear thinkers probably have a natural talent for learning how to do it if they have not been exposed to too much intellectual mush in their education. It possible to get the idea by working on a few relatively simple examples before starting on the really difficult conceptual analysis tasks, such as trying to clarify concepts like "consciousness", "mind", "emotion", "love", "faith", "free will", "good", "bad", "evil", "survival after death", "omnipotence", "omniscience", or "god".

One way to start is to consider the following questions. Each of them appears to be asking a question which requests an answer in the form of a proposition. The right answer will be a true proposition -- if there is a right answer. If the question is incoherent, no answers can be true or false.

• Which flows faster, time or the Mississippi river?
• Which is the fattest day of the week?
• How heavy is the number three?
• Does the tree in my garden grow faster than the Mississippi river flows?
• What time is it now at the centre of the earth?
• In which direction is the Universe moving?
• Does the universe weigh more at the north pole than at the equator of the earth?
• Who will be the first person to create a 3-D Penrose triangle?
  (NB: not just something that looks like a Penrose triangle -- Richard Gregory did that long ago --
  but something that is how the Penrose triangle looks.)
• How many grains of sand know that three plus two equals five?
• How many rain clouds should a scientific theory contain?
• What does the wind hope to achieve when it blows clouds?
• How angry can a cloud get at being blown off course?
• Who made the number six bigger than the number five?
• What was the last thing that happened before the beginning of time?
• Which day of the week cares most about humanity?
• Who is the tallest employer in New York who employs every individual in New York that is not self-employed and employs nobody else?
• Is the answer to this question true or false?
• How big does a circle have to be in order to have three corners?
• Who made the number ninety nine?
• Did the universe create itself on a Tuesday?
• Who will build a tower in the next fifty years that is twice as tall as the tallest tower built in the 21st century?
• How long would it take to create a catalogue of all and only the catalogues that have ever existed or will exist that do not list themselves?
• Which colour of the rainbow is the heaviest?
• After how many weeks does a fertilised human embryo acquire free will?
• How big was the first animal produced by biological evolution?
• Since every human sperm is a potential human, isn't it wrong to allow their potential to go unfulfilled?
• At precisely what stage is a foetus conscious?
• At precisely what stage does a foetus become a human being?
• What is it like to be a fertilised egg?
• What is it like to be a Tuesday?

• Who or what made the universe?
• Why would an all powerful, omniscient, perfectly good creator of the universe allow humans and other animals to suffer terrible pain and die horrible deaths?
• Why should something commanded by God be good?
• Why should something forbidden by God be bad?
• If God made everything why is he not responsible for the existence of tyrants and torturers?
• Why is it better to believe something you have been told to believe than to believe things for which you can find strong supporting evidence and only weak counter evidence?
• If it is not wicked for God to allow his creatures to be murderers and rapists why is it wicked for human parents to let their children be murderers and rapists?
• If it is not wicked for God to allow people to be killed by tornadoes, volcanoes, earthquakes, and droughts, does that mean it is not wicked for humans to allow people to die when their deaths can be prevented?