Difference Between Consequentialism and Deontology Essay

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Guidelines on Writing a Philosophy Paper
Guidelines on Writing a Philosophy
Philosophical writing is different from the writing you’ll be asked to do in other courses. Most of the
strategies described below will also serve you well when writing for other courses, but don’t
automatically assume that they all will. Nor should you assume that every writing guideline you’ve been
given by other teachers is important when you’re writing a philosophy paper. Some of those guidelines
are routinely violated in good philosophical prose (e.g., see the guidelines on grammar, below).
What Does One Do in a Philosophy Paper?
Three Stages of Writing
Early Stages
Write a Draft
Rewrite, and Keep Rewriting
Minor Points
How You’ll Be Graded
What Does One Do in a Philosophy Paper?
1. A philosophy paper consists of the reasoned defense of some claim
Your paper must offer an argument. It can’t consist in the mere report of your opinions, nor in a
mere report of the opinions of the philosophers we discuss. You have to defend the claims you
make. You have to offer reasons to believe them.
So you can’t just say:
My view is that P.
You must say something like:
My view is that P. I believe this because…
I find that the following considerations…provide a convincing argument for
Similarly, don’t just say:
Descartes says that Q.
Instead, say something like:
Descartes says that Q; however, the following thought‐experiment will show
that Q is not true…
Guidelines on Writing a Philosophy Paper
Descartes says that Q. I find this claim plausible, for the following
There are a variety of things a philosophy paper can aim to accomplish. It usually begins by
putting some thesis or argument on the table for consideration. Then it goes on to do one or two of
the following:
Criticize that argument; or show that certain arguments for the thesis are no good
Defend the argument or thesis against someone else’s criticism
Offer reasons to believe the thesis
Offer counter­examples to the thesis
Contrast the strengths and weaknesses of two opposing views about the thesis
Give examples which help explain the thesis, or which help to make the thesis more
Argue that certain philosophers are committed to the thesis by their other views, though they
do not come out and explicitly endorse the thesis
Discuss what consequences the thesis would have, if it were true
Revise the thesis, in the light of some objection
No matter which of these aims you set for yourself, you have to explicitly present reasons for
the claims you make. Students often feel that since it’s clear to them that some claim is true, it
does not need much argument. But it’s very easy to overestimate the strength of your own position.
After all, you already accept it. You should assume that your audience does not already accept
your position; and you should treat your paper as an attempt to persuade such an audience. Hence,
don’t start with assumptions which your opponents are sure to reject. If you’re to have any chance
of persuading people, you have to start from common assumptions you all agree to.
2. A good philosophy paper is modest and makes a small point; but it makes that point clearly and
straightforwardly, and it offers good reasons in support of it
People very often attempt to accomplish too much in a philosophy paper. The usual result of this is
a paper that’s hard to read, and which is full of inadequately defended and poorly explained claims.
So don’t be over­ambitious. Don’t try to establish any earth­shattering conclusions in your 5­6 page
paper. Done properly, philosophy moves at a slow pace.
3. Originality
The aim of these papers is for you to show that you understand the material and that you’re able to
think critically about it. To do this, your paper does have to show some independent thinking.
That doesn’t mean you have to come up with your own theory, or that you have to make a
completely original contribution to human thought. There will be plenty of time for that later on.
An ideal paper will be clear and straightforward (see below), will be accurate when it attributes
views to other philosophers (see below), and will contain thoughtful critical responses to the texts
we read. It need not always break completely new ground.
But you should try to come up with your own arguments, or your own way of elaborating or
criticizing or defending some argument we looked at in class. Merely summarizing what others
have said won’t be enough.
Guidelines on Writing a Philosophy Paper
Three Stages of Writing
1. Early Stages
The early stages of writing a philosophy paper include everything you do before you sit down and write
your first draft. These early stages will involve writing, but you won’t yet be trying to write a complete
paper. You should instead be taking notes on the readings, sketching out your ideas, trying to explain the
main argument you want to advance, and composing an outline.
Discuss the issues with others
As I said above, your papers are supposed to demonstrate that you understand and can think critically
about the material we discuss in class. One of the best ways to check how well you understand that
material is to try to explain it to someone who isn’t already familiar with it. I’ve discovered time and
again while teaching philosophy that I couldn’t really explain properly some article or argument I thought
I understood. This was because it was really more problematic or complicated than I had realized. You
will have this same experience. So it’s good to discuss the issues we raise in class with each other, and
with friends who aren’t taking the class. This will help you understand the issues better, and it will make
you recognize what things you still don’t fully understand.
It’s even more valuable to talk to each other about what you want to argue in your paper. When you have
your ideas worked out well enough that you can explain them to someone else, verbally, then you’re
ready to sit down and start making an outline.
Make an outline
Before you begin writing any drafts, you need to think about the questions: In what order should you
explain the various terms and positions you’ll be discussing? At what point should you present your
opponent’s position or argument? In what order should you offer your criticisms of your opponent? Do
any of the points you’re making presuppose that you’ve already discussed some other point, first? And so
The overall clarity of your paper will greatly depend on its structure. That is why it is important to think
about these questions before you begin to write.
I strongly recommend that you make an outline of your paper, and of the arguments you’ll be presenting,
before you begin to write. This lets you organize the points you want to make in your paper and get a
sense for how they are going to fit together. It also helps ensure that you’re in a position to say what your
main argument or criticism is, before you sit down to write a full draft of your paper. When students get
stuck writing, it’s often because they haven’t yet figured out what they’re trying to say.
Give your outline your full attention. It should be fairly detailed. (For a 5­page paper, a suitable outline
might take up a full page or even more.)
I find that making an outline is at least 80% of the work of writing a good philosophy paper. If you have
a good outline, the rest of the writing process will go much more smoothly.
Guidelines on Writing a Philosophy Paper
Start Work Early
Philosophical problems and philosophical writing require careful and extended reflection. Don’t wait
until two or three nights before the paper is due to begin. That is very stupid. Writing a good philosophy
paper takes a great deal of preparation.
You need to leave yourself enough time to think about the topic and write a detailed outline. Only then
should you sit down to write a complete draft. Once you have a complete draft, you should set it aside for
a day or two. Then you should come back to it and rewrite it. Several times. At least 3 or 4. If you can,
show it to your friends and get their reactions to it. Do they understand your main point? Are parts of
your draft unclear or confusing to them?
All of this takes time. So you should start working on your papers as soon as the paper topics are
2. Write a Draft
Once you’ve thought about your argument, and written an outline for your paper, then you’re ready to sit
down and compose a complete draft.
Use simple prose
Don’t shoot for literary elegance. Use simple, straightforward prose. Keep your sentences and paragraphs
short. Use familiar words. We’ll make fun of you if you use big words where simple words will do. These
issues are deep and difficult enough without your having to muddy them up with pretentious or verbose
language. Don’t write using prose you wouldn’t use in conversation: if you wouldn’t say it, don’t
write it.
You may think that since your TA and I already know a lot about this subject, you can leave out a lot of
basic explanation and write in a super­sophisticated manner, like one expert talking to another. I
guarantee you that this will make your paper incomprehensible.
If your paper sounds as if it were written for a third­grade audience, then you’ve probably achieved the
right sort of clarity.
In your philosophy classes, you will sometimes encounter philosophers whose writing is obscure and
complicated. Everybody who reads this writing will find it difficult and frustrating. The authors in
question are philosophically important despite their poor writing, not because of it. So do not try to
emulate their writing styles.
Make the structure of your paper obvious
You should make the structure of your paper obvious to the reader. Your reader shouldn’t have to exert
any effort to figure it out. Beat him over the head with it.
How can you do this?
First of all, use connective words, like:
because, since, given this argument
Guidelines on Writing a Philosophy Paper
thus, therefore, hence, it follows that, consequently
nevertheless, however, but
in the first case, on the other hand
These will help your reader keep track of where your discussion is going. Be sure you use these words
correctly! If you say “P. Thus Q.” then you are claiming that P is a good reason to accept Q. You had
better be right. If you aren’t, we’ll complain. Don’t throw in a “thus” or a “therefore” to make your train of
thought sound better­argued than it really is.
Another way you can help make the structure of your paper obvious is by telling the reader what you’ve
done so far and what you’re going to do next. You can say things like:
I will begin by…
Before I say what is wrong with this argument, I want to…
These passages suggest that…
I will now defend this claim…
Further support for this claim comes from…
For example…
These signposts really make a big difference. Consider the following two paper fragments:
…We’ve just seen how X says that P. I will now present two arguments that not‐
P. My first argument is…
My second argument that not‐P is…
X might respond to my arguments in several ways. For instance, he could say
However this response fails, because…
Another way that X might respond to my arguments is by claiming that…
This response also fails, because…
So we have seen that none of X’s replies to my argument that not‐P succeed.
Hence, we should reject X’s claim that P.
I will argue for the view that Q.
There are three reasons to believe Q. Firstly…
The strongest objection to Q says…
However, this objection does not succeed, for the following reason…
Isn’t it easy to see what the structure of these papers is? You want it to be just as easy in your own papers.
A final thing: make it explicit when you’re reporting your own view and when you’re reporting the views
of some philosopher you’re discussing. The reader should never be in doubt about whose claims you’re
presenting in a given paragraph.
You can’t make the structure of your paper obvious if you don’t know what the structure of your paper is,
or if your paper has no structure. That’s why making an outline is so important.
Be concise, but explain yourself fully
To write a good philosophy paper, you need to be concise but at the same time explain yourself fully.
These demands might seem to pull in opposite directions. (It’s as if the first said “Don’t talk too much,”
and the second said “Talk a lot.”) If you understand these demands properly, though, you’ll see how it’s
Guidelines on Writing a Philosophy Paper
possible to meet them both.
We tell you to be concise because we don’t want you to ramble on about everything you know
about a given topic, trying to show how learned and intelligent you are. Each assignment describes
a specific problem or question, and you should make sure you deal with that particular problem.
Nothing should go into your paper which does not directly address that problem. Prune out
everything else. It is always better to concentrate on one or two points and develop them in depth
than to try to cram in too much. One or two well­mapped paths are better than an impenetrable
Formulate the central problem or question you wish to address at the beginning of your paper, and
keep it in mind at all times. Make it clear what the problem is, and why it is a problem. Be sure that
everything you write is relevant to that central problem. In addition, be sure to say in the paper how
it is relevant. Don’t make your reader guess.
One thing I mean by “explain yourself fully” is that, when you have a good point, you shouldn’t
just toss it off in one sentence. Explain it; give an example; make it clear how the point helps your
But “explain yourself fully” also means to be as clear and explicit as you possibly can when you’re
writing. It’s no good to protest, after we’ve graded your paper, “I know I said this, but what I
meant was…” Say exactly what you mean, in the first place. Part of what you’re being graded on is
how well you can do that.
Pretend that your reader has not read the material you’re discussing, and has not given the topic
much thought in advance. This will of course not be true. But if you write as if it were true, it will
force you to explain any technical terms, to illustrate strange or obscure distinctions, and to be as
explicit as possible when you summarize what some other philosopher said.
In fact, you can profitably take this one step further and pretend that your reader is lazy, stupid, and
mean. He’s lazy in that he doesn’t want to figure out what your convoluted sentences are supposed
to mean, and he doesn’t want to figure out what your argument is, if it’s not already obvious. He’s
stupid, so you have to explain everything you say to him in simple, bite­sized pieces. And he’s
mean, so he’s not going to read your paper charitably. (For example, if something you say admits of
more than one interpretation, he’s going to assume you meant the less plausible thing.) If you
understand the material you’re writing about, and if you aim your paper at such a reader, you’ll
probably get an A.
Use plenty of examples and definitions
It is very important to use examples in a philosophy paper. Many of the claims philosophers make are
very abstract and hard to understand, and examples are the best way to make those claims clearer.
Examples are also useful for explaining the notions that play a central role in your argument. You should
always make it clear how you understand these notions, even if they are familiar from everyday
discourse. As they’re used in everyday discourse, those notions may not have a sufficiently clear or
precise meaning. For instance, suppose you’re writing a paper about abortion, and you want to assert the
claim “A fetus is a person.” What do you mean by “a person”? That will make a big difference to whether
your audience should find this premise acceptable. It will also make a big difference to how persuasive
the rest of your argument is. By itself, the following argument is pretty worthless:
Guidelines on Writing a Philosophy Paper
A fetus is a person.
It’s wrong to kill a person.
Therefore, it’s wrong to kill a fetus.
For we don’t know what the author means by calling a fetus “a person.” On some interpretations of
“person,” it might be quite obvious that a fetus is a person; but quite controversial whether it’s always
wrong to kill persons, in that sense of “person.” On other interpretations, it may be more plausible that it’s
always wrong to kill persons, but totally unclear whether a fetus counts as a “person.” So everything
turns here on what the author means by “person.” The author should be explicit about how he is using
this notion.
In a philosophy paper, it’s okay to use words in ways that are somewhat different from the ways they’re
ordinarily used. You just have to make it clear that you’re doing this. For instance, some philosophers use
the word “person” to mean any being which is capable of rational thought and self­awareness.
Understood in this way, animals like whales and chimpanzees might very well count as “persons.” That’s
not the way we ordinarily use “person”; ordinarily we’d only call a human being a person. But it’s okay to
use “person” in this way if you explicitly say what you mean by it. And likewise for other words.
Don’t vary your vocabulary just for the sake of variety
If you call something “X” at the start of your paper, call it “X” all the way through. So, for
instance, don’t start talking about “Plato’s view of the self,” and then switch to talking about
“Plato’s view of the soul,” and then switch to talking about “Plato’s view of the mind.” If you mean
to be talking about the same thing in all three cases, then call it by the same name. In philosophy, a
slight change in vocabulary usually signals that you intend to be speaking about something new.
Using words with precise philosophical meanings
Philosophers give many ordinary­sounding words precise technical meanings. Consult the
handouts on Philosophical Terms and Methods to make sure you’re using these words correctly.
Don’t use words that you don’t fully understand.
Use technical philosophical terms only where you need them. You don’t need to explain general
philosophical terms, like “valid argument” and “necessary truth.” But you should explain any
technical terms you use which bear on the specific topic you’re discussing. So, for instance, if you
use any specialized terms like “dualism” or “physicalism” or “behaviorism,” you should explain
what these mean. Likewise if you use technical terms like “supervenience” and the like. Even
professional philosophers writing for other professional philosophers need to explain the special
technical vocabulary they’re using. Different people sometimes use this special vocabulary in
different ways, so it’s important to make sure that you and your readers are all giving these words
the same meaning. Pretend that your readers have never heard them before.
Presenting and assessing the views of others
If you plan to discuss the views of Philosopher X, begin by figuring out what his arguments or central
assumptions are. See my tips on How To Read a Philosophy Paper for some help doing this.
Then ask yourself: Are X’s arguments good ones? Are his assumptions clearly stated? Are they plausible?
Are they reasonable starting­points for X’s argument, or ought he have provided some independent
argument for them?
Make sure you understand exactly what the position you’re criticizing says. Students waste a lot of time
Guidelines on Writing a Philosophy Paper
arguing against views that sound like, but are really different from, the views they’re supposed to be
assessing. Remember, philosophy demands a high level of precision. It’s not good enough for you merely
to get the general idea of somebody else’s position or argument. You have to get it exactly right. (In this
respect, philosophy is more like a science than the other humanities.) A lot of the work in philosophy is
making sure that you’ve got your opponent’s position right.
You can assume that your reader is stupid (see above). But don’t treat the philosopher or the views you’re
discussing as stupid. If they were stupid, we wouldn’t be looking at them. If you can’t see anything the
view has going for it, maybe that’s because you don’t have much experience thinking and arguing about
the view, and so you haven’t yet fully understood why the view’s proponents are attracted to it. Try harder
to figure out what’s motivating them.
Philosophers sometimes do say outrageous things, but if the view you’re attributing to a philosopher
seems to be obviously crazy, then you should think hard about whether he really does say what you think
he says. Use your imagination. Try to figure out what reasonable position the philosopher could have had
in mind, and direct your arguments against that.
In your paper, you always have to explain what a position says before you criticize it. If you don’t explain
what you take Philosopher X’s view to be, your reader cannot judge whether the criticism you offer of X
is a good criticism, or whether it is simply based on a misunderstanding or misinterpretation of X’s views.
So tell the reader what it is you think X is saying.
Don’t try to tell the reader everything you know about X’s views, though. You have to go on to offer your
own philosophical contribution, too. Only summarize those parts of X’s views that are directly
relevant to what you’re going to go on to do.
Sometimes you’ll need to argue for your interpretation of X’s view, by citing passages which support
your interpretation. It is permissible for you to discuss a view you think a philosopher might have held, or
should have held, though you can’t find any direct evidence of that view in the text. When you do this,
though, you should explicitly say so. Say something like:
Philosopher X doesn’t explicitly say that P, but it seems to me that he’s
assuming it anyway, because…
When a passage from a text is particularly useful in supporting your interpretation of some
philosopher’s views, it may be helpful to quote the passage directly. (Be sure to specify where the
passage can be found.) However, direct quotations should be used sparingly. It is seldom necessary
to quote more than a few sentences. Often it will be more appropriate to paraphrase what X says,
rather than to quote him directly. When you are paraphrasing what somebody else said, be sure to
say so. (And here too, cite the pages you’re referring to.)
Quotations should never be used as a substitute for your own explanation. And when you do quote
an author, you still have to explain what the quotation says in your own words. If the quoted
passage contains an argument, reconstruct the argument in more explicit, straightforward terms. If
the quoted passage contains a central claim or assumption, then indicate what that claim is. You
may want to give some examples to illustrate the author’s point. If necessary, you may want to
distinguish the author’s claim from other claims with which it might be confused.
Guidelines on Writing a Philosophy Paper
Sometimes when students are trying to explain a philosopher’s view, they’ll do it by giving very
close paraphrases of the philosopher’s own words. They’ll change some words, omit others, but
generally stay very close to the original text. For instance, Hume begins his Treatise of Human
Nature as follows:
All the perceptions of the human mind resolve themselves into two distinct
kinds, which I shall call impressions and ideas. The difference betwixt
these consists in the degrees of force and liveliness, with which they
strike upon the mind, and make their way into our thought or consciousness.
Those perceptions, which enter with most force and violence, we may name
impressions; and under this name I comprehend all our sensations, passions,
and emotions, as they make their first appearance in the soul. By ideas I
mean the faint images of these in thinking and reasoning.
Here’s an example of how you don’t want to paraphrase:
Hume says all perceptions of the mind are resolved into two kinds,
impressions and ideas. The difference is in how much force and liveliness
they have in our thoughts and consciousness. The perceptions with the most
force and violence are impressions. These are sensations, passions, and
emotions. Ideas are the faint images of our thinking and reasoning.
There are two main problems with paraphrases of this sort. In the first place, it’s done rather
mechanically, so it doesn’t show that the author understands the text. In the second place, since the
author hasn’t figured out what the text means well enough to express it in his own words, there’s a
danger that his paraphrase may inadvertently change the meaning of the text. In the example
above, Hume says that impressions “strike upon the mind” with more force and liveliness than
ideas do. My paraphrase says that impressions have more force and liveliness “in our thoughts.” It’s
not clear whether these are the same thing. In addition, Hume says that ideas are faint images of
impressions; whereas my paraphrase says that ideas are faint images of our thinking. These are not
the same. So the author of the paraphrase appears not to have understood what Hume was saying in
the original passage.
A much better way of explaining what Hume says here would be the following:
Hume says that there are two kinds of ‘perceptions,’ or mental states. He
calls these impressions and ideas. An impression is a very ‘forceful’ mental
state, like the sensory impression one has when looking at a red apple. An
idea is a less ‘forceful’ mental state, like the idea one has of an apple
while just thinking about it, rather than looking at it. It is not so clear
what Hume means here by ‘forceful.’ He might mean…
Anticipate objections
Try to anticipate objections to your view and respond to them. For instance, if you object to some
philosopher’s view, don’t assume he would immediately admit defeat. Imagine what his comeback might
be. How would you handle that comeback?
Don’t be afraid of mentioning objections to your own thesis. It is better to bring up an objection yourself
than to hope your reader won’t think of it. Explain how you think these objections can be countered or
overcome. Of course, there’s often no way to deal with all the objections someone might raise; so
concentrate on the ones that seem strongest or most pressing.
Guidelines on Writing a Philosophy Paper
What happens if you’re stuck?
Your paper doesn’t always have to provide a definite solution to a problem, or a straight yes or no answer
to a question. Many excellent philosophy papers don’t offer straight yes or no answers. Sometimes they
argue that the question needs to be clarified, or that certain further questions need to be raised.
Sometimes they argue that certain assumptions of the question need to be challenged. Sometimes they
argue that certain answers to the question are too easy, that is, they won’t work. Hence, if these papers are
right, the question will be harder to answer than we might previously have thought. These are all
important and philosophically valuable results.
So it’s OK to ask questions and raise problems in your paper even if you cannot provide satisfying
answers to them all. You can leave some questions unanswered at the end of the paper. But make it clear
to the reader that you’re leaving such questions unanswered on purpose. And you should say something
about how the question might be answered, and about what makes the question interesting and relevant to
the issue at hand.
If something in a view you’re examining is unclear to you, don’t gloss it over. Call attention to the
unclarity. Suggest several different ways of understanding the view. Explain why it’s not clear which of
these interpretations is correct.
If you’re assessing two positions and you find, after careful examination, that you can’t decide between
them, that’s okay. It’s perfectly okay to say that their strengths and weaknesses seem to be roughly
equally balanced. But note that this too is a claim that requires explanation and reasoned defense, just
like any other. You should try to provide reasons for this claim that might be found convincing by
someone who didn’t already think that the two views were equally balanced.
Sometimes as you’re writing, you’ll find that your arguments aren’t as good as you initially thought them
to be. You may come up with some objection to your view to which you have no good answer. Don’t
panic. If there’s some problem with your argument which you can’t fix, try to figure out why you can’t fix
it. It’s okay to change your thesis to one you can defend. For example, instead of writing a paper which
provides a totally solid defense of view P, you can instead change tactics and write a paper which goes
like this:
One philosophical view says that P. This is a plausible view, for the following
However, there are some reasons to be doubtful whether P. One of these reasons is
X. X poses a problem for the view that P because…
It is not clear how the defender of P can overcome this objection.
Or you can write a paper which goes:
One argument for P is the ‘Conjunction Argument,’ which goes as follows…
At first glance, this is a very appealing argument. However, this argument is
faulty, for the following reasons…
One might try to repair the argument, by…
But these repairs will not work, because…
I conclude that the Conjunction Argument does not in fact succeed in establishing
Writing a paper of these sorts doesn’t mean you’ve “given in” to the opposition. After all, neither of these
papers commits you to the view that not­P. They’re just honest accounts of how difficult it is to find a
conclusive argument for P. P might still be true, for all that.
Guidelines on Writing a Philosophy Paper
3. Rewrite, and Keep Rewriting
Now you’ve written a complete draft of your paper. Set the draft aside for a day or two.
Then come back to the draft and re­read it. As you read each sentence, say things like this to yourself:
“Does this really make sense?” “That’s totally unclear!” “That sounds
pretentious.” “What does that mean?” “What’s the connection between these two
sentences?” “Am I just repeating myself here?” and so on.
Make sure every sentence in your draft does useful work. Get rid of any which don’t. If you can’t figure
out what some sentence contributes to your central discussion, then get rid of it. Even if it sounds nice.
You should never introduce any points in your paper unless they’re important to your main argument, and
you have the room to really explain them.
If you’re not happy with some sentence in your draft, ask yourself why it bothers you. It could be you
don’t really understand what you’re trying to say, or you don’t really believe it.
Make sure your sentences say exactly what you want them to say. For example, suppose you write
“Abortion is the same thing as murder.” Is that what you really mean? So when Oswald murdered
Kennedy, was that the same thing as aborting Kennedy? Or do you mean something different? Perhaps
you mean that abortion is a form of murder. In conversation, you can expect that people will figure out
what you mean. But you shouldn’t write this way. Even if your TA is able to figure out what you mean,
it’s bad writing. In philosophical prose, you have to be sure to say exactly what you mean.
Also pay attention to the structure of your draft. When you’re revising a draft, it’s much more important
to work on the draft’s structure and overall clarity, than it is to clean up a word or a phrase here or there.
Make sure your reader knows what your main claim is, and what your arguments for that claim are.
Make sure that your reader can tell what the point of every paragraph is. It’s not enough that you know
what their point is. It has to be obvious to your reader, even to a lazy, stupid, and mean reader.
If you can, show your draft to your friends or to other students in the class, and get their comments and
advice. I encourage you to do this. Do your friends understand your main point? Are parts of your draft
unclear or confusing to them? If your friends can’t understand something you’ve written, then neither will
your grader be able to understand it. Your paragraphs and your argument may be perfectly clear to you
but not make any sense at all to someone else.
Another good way to check your draft is to read it out loud. This will help you tell whether it all makes
sense. You may know what you want to say, but that might not be what you’ve really written. Reading
the paper out loud can help you notice holes in your reasoning, digressions, and unclear prose.
You should count on writing many drafts of your paper. At least 3 or 4!! Check out the following web
site, which illustrates how to revise a short philosophy paper through several drafts. Notice how much the
paper improves with each revision:
Writing tutor for Introductory Philosophy Courses .
Minor Points
Guidelines on Writing a Philosophy Paper
Beginning your paper
Don’t begin with a sentence like “Down through the ages, mankind has pondered the problem of…”
There’s no need to warm up to your topic. You should get right to the point, with the first sentence.
Also, don’t begin with a sentence like “Webster’s Dictionary defines a soul as…” Dictionaries aren’t good
philosophical authorities. They record the way words are used in everyday discourse. Many of the same
words have different, specialized meanings in philosophy.
It’s OK to end a sentence with a preposition. It’s also OK to split an infinitive, if you need to.
(Sometimes the easiest way to say what you mean is by splitting an infinitive. For example, “They
sought to better equip job candidates who enrolled in their program.”) Efforts to avoid these often
end up just confusing your prose.
Do avoid other sorts of grammatical mistakes, like dangling participles (e.g., “Hurt by her fall, the
tree fell right on Mary’s leg before she could get out of the way”), and the like.
You may use the word “I” freely, especially to tell the reader what you’re up to (e.g., “I’ve just
explained why… Now I’m going to consider an argument that…”).
Don’t worry about using the verb “is” or “to be” too much. In a philosophy paper, it’s OK to use
this verb as much as you need to.
Secondary readings
For most classes, I will put some articles and books on reserve in Bobst Library for additional reading.
These are optional, and are for your independent study.
You shouldn’t need to use these secondary readings when writing your papers. The point of the papers is
to teach you how to analyze a philosophical argument, and present your own arguments for or against
some conclusion. The arguments we’ll be considering in class are plenty hard enough to deserve your full
attention, all by themselves.
Can you write your paper as a dialogue or story?
No. Done well, these forms of philosophical writing can be very effective. That’s why we read some
dialogues and stories in Philosophy 3. But these forms of philosophical writing are extremely difficult to
do well. They tempt the author to be imprecise and to use unclear metaphors. You need to master
ordinary philosophical writing before you can do a good job with these more difficult forms.
Aim to make your papers less than or equal to the assigned word limit. Longer papers are typically too
ambitious, or repetitious, or full of digressions. Your grade will suffer if your paper has these defects. So
it’s important to ask yourself: What are the most important things you have to say? What can be left out?
But neither should your papers be too short! Don’t cut off an argument abruptly. If a paper topic you’ve
Guidelines on Writing a Philosophy Paper
chosen asks certain questions, be sure you answer or address each of those questions.
Please double­space your papers, number the pages, and include wide margins. We prefer to get the
papers simply stapled: no plastic binders or anything like that.
Include your name on the paper. And don’t turn in your only copy! (These things should be obvious, but
apparently they’re not.)
How You’ll Be Graded
You’ll be graded on three basic criteria:
1. How well do you understand the issues you’re writing about?
2. How good are the arguments you offer?
3. Is your writing clear and well­organized?
We do not judge your paper by whether we agree with its conclusion. In fact, we may not agree
amongst ourselves about what the correct conclusion is. But we will have no trouble agreeing
about whether you do a good job arguing for your conclusion.
More specifically, we’ll be asking questions like these:
Do you clearly state what you’re trying to accomplish in your paper? Is it obvious to the
reader what your main thesis is?
Do you offer supporting arguments for the claims you make? Is it obvious to the reader what
these arguments are?
Is the structure of your paper clear? For instance, is it clear what parts of your paper are
expository, and what parts are your own positive contribution?
Is your prose simple, easy to read, and easy to understand?
Do you illustrate your claims with good examples? Do you explain your central notions? Do
you say exactly what you mean?
Do you present other philosophers’ views accurately and charitably?
The comments I find myself making on students’ philosophy papers most often are these:
“Explain this claim” or “What do you mean by this?” or “I don’t understand what you’re
saying here”
“This passage is unclear (or awkward, or otherwise hard to read)” “Too complicated”
“Too hard to follow” “Simplify”
“Why do you think this?” “This needs more support” “Why should we believe this?”
“Explain why this is a reason to believe P” “Explain why this follows from what you
said before”
“Not really relevant”
“Give an example?”
Try to anticipate these comments and avoid the need for them!
Guidelines on Writing a Philosophy Paper
Your paper should do some philosophical work
A kind of complaint that is common in undergraduate philosophy papers goes like this:
Philosopher X assumes A and argues from there to B. B seems unattractive to
me. Philosopher X just assumes A and doesn’t give any argument for it. I
don’t think A is true. So I can just reject A and thereby avoid B.
This line of thought may very well be correct. And the student may very well be right that
Philosopher X should have given more argument for A. But the student hasn’t really
philosophically engaged with Philosopher X’s view in an interesting way. He hasn’t really done
much philosophical work. It was clear from the outset that Philosopher X was assuming A, and
that if you don’t want to make that assumption, you don’t need to accept X’s conclusion. If this is
all you do in your paper, it won’t be a strong paper and it will get a mediocre grade, even if it’s
Here are some more interesting things our student could have done in his paper. He could have
argued that B doesn’t really follow from A, after all. Or he could have presented reasons for
thinking that A is false. Or he could have argued that assuming A is an illegitimate move to make
in a debate about whether B is true. Or something else of that sort. These would be more
interesting and satisfying ways of engaging with Philosopher X’s view.
Responding to comments from me or your TA
When you have the opportunity to rewrite a graded paper, keep the following points in mind.
Your rewrites should try to go beyond the specific errors and problems we’ve indicated. If you got
below an A­, then your draft was generally difficult to read, it was difficult to see what your
argument was and what the structure of your paper was supposed to be, and so on. You can only
correct these sorts of failings by rewriting your paper from scratch. (Start with a new, empty
window in your word processor.) Use your draft and the comments you received on it to construct
a new outline, and write from that.
Keep in mind that when I or your TA grade a rewrite, we may sometimes notice weaknesses in
unchanged parts of your paper that we missed the first time around. Or perhaps those weaknesses
will have affected our overall impression of the paper, and we just didn’t offer any specific
recommendation about fixing them. So this is another reason you should try to improve the whole
paper, not just the passages we comment on.
It is possible to improve a paper without improving it enough to raise it to the next grade level.
Sometimes that happens. But I hope you’ll all do better than that.
Most often, you won’t have the opportunity to rewrite your papers after they’ve been graded. So
you need to teach yourself to write a draft, scrutinize the draft, and revise and rewrite your paper
before turning it in to be graded.
Guidelines on Writing a Philosophy Paper
I don’t want to claim undue credit for this work. A lot of the suggestions here derive from writing
handouts that friends and colleagues lent me. (Alison Simmons and Justin Broackes deserve special
thanks.) Also, I’ve browsed some other writing guidelines on the web, and occasionally incorporated
advice I thought my students would find useful. Peter Horban’s site deserves special mention. Thanks to
Professor Horban for allowing me to incorporate some of his suggestions here.
Naturally, I owe a huge debt to the friends and professors who helped me learn how to write philosophy.
I’m sure they had a hard time of it.
If you’re a teacher and you think your own students would find this web site useful, you are free to point
them here (or to distribute printed copies). It’s all in the public good.
Full licensing details are here.
Created and maintained by jim.pryor@nyu.edu
This work licensed under a Creative Commons License
URL: http://www.jimpryor.net/teaching/guidelines/writing.html
Updated: 6­Sep­12 11:35 AM
Philo 2: Puzzles and Paradoxes
Paradoxes of Analysis
Three paradoxes of understanding and interpretation:
• Paradox of Analysis
• Problem of the Criterion
• Hermeneutic Circle

Plato (428/427 or 424/423 – 348/347
BC). Philosopher in Classical Greece.

George Edward Moore (1873–
1958). British philosopher who taught
at the University of Cambridge. He
worked in ethics, epistemology, and
What is Conceptual Analysis?
To analyze a concept F is to give an account of what is it to fall
under that concept — of what that concepts means.
To so so, it seems like we need to come up with a necessary
and sufficient condition, G, for being an F…
(1) The analysis should take the logical form of a
universally quantified biconditional:
(2) This biconditional should be a necessary truth – in
particular, it should be a conceptual truth.
(3) The analysis should be informative.
(4) An analysis should be knowable a priori – in particular, it
should knowable via reflection on the relevant concepts.
Necessary/Sufficient Conditions
• To say that X is a necessary condition for Y is to say that it is
impossible to have Y without X.
• In other words, the absence of X guarantees the absence of Y.
• Example: Having four sides is necessary for being a
• To say that X is a sufficient condition for Y is to say that the
presence of X guarantees the presence of Y.
• In other words, it is impossible to have X without Y.
• Example: Being a square is sufficient for having four sides.
• See lecture 2, slide #34
Conceptual Truths
A conceptual truth (or analytic truth) is a fact that holds in virtue of
the meanings of the relevant terms or concepts.
In other to understand why a conceptual truth is true, we don’t need
to consider how the world is, independently of our concepts or words
— we only need to consider the meaning of our concepts or words
themselves. For this reason, conceptual truths are necessary – as
opposed to contingent. They hold not matter what the world is like.
Moreover, if we fully understand the concepts or words we are using
— we should be able to know conceptual truths via reflection on
these meanings without any appeal to empirical evidence or data.
For this reason, conceptual truths are knowable a priori.
1. A brother is a male sibling.
2. A square is a four-sided polygon with four equal sides.
3. Knowledge is justified, true belief?
4. Something is pious just in case it is loved by the Gods?
Much of philosophy and mathematics (etc) seems to involve
forms of conceptual analysis.
The Paradox of Analysis
• The basic thought: for a conceptual analysis to be informative, it
must be incorrect; and to be correct, it must be uninformative.
• If it is in fact a conceptual truth that two descriptions are
equivalent, then anyone who understands the relevant concepts
should recognize that these descriptions are equivalent. In which
case, pointing out that these descriptions are equivalent will be
• Alternatively, if the equivalence is informative, then it must not be
obvious to everyone who understands the two descriptions. But
then it must not be a conceptual truth that these descriptions are
equivalent. In which case, the claim that they are equivalent
cannot count as a correct conceptual analysis.
The paradox of analysis goes back to Plato (Meno 80e).
The 20th century formulation of the paradox is due to C.H.
Langford (1895-1964):
“Let us call what is to be analyzed the analysandum, and let us
call that which does the analyzing the analysans. The analysis
then states an appropriate relation of equivalence between the
analysandum and the analysans. And the paradox of analysis is to
the effect that, if the verbal expression representing the
analysandum has the same meaning as the verbal expression
representing the analysans, the analysis states a bare identity and
is trivial, but if the two verbal expressions do not have the same
meaning, the analysis is incorrect“ (Langford 1942: 323).
The paradox of analysis is doubly paradoxical because the
paradox is a surprising result derived from an analysis of the
concept of analysis.
One reconstruction of the paradox of analysis:
1) An analysis of a concept, F, should say what F is identical (or
equivalent) to.
2) Suppose that a given analysis of the concept F says that it is
identical to the concept G.
3) If the concepts F and G are not identical, the analysis is false.
(1, 2)
4) If the concepts F and G are identical, then what the analysis
says (namely that F = G) has the same content as the claim that
the concept F is identical to the concept F.
5) But it is uninformative (trivial) that the concept F is identical to
the concept F.
6) So if the concepts F and G are identical, what the analysis says
is uninformative. (4, 5)
C) Therefore, the analysis is either false or uninformative. (3, 6)
End of Part 1
Solutions to Paradox of Analysis
• Two proposed solutions:
– Distinction between Sense and Reference (Gottlob
– Family Resemblance (Ludwig Wittgenstein)
Gottlob Frege (1848–1925). A
German mathematician, logician and
philosopher. He is considered to be
one of the founders of modern logic,
made major contributions to the
foundations of mathematics, and is a
founding figure of “analytic
Ludwig Wittgenstein (1889 – 1951).
Austrian philosopher who worked
primarily in logic, the philosophy of
mathematics, the philosophy of mind,
and the philosophy of language. He
taught at the University of Cambridge.
Sense and Reference
Frege‘s Proposal: the paradox of analysis dissolves once
we distinguish between the sense and the reference of a
word or phrase.
The object denoted by a word or phrase. What the word
refers to.
The mode of presentation of the object denoted by the
word or phrase. How the word presents its referent.

For example, suppose:
• That John is Mary’s only brother.
• And that John is Joe’s dearest friend.
Then “John”, “the brother of Mary”, and “Joe’s dearest friend” all refer to
John. But these phrases have different senses…

If two expressions have the same sense, then they have the same
referent (if they have a referent at all)

But two expressions with the same referent need not have the same
sense. E.g., “Mary’s brother” and “John”

Senses can be thought of as rules for finding the referent of a concept
— or as descriptions of the object that concept refers to.
More examples for expressions with the same reference but
different senses:
• “Mark Twain is Samuel Clemens“.
• “Lines travel exactly the same direction if and only if they are
parallel to one another“.
• “Alvin believes that the greatest student of Plato was a
philosopher” vs. “Alvin believes that the greatest teacher of
Alexander the Great was a philosopher”.
• “Alvin believes that 2 + 2 = 4” vs. “Alvin believes that 2 + 2 =
the positive cube root of 64”.
• “John” and “Mary’s brother“ have the same reference but
different senses. This is why “John = Mary‘s brother“ is
informative but “John = John“ is not.
1. John is Mary‘s brother
2. John is John
• (2) is trivially true. (1), however, is informative because
someone might learn something new upon reading (1).
• Hence (1) and (2) differ in cognitive significance. In
particular one can rationally believe (2) without believing (1).
• “Brother“ and “male sibling“ also have the same reference
but different senses/meanings. “A brother is a brother“ is
trivially true. “A brother is a male sibling” is informative.
Family Resemblance
• Wittgenstein‘s Proposal: We should abandon the search for
necessary and sufficient conditions for philosophical concepts
and instead look for family resemblances.
• Example: What are necessary and sufficient conditions for
something being a game?
– Not all games involve competition (e.g., Solitaire)
– Not all games are fun for the participants (e.g., gladiatorial
– Not only games are governed by rules (e.g., political
– Not only games have objectives (e.g., initiation ceremonies)
• Pairs of games resemble each other in certain respects, but
what respects these are differs from game to game.
• Analogy: Faces of pairs of people from the same family may
resemble each other in certain respects but what these
respects are differ from pair to pair.
End of Part 2
Three paradoxes of understanding and interpretation:
• Paradox of Analysis
• Problem of the Criterion
• Hermeneutic Circle

Sextus Empiricus (160-210
AD). Physician and philosopher
who lived in Egypt, Italy and
Greece. Famous for his
compilation of skeptic arguments.

Georg Wilhelm Friedrich Hegel
(1770 – 1831). German
philosopher of the late
Enlightenment. Father of the
dialectical method. Influential on
Marx and others.

Roderick Chisholm (1916 –
1999). American philosopher
known for his work on
epistemology, metaphysics, free
will, value theory, and the
philosophy of perception.
Theory of Knowledge
Two questions in the theory of knowledge (epistemology):
A. What do we know? What is the extent of our knowledge?
Can we know anything at all?
B. What is knowledge? What are the necessary and sufficient
conditions (or criteria) of knowledge? What does the term
‘knowledge’ mean?
• Knowledge has traditionally been defined as justified true
belief. But this analysis of the concept of knowledge has
come under attack. There are now many competing
analyses of the concept of knowledge.
Problem of the Criterion
Question A: What do we know? What is the extent of our
knowledge? How much do we know?
Question B: What are the necessary and sufficient conditions
of knowledge? What are the criteria for something counting as
1) You cannot answer question A until you have answered
question B.
2) You cannot answer question B until you have answered
question A.
C) Therefore, you cannot answer either question.
• We cannot answer question A without knowing the answer
to B:
• You can only identify instances of knowledge if you
already know what the necessary and sufficient
conditions for knowledge are.
• For example, in order to decide whether a seeming
instance of knowledge is actually an instance of
knowledge, we need to have some sort of standard that
we can appeal to.
• And we cannot answer question B without knowing the
answer to A:
• You can only know what the necessary and sufficient
conditions for knowledge are if you are already able to
identify instances of knowledge.
• For example, in order to answer B, we need to know
whether we can know that there is external world.
Solutions to Problem of the Criterion
• Methodists assume they have an answer to B on the
basis of which they figure out their answer to A.
• Methodists assume they can know what the criteria for
knowledge are on general grounds, and then proceed
on this basis to consider the issue of what (if anything)
we actually know.
• For instance, Descartes believed that “clear and
distinct perception” was a sure criterion of knowledge
— since he believed that God would not deceive us
by making such perceptions misleading. Then he
used this criterion to explore what we can know.
• Particularists assume they have an (at least partial)
answer to A and on the basis of it they work out their
answer to B.
• Rather than assuming that one can identify the criteria
for knowledge independently of examining any particular
instances of knowledge, particularists claim that one
should instead assume that one can correctly identify
particular instances of knowledge and proceed on this
basis to determine what the criteria of knowledge are.
• For example, Moore believed that many particular
knowledge claims were obvious and beyond doubt
— e.g. my knowledge that I have two hands. (This is
sometimes called the “common sense” response to
• Skeptics claim that neither question can be answered
in a non-circular way.
• For example, a skeptic might say that knowledge is
impossible for human beings to achieve because we
can never get an independent grip on either half of the
problem of the criterion.
Pros and Cons
• Pro methodism: Methodism leaves it open whether
skepticism is true (whether there is anything that meets
the criteria of knowledge). Thus, it might allow one to give
a principled or non-question-begging response to the
• Con methodism: It is a mystery how we can get a grip
on the criteria for knowledge without appealing to
particular instances of knowledge.
• In general, it seems more obvious that we know certain
particular things than that any general criterion for
knowledge is correct
• Pro particularism: It seems more plausible to suppose
that we can correctly identify particular cases of
knowledge independently of a definition of knowledge,
than to suppose that we can identify what the criteria for
knowledge are without prior appeal to facts about what
we know.
• Con particularism: It assumes a position about
skepticism. For example, Moore assumes that skepticism
about the external world is false – e.g. that I do know that
I have hands.
• Thus, it seems as though the particularist is left without a
principled response to the skeptic.
End of Part 3
Three paradoxes of understanding and interpretation:
•Paradox of Analysis
•Problem of the Criterion
•Hermeneutic Circle
• Hermeneutics is the art or theory of interpretation. Originally
concerned with interpreting sacred texts, the term now has
a broader meaning.
• Hermeneutics is also a sub-discipline of philosophy or
literary theory that is is concerned with questions of
• Etymology: In Greek mythology
Hermes has the role of messenger of
the Gods. Hermes is also considered
the inventor of language and speech.
Hermeneutics is concerned with understanding and
interpreting the meaning of a text.
“Interpretation, in the sense relevant to hermeneutics, is an
attempt to make clear, to make sense of an object of study. This
object must, therefore, be a text, or a text-analogue, which in
some way is confused, incomplete, cloudy, seemingly
contradictory — in one way or another, unclear. The interpretation
aims to bring to light an underlying coherence or sense.”
– Taylor, “Interpretation and the Sciences of Man”, p. 3
We’ll focus here on two forms the Hermeneutic circle can
Hermeneutic Circle 1
• The word of God/Allah/Yahweh is revealed in the Bible/Quran/
• Faith in God/Allah/Yahweh presupposes an understanding of
what the Bible/Quran/Torah says.
• But one cannot really understand what the Bible/Quran/Torah
says unless one has faith.
• Hence: in order to have faith, you have to understand – and in
order to understand, you have to have faith.
Hermeneutic Circle 2
• In order to understand a text in its entirety we have to
understand each part of it.
• In order to understand the parts of a text we have to
understand the whole text.
• Hence: in order to understand the whole text you have to
understand the parts – and in order to understand the parts
you have to understand the whole.
• The 2nd hermeneutic circle arises when one element in a text
(e.g., a sentence, a word) can only be understood in terms of
the meanings of others or of the whole text, yet understanding
these other elements, or the whole text, in turn presupposes
understanding of the original element.
• Similarly, we may hold that the past can only be understood in
the light of the present, and the present can only be
understood in the light of the past.
• Similarly, we may hold that some part of a political process can
only be understood in light of the whole of society, and the
society can only be understood in light of the parts.
• All of these are forms of holism about meaning.
The Hermeneutic Circle 2 Paradox:
1) We can determine the meaning of texts.
2) One cannot firmly determine the meaning of a word
without a firm grip on the meaning of its context.
3) One cannot firmly determine the meaning of a word’s
context without a firm grip on the meaning of the component
words that make up that context.
C) Therefore, contrary to (1), it is not possible to get a firm
grip on the meaning of a text. (2, 3)
Solutions to Hermeneutic Circle 2
• One solution is insist on atomism about meaning. That meaning
of the parts of a text can be understood without understanding
the whole.
• “Another is to say that “firm grip on meaning“ is a matter of
• When interpreting a text we enter into a feedback loop,
alternating between word and context (sentence, paragraph,
chapter) interpretation. This provides an increasingly firm
grip on the meaning of the word and the context alike.
• The hermeneutic circle is in fact a hermeneutic spiral.
Philo 2: Puzzles and Paradoxes
Moore‘s Paradox
Language and Thought
• Language structures both our thoughts themselves and how we
express those thoughts in speech and writing.
• We can call the sort of language we use in ordinary speech and
writing, public language. This is the sort of language that we
share with other speakers. For example, English, Spanish,
Arabic, Mandarin, etc are public languages in this sense.
• Public languages are at least partially conventional.
• For example, there is no natural resemblance between the
word “dog” and dogs. Rather “dog” comes to refer to dogs
because of certain conventions or rules of use that say, in
effect, that it refers to such things.
• At the same time, many linguists and philosophers think there is
also a more basic sort of innate “language” or “proto-language”
that structures thought – and which may not be conventional in
the same way – we can call this the language of thought.
Language and Thought
• What is the relationship between public (spoken/written)
language and thought?
• Priority of Thought: Thought is prior to public language. We
can understand public language by beginning with an
understanding of (certain forms of) thought and then using
them to explain how public language works.
• Priority of Language: Public language is prior to thought. We
can understand thought by beginning with public language and
then using it to explain what thought is.
• No Priority: Neither thought nor public language can be
understood without the other.
Priority of Thought
• Priority of Thought: Thought is prior to language. We can
understand language by beginning with an understanding of
thought and then using that to explain how public language
• For example, acts of speech and writing seem to be intentional
actions, which are caused by our beliefs, desires, and intentions.
So perhaps we need to understand speech and action in terms
of a prior understanding of belief, desire, and intention.
• Paul Grice offered a famous version of this thought. He claimed
that the content or meaning of an act of speech needed to be
understood in terms of what the speaker intended to
communicate by that speech act. (We’ll come back to this
Priority of Thought
• Priority of Thought: Thought is prior to language. We can
understand language by beginning with an understanding of
thought and then using that to explain how public language
• But this view faces certain problems. In particular, to make
sense of it, we need to have a way of thinking about the
content of beliefs, desires, and intentions which doesn’t bring
public language into the story.
• But it’s hard to think about the content of many of our beliefs or
intentions in terms that are separable from public language.
For example, when I intend to do something, I usually
conceive of that action using terms from English.
Priority of Language
• Priority of Language: Public languages are prior to thought.
We can understand thought by beginning with public language
and then using it to explain what thought is.
• For example, perhaps thought is best understood as a form of
inner speech. In other words, perhaps thinking is just like
talking, except one is just talking to oneself.
• This fits well the phenomenology of conscious thinking in many
ways, but…
Priority of Language
• Priority of Language: Public languages are prior to thought. We
can understand thought by beginning with public language and
then using it to explain what thought is.
• This view also has problems. For example, it seems as though
part of what makes a public language a language – as opposed to
just a rule-governed game of some kind – is its connections with
thought. When I assert something, that counts as the speech act
it is because it expresses some belief. So how can I understand
public language without already bringing thought into the picture?
• Also, other forms of thought – like those involved in pictorial
imagination – seem to fit poorly with this view, unless we try to
understand imagining as “drawing to oneself”?
No Priority?
• No Priority: Neither thought nor public language can be
understood without the other.
• The problems with each of these views might tempt us to think
that neither thought nor public language is intelligible without
the other.
• Or perhaps there are different forms of thought, some of which
are intelligible without public language, while others require the
presence of public language to be possible?
End of Part 1
Paradoxes in Speech and Belief
• Our goal today is to explore the relationship between thought
and language, by looking at some puzzling ways in which we
can “contradict” ourselves in speech and thought.
• These forms of self-contradiction are similar in some ways to
the liar paradoxes, but they are also importantly different from
• In discussing these issues, we’ll move from our discussion of
the philosophy of language into a discussion of epistemology i.e. rational belief and knowledge.
Logical vs. Performative Contradiction
• A logical contradiction is the conjunction of a statement p
and its denial, not-p. (Or something that logically implies such
a conjunction.)
• According to the law of non-contradiction (more or less the
same as the principle of bivalence), a statement and its denial
cannot both be true. Thus, logical contradictions are
necessarily false.
– It is raining and it is not raining.
– I know that nothing can be known. (Logically implies that I
know something and that I don’t know anything.)
• A performative contradiction occurs when the content of a
statement contradicts either the act of asserting it or the
presuppositions of asserting it.
• The contradiction is between the act of assertion and the
content asserted.
• “I cannot speak a single sentence of English.”
• “Nothing exists.”
• “I am not saying anything.”
• A performative contradiction is not a logical contradiction
because it does not violate the law of non-contradiction. The
content of the above utterances may be true. But it is impossible
to successfully assert them.
• Some versions of the liar paradox are performative
• A Cretan who intends to speak the truth while saying “All
Cretans are always liars“ commits a performative contradiction.
• Suppose his assertion is true, then it must be false because in asserting a truth, a Cretan has told the truth.
• So his assertion must be false, but then he has failed to do
what he intends to do – namely, speak the truth.
• Thus, for the Cretan, the act of asserting this statement is
doomed to fail.
Moore‘s Paradox
1. “It is raining, but I don‘t believe it is.“ (Moore 1942: 543)
2. “I went to the pictures last Tuesday, but I don‘t believe that I
did.“ (Moore 1942: 543)
3. “I believe that he has gone out, but he has not.“ (Moore 1944:
Moore claims that it is “absurd“ or “odd“ to assert statements like (1)(3). There seems to be something fundamental irrational or selfdefeating about them.
Moorean statements have either of two forms:
1 Omissive form: p & I do not believe that p
“Omissive“ because it self-reports a lack of true belief.
Commissive form I: I believe that p, but it is not the case that p
Commissive form II: p & I believe that not-p
“Commissive“ because it self-reports a mistaken belief.
• Moorean statements are not logical contradictions.
• If the Moorean statement (1) were a logical contradiction, it
would be a necessary falsehood.
• But the statement (1) – It is raining and I do not believe it is could easily be true. After all, Karl is not omniscient, so it is
possible for it to be raining and for Karl to be ignorant of this
• Thus, Moorean statements are not logical contradictions – they
describe perfectly coherent possible scenarios.
• This is one way in which Moorean statements are different
from liar-type statements.
Even though Moorean statements are not logical contradictions
asserting them seems absurd or self-defeating in much the same
way as asserting a contradiction is:
P & I do not believe that P
• It can be true at a particular time both that p, and that I do not
believe that p.
• I can assert or believe one of them at a particular time.
• But I cannot, without absurdity, assert or believe both of them at
the same time.
Moore‘s paradox is the problem of explaining why Moorean
statements cannot be sincerely asserted without absurdity even
though they describe coherent possibilities that might be true.
Not So Moorean Statements
• The absurdity of (1) is not present in its future and past tense
– “It was raining but I did not believe so.“
– “It will be raining but I will believe otherwise.“
• The absurdity of (1) is not present in the third (and second)
person counterpart:
– “It is raining but he believes that it is not raining“
• The absurdity of (1) is not present in its modal counterpart:
– “It is raining but it is possible that I don‘t believe it“
• The non-absurdity of these “fake Moorean statements” makes
sense, given that they all describe coherent possibilities in a
normal way.
• The absurdity of Moorean statements also seems to be
preserved if they are only thought but not uttered.
• Suppose I believe the following: P but I do not believe that P.
There seems to be something self-defeating about that as well.
• Upshot: The absurdity of the Moorean statements seems to be
closely connected with their first-personal, present-tense
End of Part 2
Three Explanations of Moore’s
• Moore’s explanation
• Wittgenstein’s explanation
• Baldwin’s explanation
Thomas Baldwin (1947-). British philosopher who
teaches at the University of York.
Moore‘s Explanation
Omissive form: p & I do not believe that p
• Moore claims that in making a first-person present-tense indicative
assertion, one “implies” in some sense that one believes it:
Moore‘s First Principle (1942):
If one asserts that p, then one implies that one believes that p.
• Since asserting a conjunction involves asserting its conjuncts,
when I assert that (p & I don‘t believe that p), I assert that p. Hence I
“imply” that I believe that p, which contradicts the second conjunct of
my assertion. So what I assert contradicts what I “imply” by
asserting it.
• Note that this is not a logical implication of the content I assert,
but an implication of a different sort of the act of asserting it.
Commissive form (p & I believe that not-p)
Moore‘s Second Principle (1944):
If one asserts that p, then one implies that one doesn‘t believe that
• If I assert that (p & I believe that not-p), then I assert that p. So I
“imply” that I don‘t believe that not-p, which contradicts the
second conjunct of my assertion. So what I assert contradicts
what I “imply” by asserting it.
• Given the two principles, both the omissive and the
commissive form are cases of a contradiction between what
I assert and what that assertion “implies”.
• In the omissive form I “imply” and/or assert that I do and
don‘t believe that p.
• In the commissive form I “imply” and/or assert that I do and
don‘t believe that not-p.
Problems with Moore‘s Explanation
• The basic question: What is the sense of “imply” at issue here?
We are not speaking about the logical implications of the content I
assert, but rather the “implications” of the act of assertion. How do
we understand that?
• Moore (1942: 542-3) claims that his first principle:
“… arises from the fact, which we all learn by experience, that in
the immense majority of cases a man who makes such an
assertion does believe or know what he asserts: lying, although
common enough, is vastly exceptional“
• But then we should expect that performative contradictions uttered
by a known habitual liar do not sound absurd. But they do.
• Moore (1942: 541) also says
“…the sense of ‘imply’ in question is similar to that in which,
when a man asserts anything that might be true or false, he
implies that he himself, at the time of speaking, believes or
knows the thing in question.”
• So, according to Moore, to assert
“It is raining but I don’t know that it is raining”
would likewise be “absurd.” But it is not clear that it is absurd.
And if it is, the explanation of why it is absurd seems to be
different. See below.
End of Part 3
Wittgenstein‘s Explanation
• Wittgenstein claims that asserting ‘I believe p’ means roughly
the same as ‘p’ (1980a, §472).
• On this view, the absurdity of Moorean statements lies in:
Wittgenstein’s First Principle:
If one asserts that one believes that p, then one asserts that p.
• This explains the absurdity of the commissive assertion, for in
asserting that (p & I believe that not-p) I assert that I believe
that not-p and so assert that not-p, which contradicts my
assertion that p.
• So although what I have literally asserted is not a contradiction,
my assertion of it involves contradictory assertions.
• Wittgenstein’s first principle cannot explain the absurdity of
the omissive assertion. For in asserting that (p & I don’t
believe that p) I assert a lack of belief, to which Wittgenstein’s
first principle does not apply.
• To deal with the omissive case (p & I don’t believe that p) we
can introduce a related principle:
Wittgenstein’s Second Principle:
If one asserts that one doesn’t believe that p, then one denies that
• If I assert that (I don’t believe that p), I deny that p which
contradicts my assertion that p.
• But given Wittgenstein’s Second Principle, an agnostic who
truthfully reports, “I neither believe that God exists nor believe
that he does not” would be making contradictory assertions.
But he does not. So this principle must be false.
Baldwin‘s Explanation
• Baldwin picks up on Grice’s view about speech acts as
intentional actions. Simplifying some, he claims:
• If I assert that p to you, then I have the intention that you
will come to believe that p because you recognize that I
believe that p and intend to communicate this belief to you.
• So, in asserting that p to you, I am trying (in part) to make
you do 2 things: (i) to make you believe that p and to make
you believe that I believe that p.
• (Otherwise I would be intending to make you believe that I
am misleading you.)
Baldwin‘s Explanation
• Given this, in the omissive case (p & I don‘t believe that p), I
• (i) Assert that p and so intend to make you believe that I
believe that p
• And (ii) Assert that I don’t believe that p and so intend to
make you believe that I don‘t believe that p.
• So I intend to make you form contradictory beliefs about what I
believe — that I both believe that P and don’t believe that P.
• Similarly, in the commissive case (p & I believe that not-p), I
intend (i) to make you believe that I believe that p and (ii) to
make you believe that I believe that not p.
• So I intend to make you think that I believe both of two
contradictory claims.
Baldwin‘s Explanation
• In either form of Moore‘s paradox, the problem is then that the
speaker has self-defeating intentions (see Baldwin 2007:
77-8). The speaker is trying to get the hearer to believe a
combination of things that are unbelievable.
• This can be seen as an attempt to make sense of the sense in
which the act of assertion “implies” that I believe what I am
• This sort of implication is now called pragmatic implicature since it has to do with the acts of speech as opposed to their
Problems w. Baldwin‘s Explanation
• But there seem to be counterexamples to Baldwin‘s
assumptions about the intentional structure of assertion:
• A speaker can make an assertion without the intention of
thereby making his audience believe what he asserts.
• Example: when the speaker is being tested by
someone whom he takes to know the answers already.
• A speaker can make an assertion with the intention of
making his audience believe the opposite of what he
• Examples: sarcasm, irony (“This is a brilliant lecture”).
• Baldwin‘s explanation also doesn‘t work for Moore‘s paradox
in thought. So the paradox is yet to be solved.
Knowledge Version of Moore‘s Paradox
P & I do not know that P
• There are two explanations of the (alledged) absurdity of this
• One explanation assumes that knowledge is the norm of assertion
– Knowledge explanation.
• The other explanation assumes that justification is the norm of
assertion – Justification explanation.
Knowledge Explanation
• Knowledge as the Norm of Assertion: Assert that p only if you
know that p.
• Knowledge Distribution: Knowing a conjunction implies knowing
each conjunct.
• Factivity of knowledge: Whatever is known is true.
• Given the norm of assertion, if I assert that (p & I don‘t know that
p), then I should know that (p & I don‘t know that p).
• Given knowledge distribution, if I know that (p & I don‘t know that
p), then I know that p and I know that (I don‘t know that p).
• But, given the factivity of knowledge, if I know that (I don‘t know
that p), then it is true that I don‘t know that p.
• Therefore, I do and don‘t know that p. Contradiction!
Justification Explanation
• Justification Principle: If one is justified in believing that p and
one knows that one believes that p, then one is justified in believing
that one knows that p.
• Norm of Sincerity: Assert that p only if you believe that p.
• Justification as the Norm of Assertion: Assert that p only if you
are justified in believing that p.
• Given my conformity to the norm of sincerity and justification, if I
assert that (p & I don‘t know that p), I am justified in believing that
• Given that I know whether I am sincere, I know that I believe that p.
• And given the justification principle, I am justified in believing that I
know that p.
• But this means that I must not be justified in believing that I do not
know that p. But I have also asserted that I do not know that p.
Philo 2: Puzzles and Paradoxes
Pascal‘s Wager
The Argument from Design for
God‘s Existence
1) Human artifacts are the products of intelligent design.
2) The universe in general – and living things in particular resemble human artifacts in their organization and apparent
3) Therefore, the universe is likely to also be a product of
intelligent design.
C) Therefore, the author of the universe is probably an
intelligent being.
Thomas Aquinas
Cosmological Argument
1) A contingent being exists. For example, Karl Schafer exists.
2) There must be a cause of Karl Schafer’s existence.
3) The cause of Karl Schafer’s existence must be something other than
Karl Schafer (unless KS is God).
4) What causes the existence of Karl Schafer must either be some
other contingent being(s) or a non-contingent (necessary) being.
5) If the cause of the existence of Karl Schafer is some other contingent
being(s) then something else must cause these being(s) to exist.
6) Thus, contingent beings alone cannot provide a wholly adequate
explanation for the existence of a contingent being – every contingent
being must be caused to exist by some further contingent being. So
if there are only contingent beings, we face an infinite regress of
C) But such a regress of causes is impossible. Therefore, whatever
causes the existence of Karl Schafer must include a non-contingent
(necessary) being. Therefore, a necessary being exists.
Ontological Argument for God
1) God is a being, which is greater than any other being we can
conceive of.
2) We can conceive of God. Thus, God exists as an idea in the mind.
3) A being that exists as an idea in the mind and in reality is greater
than the same being that exists only as an idea in the mind.
4) Thus, if God exists only as an idea in the mind, we can conceive of
something that is greater than God – namely, the being which is like
God except that it exists both as an idea in the mind and in reality.
5) But, by (1), we cannot conceive of something that is greater than
God. For that would be to conceive of a being which is greater than
the greatest being we can conceive of.
C) Therefore, God exists both in the mind and in reality.
Anselm of Canterbury
Blaise Pascal (1623-1662)
French mathematician, physicist,
inventor, writer and Christian
philosopher. He was a child prodigy
who was educated by his father, a tax
collector in Rouen.
Pascal‘s Wager
• Pascal begins with the failure of these arguments. Nonetheless,
he claims that if you don‘t already believe in God, then you
rationally ought to come to believe in God. Why?
• Suppose God does exist. Then, if you believe in God, you
can expect an infinity of heavenly joy. And if you do not
believe in God, you can expect to be punished in hell.
• On the other hand, suppose that God does not exist, then the
costs and benefits associated with either belief or disbelief in
God will be finite.
• Thus, provided that the probability of God‘s existence is
greater than 0, the expected value of believing in God is
infinite! (Any finite fraction of infinity is itself infinite, and so is
bound to be greater than any finite good the atheist
End of Part 1
Pascal’s argument for belief in God’s existence:
1) The chance that God exists is positive and finite.
2) If you believe in God and he exists, you’ll get an infinite reward. If
you believe in God and he doesn’t exist, you’ll have at most a
finite loss.
3) Therefore, believing in God has an infinite expected utility.
4) If you don’t believe in God and he exists, you’ll suffer an infinite
loss. If you don’t believe in God and he doesn’t exist, you’ll win
only a finite gain.
5) Therefore, not believing in God has a infinite negative expected
6) Therefore, believing in God has a much higher expected utility
than not believing in God.
7) You should do that which has the higher expected utility.
C) Therefore, you should believe in God.
Pascal’s Presentation
• Pascal poses the problem of belief in God’s existence as follows:
“Let us examine this point of view and declare: ‘Either God exists, or
He does not.’ To which view shall we incline? Reason cannot decide
for us one way or the other: we are separated by an infinite gulf. At
the extremity of this infinite distance a game is in progress, where
either heads or tails may turn up. What will you wager? According to
reason you cannot bet either way; according to reason you can
defend neither proposition” (Pascal, Pensées, p. 2)
• Pascal expresses skepticism about the ability to either prove or
disprove the existence of God.
• But, he says, the inability to prove or disprove the existence of
God does not remove the requirement that we make a choice on
this point.
“Yes; but a bet must be laid. There is no option: you have joined
the game. Which will you choose, then? Since a choice has to be
made, let us see which is of least moment to you. You have two
things to lose, the true and the good; and two things to wager;
your reason and your will, your knowledge and your happiness;
… Your reason suffers no more violence in choosing one rather
than another, since you must of necessity make a choice. … But
what about your happiness? Let us weigh the gain and the loss
involved in wagering that God exists. Let us estimate these two
probabilities, if you win, you win all; if you lose, you lose nothing.
Wager then, without hesitation, that He [God] does exist” (Pascal,
Pensées, p. 2).
• Pascal does not provide us any evidence for thinking that
God exists. He gives us prudential rather than evidential
reasons for forming a belief that God exists.
The word ‘reason’ is ambiguous:
• Prudential Reason: There is a prudential reason to believe p
if and only if believing p would make you better off.
• Evidential Reason: There is an evidential reason to believe p
if and only if there is evidence that p is actually true – e.g., a
good argument for the conclusion that that p is true.
• So prudential reasons are aimed at making you better off.
• While evidential reasons are aimed at the truth.
Since there is an equal risk of winning and of losing, if you had only two
lives to win you might still wager; but if there were three lives to win, you
would still have to play …; and being thus obliged to play, you would be
imprudent not to risk your life to win three in a game where there is an
equal chance of winning and losing. … But here there is an infinity of
infinitely happy life to win, one chance of winning against a finite number
of chances of losing, and what you stake is finite. That removes all doubt
as to choice; wherever the infinite is, and there is not an infinity of chances
of loss against the chance of winning, there are not two ways about it, all
must be given. And so, when a man is obliged to play, he must renounce
reason to preserve his life, rather than risk it for infinite gain which is just
as likely to occur as loss of nothing” (Pascal, Pensées, p. 2)
• Pascal thinks that there is some analogy between believing in
the existence of God and making an even-odds bet in which
you stand to win three times as much as you stand to lose.
• Let’s introduce some concepts from decision theory, i.e., the
study of the principles which govern rational decision-making.
End of Part 2
The Wager & Decision Theory
• Suppose that you have two courses of action between which you
must choose, and the consequences of each choice depend on
some unknown fact.
• For instance, you have to bet on whether a coin will come up
heads or tails. Imagine first a simple bet in which if you guess
correctly, you win $1, and if you guess incorrectly, you lose $1. The
choices can be represented like this:
Course of Action
Possibility 1:
Coin comes up heads
Possibility 2:
Coin comes up tails
Choose heads
Win $1
Lose $1
Choose tails
Lose $1
Win $1
• Should you choose heads or tails? It doesn’t matter. Neither option
is better.
• More complicated bet: if you choose heads, and the coin comes
up heads, you win $10; if you choose heads, and the coin
comes up tails, you win $5. However, if you choose tails, and
the coin comes up heads, you win $2; but if you choose tails,
and the coin comes up tails, you win $5. The choices can be
represented like this:
Course of Action
Possibility 1:
Coin comes up heads
Possibility 2:
Coin comes up tails
Choose heads
Win $10
Win $5
Choose tails
Win $2
Win $5
• Should you choose heads or tails? You should choose heads.
For if the coin comes up heads, then you are better off if you
chose ‘heads.’ If it comes up tails, then it doesn’t matter which
option you chose.
• The worst outcome of choosing ‘heads’ is as good as the
best outcome of choosing ‘tails’, and the best outcome of
choosing ‘heads’ is better than the best outcome of choosing
• When this is true, we say that choosing ‘heads’ superdominates choosing ‘tails.’ In other words, ‘Heads’ is as at
least good (and sometimes better) than ‘tails’ no matter what.
• Super-dominance is one important concept from decision
theory. Anther one is expected utility. The expected utility of a
decision is the amount of utility (i.e., reward) that you should
expect that decision to yield.
• Consider again the more complicated bet:
Course of Action
Possibility 1:
Coin comes up heads
Possibility 2:
Coin comes up tails
Choose heads
Win $10
Win $5
Choose tails
Win $2
Win $5
• Now suppose that you are offered the chance to take this bet on
a fair coin toss, but have to pay $7 to make the bet.
• Supposing that you want to maximize your money, should you
pay $7 to have the chance to bet ‘heads’?
• Which is higher: the expected utility of paying $7 and
betting ‘heads’, or the expected utility (expected dollars
earned) of not paying and not betting?
• The expected utility of not paying to take the bet is $0.
• The expected utility of paying $7 and betting heads = the
expected utility of paying $7 + the expected utility of betting
• Suppose we say that the expected utility of paying $7 = -7
Then the expected utility of paying $7 and betting heads =
the expected utility of betting ‘heads’ – 7.
• (There’s a tricky issue here involving whether utility
increases linearly with monetary value.)
• So… what is the expected utility of betting heads?
• There are two possibilities: the coin could come up heads, or
could come up tails. There is a ½ probability that either will
happen, since the coin is fair. If the coin comes up heads, you
get $10; if it comes up tails, you get $5. Since there is a ½
chance of each, what you should expect from the bet =
½ x 10 + ½ x 5 = 7.5
• You should expect the bet to yield $7.5. Since you only have to
pay $7 to take the bet, and $7.5 > $7, you should pay to take
the bet.
• The method employed can be summed up as follows:
If deciding between a number of options, choose the option
which has the highest expected utility.
Three Versions of the Wager
• Pascal offers a prudential reason for believing in God’s
existence. The wager can be understood as an
• (1) Argument from super-dominance
• (2) Argument from expected utility
• (3) Generalized argument from expected utility
• The super-dominance version of the argument conveys the
basic Pascalian idea, the expected utility version refines it, and
the third version gives a even more sophisticated version of it.
Argument from Super-Dominance
• One version of Pascal’s argument is that the decision to believe
in God super-dominates the decision not to believe.
“… if you win, you win all; if you lose, you lose nothing” (Pascal,
Pensées, p. 2)
• The situation then looks like this:
Course of Action
Possibility 1:
God exists
Possibility 2:
God does not exist
Believe in God
Infinite reward
Lose nothing, gain nothing
Not Believe in God
Infinite loss
Lose nothing, gain nothing
• Here belief in God super-dominates non-belief: the worst case
scenario of believing in God is as good as the best case
scenario of non-belief, and the best case scenario of believing in
God is better than the best case scenario of non-belief.
• Pascal imagines an opponent replying:
“That is all very fine. Yes, I must wager, but maybe I am wagering
too much” (Pascal, Pensées, p. 2)
• The idea is that if one decides to believe in God, and it turns out
that God does not exist, there has been some loss. You will
have lost “the truth”. (And maybe also some pleasure?)
• The revised decision matrix looks like this:
Course of Action
Possibility 1:
God exists
Possibility 2:
God does not exist
Believe in God
Infinite reward
Finite Loss
Not Believe in God
Infinite loss
Finite Gain
• Belief in God no longer super-dominates non-belief in God.
Argument from Expected Utility
• Does belief in God have a higher expected utility than nonbelief?
• Let’s suppose that probability of God’s existence is ½. Let’s
further suppose that wagering for God brings infinite reward if
God exists. The decision matrix then looks as follows:
Course of Action
Possibility 1:
God exists
Possibility 2:
God does not exist
Believe in God
Positive infinity (∞)
Finite loss (-n, where n is some finite
Not Believe in God
Negative infinity (-∞)
Finite gain (+m, where m is some finite
• Expected utility of belief in God
= ½ x (utility of belief in God, given that God exists) + ½ x
(utility of belief in God, given that God does not exist)
= ½ x ∞ + ½ x (-n)
• Expected utility of non-belief in God
= ½ x (utility of non-belief in God, given that God exists) + ½
x (utility of non-belief in God, given that God does not exist)
= ½ x (-∞) + ½ x m
= -∞
• Thus, you ought to believe in God because the expected utility of
belief in God is infinite, and the expected utility of non-belief is
negative infinity.
Argument from Expected Utility
• But maybe it’s a mistake to assign equal probabilities to the
possibilities that God does, and does not exist.
• Perhaps it is rational to assign a very low probability to the
possibility that God exists.
• Or perhaps we simply are ignorant even of what probability we
should assign to God’s existence. (Risk vs. uncertainty)
• Pascal shows that the argument from expected utility goes
through whatever probability is assigned to God’s existence – as
long as it is greater than 0. Because of the positive infinity, if God’s
existence is assigned any non-zero and finite probability then the
expected utility of believing in God will be infinite.
End of Part 3
Objections to Pascal’s Wager
• Impossibility of believing at will.
• Rationality does not require maximizing expected utility.
• Many gods objection.
• Moral objections to wagering for God.
• Zero probability to God’s existence.
Impossibility of Believing at Will
• Objection: It is impossible to adopt a belief simply
because you decide to.
• Example: I offer you $100 if you believe that it will rain at
the end of todays lecture.
• This incentive is not the kind of reason that makes
you believe. To believe, you need a reason that bears
on the truth of the proposition. You need an
evidential, not a prudential reason.
• Reply 1: If you act as if you believe, over time, you may end up
• Reply 2: Even if you cannot adopt a belief simply by deciding to,
you can bring about the right circumstances for the adoption of the
“That is true. But understand at least that your ability to believe is the
result of your passions; for, although reason inclines you to believe, you
cannot do so. Try therefore to convince yourself, not by piling up proofs of
God, but by subduing your passions” (Pascal, Pensées, p. 3).
• Reply 3: No mere exercise of will can guarantee that you will end
up believing in God’s existence, but neither can any exercise of will
guarantees that you succeed in doing anything else you decide to
do. If there is a difference between your ability to voluntarily believe
in God’s existence and your ability to voluntarily wiggle your toe, it
is a difference in degree of likely successes, not a difference in
logical kind.
Rationality does not Require
Maximizing Expected Utility
• Objection: Maximizing expected utility can lead you to
perform intuitively sub-optimal actions. This is the point of the
St. Petersburg Paradox.
• The St. Petersburg Paradox was discovered by Nicolaus
Bernouilli, and acquired its name because it was first
published in an article published in the St. Petersburg
Academy Proceedings in 1738
Nicolaus Bernouilli
• St. Petersburg Paradox:

Imagine tossing a coin until it lands heads-up, and suppose that the
payoff grows exponentially according to the number of tosses you
make. If heads comes up on the first throw you get $2, if it comes up
on the second throw you get $4, on the third $8, and so forth, ad
The chance of heads on the first throw is ½. The chance that the
second throw happens and that heads comes up = the chance of tails
on the first throw x ½ = ¼. The chance that the third throw happens
and heads comes up is ½ x ½ x ½ , and so on.
The expected gain from the first toss is $2 x the probability that it is
heads (½) = that is 1. The expected gain associated with the possibility
of the second throw is $4 x ¼ = $1. And with the possibility of the third,
it is $8 x 1/8 = $1, and so on.
Since there is no limit to the possible number of throws before heads
comes up, the sum for the expected gains, 1+1+1+1 … goes one
forever. The expected utility of playing is thus infinite. It follows you
should be willing to pay any finite amount for the privilege of playing
this game. Yet it clearly seems irrational to pay very much at all.
• Video: https://www.youtube.com/watch?v=Bqv90clW8so
• Reply: Nicolaus Bernouilli‘s brother Daniel used the notion of
diminishing returns to solve the paradox.
• Suppose you start off earning $700 a month, and in
successive months get a raise of $100 a month. At first the
raise has considerable value for you, but a few years later
when you are earning $8,000 a month the extra $100 is of
much less value to you: the returns from the $100 increments
diminish as you get more and more of them. (So utility does
not increase linearly with monetary value.)
• Question: Does this really solve this paradox?
The Many Gods Objection
• Objection 1: The wager argument deals only with the
Christian God. But there are many possible gods (Yahweh,
Allah, etc.), each with a finite chance of existing, who each
might grant those who believe in them infinite paradise.
• Since there are infinitely many such possible gods this makes
the chance of a god‘s existing infinitesimal, and if you
multiply the infinite by an infinitesimal you get a value of 1,
i.e., a finite value.
• Reply: Pascal‘s wager cannot decide among religions but it
at least gets you to theism?
• Objection 2: Given that there are many possible gods we can also
imagine a Perverse God. This God rewards those who believe only
what can be established on the basis of evidential reasons. He is a
God of theoretical rationality, whose wrath is reserved for those who
decide epistemological matters by means of prudential reasons.
• Given that there are no compelling theoretical grounds for believing
that any sort of God exists, the Perverse God punishes those who
believe in God and rewards those who were sensible enough to
reserve their judgment.
• If we suppose that there are no compelling theoretical grounds for
atheism, the Perverse God will punish atheists and theists alike. We
may suppose that his punishments and rewards are also infinite -infinite happiness for those who suspend judgment, infinite misery for
those who do not. Given this possibility, the payoff matrix looks like
Christian God exists Perverse God exists No God exists
Believe that a God
Positive infinity (∞)
Negative infinity (-∞)
Suspend judgment
Negative infinity (-∞)
Positive infinity (∞)
Deny God’s
Negative infinity (-∞)
Negative infinity (-∞)
• Given this decision matrix, it appears that the rational agent
ought to suspend judgment.But these calculations work out as
they do because we have included only two theistic
• If we were to add others – a Jealous God who rewards only
those who believe in him and call him by name, punishing the
rest, including the Christian believers – a Shy God who rewards
only those who believe in some other God while punishing
atheists, agnostics, and those who believe in him, etc. – we can

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