Descartes which as we know represents the beginning of modern philosophy and with several agendas behind his thoughts, but one that stands out the most is the desire to show that reason is a useful tool with which to discover truths about the world. Descartes claims that all systematic knowledge based on unquestionable foundations is evident, certain and felt that the only way through which his agenda could be met was by uncovering the faulty foundations of philosophical thought and shoring them up by laying a new foundation. Descartes considered his mind to be the most knowledgeable of his beliefs, and sought to infer an external world including matter from such introspection. Descartes contrasts with probable cognition, and regards arithmetic and geometry as a paradigm. In the first mediation after entertaining the dream and the powerful deceiving god hypotheses, Descartes adopts the strict policy of regarding all his ordinary opinions as they were false. The justification of this is that he points out that although most of his previous beliefs are in need of a solid foundation, they are highly possible. He doubts his out thoughts and skeptical those hypotheses are needed to counteract what he feels and thinks of how he views the world, and feels that he can never get out of the habit of assenting to these opinions unless he can in fact claim them to be what they are that is highly probable opinions. His opinions which he feels in a sense that they are doubtful, it is still much more reasonable to believe than to deny. Descartes raises some really good possibilities that even the most trustworthy of our faculties might deceive us at some point in time; we can ignore that even after a dream which concerns our knowledge by means of the senses of the existence. The mentioning of a real conclusion that might come from physics, astronomy, medicine, and all other disciplines which depend on the study of compound things are doubtful, we can’t turn our backs on the facts that while arithmetic, geometry, and other subjects of this kind are in the simplest of things whether they truly exist all contain something certain. Deception comes in many fashions, but we can’t let truth deceive of us of the truth whether we are awake or sleeping of the simpler logical truth of things. Whether it’s the simple things in life such as adding two and three equals five, and a square has no more than four sides we can still be deceived in our minds with even the most transparent ideas. No matter the situation Descartes reveals that he is still concerned with the possibility of being deceived all the time in the exercise of our mind, even though now the doubt seems to be restricted, even for the pure intellect or not we can be still be fallible even for the most attentive and well trained mind. Hume’s who has remained neutral on his argument about demonstrative reasoning of whether pure intellect versus other things such as memory or the imagination. He points out that to produce a challenge general enough to call into question the certainty of inference as such, in whatever way we conceive it. Hume points out very clearly “In all demonstrative sciences the rules are certain and infallible”, but these does not necessary mean he endorses a rationalist conception of the objectivity of mathematical rules. What is trying to be said by Hume is that in common life and science, in particular mathematical calculations we assume that the method of establishing claims by demonstrative reasoning provides certain knowledge. Even in our daily life’s we are plagued with certainly and even ordinary doubts about the conclusions. Fallible and uncertain rules can evolve into error and does not matter how experienced you might be we all realize that we cannot be truly certain in all us because we fall under imperfect faculties. In common life and in science we take into consideration past experiences with us in estimating the degree of reliability mainly due to the inferences to several tests which we can include repeatedly that we go through and trying to seek agreement, but with the gradual increase in confidence after obtaining positive results do we see a union of causes and effects from our past experience and observation. These experiences provided the balance and ability to see positive test results of the past experiences of drawing conclusions and having them certified by careful examination, and only then do we see the impact of the present and next inferences of what we do. What happens when we are certain that are demonstrative knowledge only turns these ordinary doubts into a skeptical doubt of our human performances. Contrary to what we already know we still and common life and science confidence naturally acquired of our reasoning, this can lead to a gradual increase of our fallible faculties and bring nothing more but new probabilities of uncertainly. Descartes begins with a claim he finds intuitive namely that “common sense or reason” is naturally equal in all men. Descartes simple claim is that reason will be his guide, not past efforts in philosophy. His reason tells him that in his quest for the truth he should reject as being absolutely false everything in which he can see or have reason for doubt. Descartes finds that he can doubt everything except him whether or not he is correct in his reasoning about his point or any other he has done something extremely important in that life has no ultimate purpose or meaning. Descartes felt that in some way we must start from scratch to develop a new metaphysical doctrine which would serve as the proper foundations for certain knowledge. The thought behide this was to only accept as true of those things that are evidently true in a clear and distinct manner which can take form of breaking them down these complex issues that are too difficult to understand in their true form, and divide it in the simplest parts possible so that they can be independently, distinctly, and clearly understood. This made a lot of sense and holds true to this day in complex issues such as the ones he pointed out; in this case I will use mathematics. The complexity of breaking down mathematical problems will give you a foundation to relate these parts step by step again until you reach the whole once again. The reasoning behind this is that you will understand the complexity because you understand the parts and how they are interact with one other. Convincing is not enough, but by doing as was done by Descartes gives you the opportunity to give doubt to anything that would lead you to the slightest doubt or false conclusion to discard completely all that was taught as a kid, or facts that were opinionated as we have all been, thus leading to options that was misleading. Hume pointed out that knowledge and probability cannot run insensibly into each other, because no matter how successful it still introduces uncertainty, and it can never establish the relations of qualitative identity or difference. This may hold true, but I feel that breaking it down and putting it in simple terms can really shed light to all we do, feel, think, and even perceive life as we know it. In order to paint a clear picture of who we are or to rule out any second thoughts of being mislead we need to break things down in order to come to a conclusion that we are satisfied with the result of the true answer we are seeking without doubt. One of the last things we want to do is deceive ourselves from the truth by pretending that our options are false and imaginary. Hume has stated that there is no certainty, self-evident knowledge of anything, and that our knowledge is confirmed to impressions and ideas. We are in no position to declare the existence of either material objects or of spiritual entities. A particular effect is produced by a particular cause, and the result of our association of ideas, a habitual or customary observation of such relations. What is open to us is only a probability and no certainly or produce particular effects. Hume points out that we are limited to perceptions, images, and when the notion of causality itself is unfounded, then how can we be sure that our perceptions are caused by external objects. Hume doubts everything and believes that all that we know is of a doubtful nature, and he has no doubts regarding the certainly of the truth of his own theories. A consistent septic can’t be certain whether what he declares to be the truth has any certainly in it. It is obvious that a negation of validity of one’s own position would end in an utter confusion of thought. It was Descartes who came to the conclusion that the basis of doubt itself cannot be doubted. Descartes recognized that the principles of philosophy should be based on the self-evident truths, which are certain for all time and free from doubt and dispute from which we can correctly presume all other truths in a logical order, provided we don’t go wrong in our calculation and reasoning.