During his meditations, Descartes starts by doubting everything unless it can be indubitably known to be true. After much questioning and scepticism, Descartes comes to the conclusion: “I am, I exist”.  This seems to state that the ‘I’ Descartes describes (usually defined as the conscious mind) must exist for an individual to exist. Because for every time the ‘I’ makes the above proposition, the mind or conscious self is engaged in thought and therefore demonstrates its own existence.
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After conclusively grounding his existence, Descartes inquires as to what makes up a person. He eventually deduces that “I am not more than a thing that thinks”  . Because to assume that his body exists is to rely on his senses that could be deceived. Therefore through intellect alone, Descartes concludes that he must be essentially a thing that thinks. When returning to the contemplation of the mind and body in his Sixth Meditation, Descartes then asserts that “I [that is to say, my soul by which I am what I am], is entirely and absolutely distinct from my body, and can exist without it.”  How and why he goes from a thinking thing, to a mind distinct from body is a perplexing problem both for Descartes and for his critics. In both the Second meditation, but more clearly in part four of his ‘Discourse on the Method’ Descartes presents what is commonly known as ‘the argument from doubt’: “I saw that I could conceive that I had no body, and that there was no world nor place where I might be; but yet I could not for all that conceive that I was not. On the contrary, I saw from the very fact that I thought of doubting the truth of other things, it very evidently and certainly followed that I was; on the other hand if I had only ceased from thinking, even if all the rest of what I had ever imagined had really existed, I should have no reason for thinking that I had existed. From that I knew that I was a substance the whole essence or nature of which is to think, and that for its existence there is no need of any place, nor does it depend on any material things; so that this ‘me’, that is to say, the soul by which I am what I am, is entirely distinct from body, and is even more easy to know than is the latter; and even if body were not, the soul would not cease to be what it is.”  This argument can be displayed as such  :
I can doubt that I have a body.
I cannot doubt that I exist.
Ergo, I am not a body. 
There have been many famous refutations of this argument from doubt. One problem with the argument, forwarded by Norman Malcolm, is that arguments using the same logic can be formed that lead to ridiculous results. For example:
I can doubt that the author of the pamphlet “Why I Am Not a Christian” exists
I cannot doubt that Bertrand Russell exists
Ergo, Bertrand Russell is not the author of that pamphlet.” 
However as Malcolm himself points out, this counter-example is based on contingent propositions, whereas Descartes argument is intended to be based on a priori propositions. But whether the subject of the proof is a posteriori or a priori, the reasoning behind the proof can still be called into question.
Descartes can think of his mind without his body, but this does not necessarily mean that this is the case, that without his body his mind can still exist. In this form of reasoning, Descartes is attempting to use Leibniz’s law of the indiscernibility of identicals. However Leibniz’s law states that “no two objects have exactly the same properties.”  Therefore, if it is true that two things (the body and the self) have different properties, then they cannot be the one same thing and there must be different objects. But it is mistaken to say that if one believes that two things have different properties then they cannot be identical. This is because what people know or think they know about an object, is not a property of that object. Therefore when Descartes claims that he doubts his body exists, this does not mean that the body has a different property than if he did not doubt its existence. He also claims he cannot doubt that his mind exists, but if his mind is a part of his body then we can doubt that his mind, apart from the body could exist. For the doubt argument to work, Descartes needs a provable reason for us to think that the mind and the body are truly distinct.
The second argument Descartes employs is often referred to as ‘the argument from conceivability’. It is also presented in the sixth meditation and through it Descartes sets out to prove that one can exist as a ‘thinking thing’ distinct from the physical body it goes as follows: “I know that all things which I apprehend clearly and distinctly can be created by God as I apprehend them, it suffices that I am able to apprehend one thing apart from another clearly and distinctly in order to be certain that the one is different from the other, since they may be made to exist in seperation at least by the omnipotence of God…I rightly conclude that my essence consists solely in the fact that I am a thinking thing (or a substance whose whole essence or nature is to think). And although possibly (or rather certainly, as I shall say in a moment) I possess a body with which I am very intimately conjoined, yet because, on the one side, I have a clear and distinct idea of myself inasmuch as I am only a thinking and unextended thing, and as, on the other, I possess a distinct idea of body, inasmuch as it is only an extended and unthinking thing, it is certain that this I (that is to say my soul by which I am what I am), is entirely and absolutly distinct from my body, and can exist without it.”  This argument can also be split into three parts:
I can clearly and distinctly conceive of myself existing (as a thinking thing) apart from my physical body.
Anything I perceive clearly and distinctly is logically possible.
If I can clearly and distinctly perceive of myself as an unextended thinking thing, and my body as an extended unthinking thing, then it is logically possible that my body and my mind can exist apart.
One obvious objection to this argument is that just because one can perceive of themselves as existing without physical properties, does not mean that they do exist without physical properties.  Another problem is that the second premise seems to be rather weak. To perceive something clearly and distinctly is not necessarily the same as it being logically possible. Descartes may be able to clearly and distinctly conceive of himself as an unextended thinking thing, and his body as an extended unthinking thing, but that does not mean he can conclude “that my essence consists solely in the fact that I am a thinking thing.”  He may only have an incomplete understanding of his mind and his body (with the scientific advancements of the past 300 years this seems very plausible). He has not shown that thought is the sole property of the mind, other properties could still be essential for the mind to exist (such as extension). In order for Descartes to prove the minds distinct separation from the extended body he must prove that it is impossible for the mind to be extended or to have extension as another essential property. Therefore Descartes’s argument from conceivability only stands up if one agrees that clear and distinct perception is all we need to have a complete knowledge of the world, and this seem a very weak conclusion to draw.
Another argument posed by Descartes is the argument from divisibility. This argument tries to prove that the mind and body are clearly distinct due to their difference in divisibility. It is set out, in the Sixth Meditation, as follows: “I here say, in the first place, that there is a great difference between mind and body, inasmuch as body is by nature always divisible and the mind is entirely indivisible.”  He then describes this assertion: “when I consider the mind, that is to say, myself inasmuch as I am only a thinking thing, I cannot distinguish in myself any parts, but apprehend myself to be clearly one and entire…yet if a foot, or an arm, or some other part, is separated from my body, I am aware that nothing has been taken away from my mind.”  Here Descartes is offering the following reasoning: all extended matter is divisible, the mind is not divisible, therefore the mind is not made of extended matter.
It is clear here that the second premise of the divisibility argument: ‘the mind is not divisible’ is problematic. There are many objections here that can be raised against the second premise, an obvious objection is the scientific evidence has shown convincing evidence that different areas of the physical brain are responsible for different mental states (memory, rational thought, language, emotions etc). Therefore if one removed parts of the physical brain, that persons mind would most definitely be altered. This does not mean that one must reject the idea that thoughts cannot be spatially mapped, merely that the brain in which they are contained and processed can be spatially and physically altered, and that this alteration would have a direct effect on the state of the mind. The only way that the divisibility argument can plausible is if one believes the second premise, that the mind is an immaterial substance distinct from both the body and the brain. This is highly improbable and would oppose everything that has been discovered by scientifically studying the brain.
This conclusion leads on to the biggest objection to the Cartesian claim that the mind and body are clearly distinct. How can an immaterial mind, distinct and separate from all other matter, interact with the physical body? This is the brick wall that Cartesian dualism runs up against. And there has been no convincing answer, from Descartes to the present. It is more common now for philosophers to talk of the mental and the physical as two aspects of one reality. Indeed, one could go a step further and argue why have a single entity? The mind or self is not a single thing, a unified identity that travels from cradle to grave, but merely a catch all label for our swirling fragmentary perceptions of the world and reactions to it. The reason we create this self, an inner puppeteer directing our behaviour, is due to our ability to view ourselves from the outside. After all isn’t this what consciousness is, to be self aware? Personally I find R.A. Brook’s description of robot behaviour much more plausible, when thinking about the immaterial self so elusive to Descartes  : “It is only the observer of the creature who imputes a central representation or central control. The creature itself has none: it is a collection of competing behaviours. Out of the local chaos of their interactions there emerges, in the eye of the observer, a coherent pattern of behaviour.”