Utilizing Descartes' Regulae, the Preface to the Principles of
Philosophy and the Principles of Philosophy, the relevant portions of the
first and third meditations, and the Replies to Objections 11, discuss as fully
as you can a) Descartes' views on the role Mathematics plays in
revolutionizing learning. Discuss also b) key points of difference that
Descartes identifies between mathematics and the quest for first principles
in metaphysics the subject matter of his Meditations; and c) the 3 reasons
he offers in the first meditation and Principle V for holding that
mathematics can be regarded as dubitable .
(In your answers, make certain that each relevant work is discussed, and
that the specific contribution of each of these works is detailed.)
Descartes believed mathematics is the only true and most pure way to learn
generally. The question at hand is, “what can I know.” In order to learn generally, we
must emulate the sciences through both the Empirical and theApriori sciences. He
strongly believes that mathematics is indubitable and can never be doubted. Descartes
strongly believes in learning generally with theApriori sciences because only withA
priori is certainty achievable and eternal. Descartes was seeking truth that is eternal for
all time. In “the Regulae” he talks about various rules and principles pertaining to
learning generally, they show how both arithmetic and geometry are certain and in no
situation would they ever be uncertain. Empirical knowledge is something that can be
doubted or is on a level of both certainty and uncertainty. For example, the sentence
“my shirt is red” represents empirical knowledge, something empirical is a “temporal”
truth and may not always be true. Due to this reason, the statement may be manipulated
and as a result can have an infinite amount of meanings, such as “my shirt is green” or
“my shirt is blue” etc, whereas in mathematics truth is eternal for all of time. Take for
example the equation 2+2=4, this equation can never be false or changed due to the
nature of mathematics. The number 2 cannot be changed to 1 because it would then not
equal 5, or the number 4 cannot be changed to 3 because 2+2 cannot equal 3. Therefore,
the equation is certain and will be true until the end of time – just as Descartes seeks. In
the beginning of the 3 meditations, which includes his prior experiences that he thought
to be true and certain, he casts them into doubt and states only arithmetic and
geometry are certain.
Descartes explains that mathematics and the 1 principles of metaphysics are
different, he says mathematics is a method of synthesis and produces its own axioms
(self-evident truths) whereas metaphysics is a method of analysis and it has to find its
axioms; mathematical truth have nothing to do with the senses. Even with all of our
prejudices and sensory knowledge, we still accept them as truths, whereas in
metaphysical truths, getting rid of our senses is necessary. Every person accepts self-
evident truths in mathematics because mathematics is always goes down from the
premise to the conclusion. Math is certain because of deduction. It is infallible, but
only when you properly prepare yourself. Errors in mathematics are always human
errors; the only possibility of error in mathematics is based on inadvertence (lack of
attention/inattentiveness) and/or a person not able to properly understand the material
(little/no understanding of the premises). Mathematics is pure and uncomplicated; it is based on actual observation or experimental data. However, metaphysical axioms are
always in contradiction with the senses. Descartes says that the human being is the
conjunction of the body and mind, but our senses prove we are identical with our
bodies and the conclusion is that the self is a material thing. So the method of
metaphysics has to be analysis, if the reader follows the method he would find his
answers as if he found it himself. Descartes says the true starting point in philosophy is
indifference, and also to not be prejudice. Therefore, by the end of meditations 1,
Descartes believes indifference has been achieved and is dubitable and, in the Regulae,
he believes mathematics is certain. Metaphysics involves us to detach ourselves from
our senses and requires commitment of un-prejudice.
In principle 5, Descartes regards mathematics as dubitable because of three main
ideas. The first is that God can deceive us, “ God who created us can do all that He
desires… He may not have desired to create us in such a way that we shall always be
deceived, even in the things that we believe ourselves to know best “ (Pg. 39, Course kit).
Second, Descartes argues that we may be in a state of dreaming since we are unable to
differentiate dreaming from a waking consciousness. Things we do in our consciousness
we can also do in our dreams; how do we know we are not asleep? Descartes says there is
no definite sign to distinguish dream elements from waking elements, so he accepts the
possibility that he is dreaming and all his perceptions are false. The third argument
Descartes raises is the evil demon argument, Descartes says even if he were to assume
that there is a deceiver, the very fact that he is deceived by it follows that he exists.
Therefore: if the basis of mathematical knowledge is psychological irresistibility, the
foundation is unreliable since you believe wrong answer…. It is PL is not a criterion of
He speaks of math dubitably, and he does not yet know the existence of God.
What he surmises is: God is his creator. God is a deceiver and God is omnipotent.
What do we do about atheists, who say they don’t believe in GOD? NONE OF THIS
MATTERS, because I don’t believe in God!
“Yet the less perfect we suppose the author to be…”
Non Believer But I don’t believe in any of these facts about God!
Alternatives; A) I created myself, b) or (since you’ve ruled out God) some finite being
has created me.
So wouldn’t this be a limited form of power?!
So Descartes derives from this:
If God didn’t create me, then something else did. Well this being is conscious, and might
even WANT us to only achieve truth…. Intention we won’t be deceived.
2) “To these reasons I have certainly nothing to reply, but at the end I feel
constrained to confess that there is nothing in all that I formerly believed to be
true, of which I cannot in some measure doubt…for reasons which are very
powerful and maturely considered.” (Descartes’ Meditations on First
Philosophy, page 49) Discuss as fully as you can, Descartes’hyperbolic doubts against his former
beliefs, as he discusses this matter in the first meditation.
In the first meditation Descartes discusses the reasons for his hyperbolic doubt against his
former beliefs. He states that all his former beliefs were learned through sensory
experience and if the senses can be deceptive, then how can he trust his own beliefs. He
talks about principles of evidence, initially accepting all possibilities and eventually
rejecting each principle. Principles of evidence are based on clarity and distinctness.
In the first meditation, he launches an attack on the notion of representative realism
(theory of perception), which states that you’re not fully in contact with an actual object,
but instead you’re getting sensations of the object. Take for example a desk, you’re never
fully in contact with the actual desk, you’re getting sensations of the desk and the concept
of the desk behind the senses; the only way to know the desk it to leave the body. In
meditation 1, he asks how we know if our perceptions correspond with reality. Descartes
also talks about dialectic process, where we take two things that need one another and
compare them. He is looking for a way to say that our senses correspond with reality
and are in a sense, real. Descartes says we must find certain features within perception,
which if present, guarantee that perception corresponds to the object. If these features
are absent, then perception does NOT correspond with the object. Descartes coined these
features as clarity and distinctness.
The first principle of evidence is indiscriminate in what it allows as true (it does not
care about what it lets in) and it gives no true definition to clarity and distinctness stating
that all perceptions are clear and distinct. Descartes says sometimes the senses can
deceive us and we shouldn’t trust anything that has deceived us in the past. He uses the
examples of distance, fog and the stars; these factors affect our perceptions and can be
completely inaccurate in what they tell our senses. He then rejects principle of evidence
1 and moves onto principle of evidence two. This principle suggests that our senses turn
out to be reliable when our perceptions are clear (highly perceptible) and distinct (knows
the components), the more you know about the object, the more distinct the knowing is.
To this principle, Descartes counter argues the idea