The Pre-Enlightenment Period
The principal feature of the enlightenment period is that acquiring knowledge and truth is based on human experience. In the pre-enlightenment period, the sources that contained all truth were the Bible, which is said to be the revelation, and works of the Ancient Greek Philosophers particularly Plato and Aristotle that were based on reason. As such, medieval learning was reckoned as exegesis: the study and interpretation of a text. Medieval philosophy took a theocentric approach that encompasses God and the Bible/religious scriptures as the subject of study. The ancient Greek philosopher Aristotle, used syllogism in his teachings. The most famous syllogism
This approach to learning was completely discarded by the thinkers in the Enlightenment …show more content…
as no proper body of knowledge was born in the medieval period. Syllogism is syntactical – new knowledge is merely taught, whereas, knowledge is always subjected to revolution. Hence, a proper method, which is not biblically based nor derived from Aristotelian Philosophy had yet to be developed to enable learning in a systematic way. The Enlightenment thinkers concurred that learning generally should emulate a method adapted from existing areas of enquiry that has already been successful. Descartes argued that the method that we seek in philosophy is not endocentric. Thus, to undertake this revolutionary approach, he contended that mathematics holds the key to a new method for learning as mathematics yield certainty, indubitable knowledge and is eternal. Mathematicians had the elements for developing mathematical knowledge; their methods were inborn and not learned. Thus, we should direct our attention to studying the knower so as to establish answers to questions in areas such as epistemology, moral philosophy, and esthepology.
The outset of the Meditations on First Philosophy presents the reader with epistemic doubts, which regards knowledge that comes from senses. For instance, if you put a straw in a glass of water, you will observe that the straw appears distorted, despite the fact that it is not true. In addition, dreams seem as veridical as reality and is questionable whether we can disregard that our whole life is but a dream. These doubts raise the question whether we can trust our senses, for they are empirical and liable to change. On the other hand, Descartes correctly believed that mathematics is non-empirical and must be thusly innate. In Rule II, he asserts that we ought to study the subjects which our mind appears to know indubitably. Mathematical knowledge provides a model that discerns the modality of necessity, which is not apprehended by sense; instead, it is characterized by indubitability. Descartes believed that intuition is God-given and thus, should be the basis of knowledge; before other things can be known. Mathematics is hierarchical: some things can only be known through other things. Therefore, God gave us mathematical knowledge. It follows that on top of the hierarchy and the first step of the proof is the Axiom, which is regarded to be self-evident. For example, the equation 2+2=4, can never be false or 2 cannot change to 1 as the equation would then not be equal to 4. Therefore, the propaedeutic power of mathematics is self-evidence. In the cynic uncertainty that mathematics is equivocal, the first is inattention and the second is not understanding the subject properly. Nonetheless, Descartes identifies 2 virtues that dispel these doubts. He argues that the primal skeptical concern can be acquiesced with prudence, and through scrupulous examination of the matter in hand.
Therefore, it can be inferred that knowledge gained through sensory perception is subject to change, while mathematical knowledge is infallibly certain, indubitable and eternal. Hence, to achieve pure knowledge, the epistemological method: rationalism of mathematical model dependence must be followed.
The principal difference between the Meditations and the Principles can be explained by the fact that the first principles in metaphysics are written in conformity with the analytic method, while those of mathematics with the synthetic method. The main source of Descartes’ distinction between synthesis and analysis is cited in Replies to Objections II, where he is requested to present his argument in a geometrical fashion.
As such, from the Replies to Objection II, we know that Analysis is the method of discovery; Synthesis contrariwise is a technique which is derivative from what already exists and Mathematics is a method of synthesis.
Mathematical ideas are innate and self-evident, which produce their own axioms, whereas metaphysics is a method of analysis and it has to find its own axioms. The Axiom of equality is never in conflict with whatever the senses reveal to us. Hence, mathematical truth have nothing to do with the senses. However, metaphysical axioms are always in contradiction with the senses. We are bereft of primary notions for they are the presuppositions that harmonize with the use of our senses which we have readily accepted. We’ve accustomed ourselves to the preconceptions of our senses since our early years, that we cannot apprehend the truth. Descartes believed that the true starting point in philosophy is indifference, which is eliminating any reliance on empirical ideas. Metaphysics involves us to discredit beliefs based on senses and withdraw our minds from corporeal matters. Descartes proposed a cognitive process no less unsettling than demolishing and rebuilding a premise. In order to be sure that we acknowledge only what is unequivocal, we should deliberately repudiate all preconceived beliefs, including sensory prejudices that we have acquired through education or experience. Thus, analysis is a demonstration designed to bring the attention to the point where all prejudices have been removed and the relevant primary notions can be
intuited.
Descartes questions the reliability of mathematics: in both meditations 1 & 3 and also in Principle V, whereby his concern with mathematics stems from God’s infinite power. Now, given the Regulae accepts the certainty of mathematics, while in the meditations mathematics is subjected to doubt, it appears that Descartes has utilized a method in the meditations other than the mathematical-type method developed in the Regulae.
Reasons for why maths is dubitable are: Errors, psychological irresistibility, hypothesis of a deceiving deity and atheists/non-believers. Descartes believed that intellect can never be erroneous if it is used correctly. Reason, per se cannot be faulty, therefore errors in mathematics are human errors; inadvertence/inattentiveness or lack of attention or not properly understanding the material. In the First Meditation, Descartes considers various potential outcomes which suggest that we might be incorrect about outcomes that are most evident to us. In mathematics, there is a psychological element that makes the equations irresistible. Regardless of right or wrong, both answers are psychologically irresistible. According to the 3rd meditation, geometric-type demonstrations will always be susceptible to doubt until we know that God exists and is not a deceiver. Thus, the second reason is the deceiving deity; we have been created by a supremely good God, but for reasons unbeknownst to us, Therefore, if God is a deceiver, but also the creator of everything, then divine deception would work in such a way that God would constituted our minds that every time we add 1+1 = 2, we cannot think otherwise. On this view, there’s nothing inherently wrong with our reasoning, but, if we believed that a deceiving deity interferes with our thoughts, the results may be unreliable. The 3rd reason is skeptics and atheists; Skepticism points at the unreliability of creator’s infinite power. Non-believer who cannot accept the truth, can never achieve certainty in mathematics. Atheist must believe in the finite cause of our existence, for it decides that it’s going to create us. It is relevant and veracious. The less power you ascribe to the cause of your existence, the more likely you’re to make mistakes. Thus, Descartes concluded that Atheism is incompatible with the truth of certainty in mathematics.
This approach to learning was completely discarded by the thinkers in the Enlightenment …show more content…
as no proper body of knowledge was born in the medieval period. Syllogism is syntactical – new knowledge is merely taught, whereas, knowledge is always subjected to revolution. Hence, a proper method, which is not biblically based nor derived from Aristotelian Philosophy had yet to be developed to enable learning in a systematic way. The Enlightenment thinkers concurred that learning generally should emulate a method adapted from existing areas of enquiry that has already been successful. Descartes argued that the method that we seek in philosophy is not endocentric. Thus, to undertake this revolutionary approach, he contended that mathematics holds the key to a new method for learning as mathematics yield certainty, indubitable knowledge and is eternal. Mathematicians had the elements for developing mathematical knowledge; their methods were inborn and not learned. Thus, we should direct our attention to studying the knower so as to establish answers to questions in areas such as epistemology, moral philosophy, and esthepology.
The outset of the Meditations on First Philosophy presents the reader with epistemic doubts, which regards knowledge that comes from senses. For instance, if you put a straw in a glass of water, you will observe that the straw appears distorted, despite the fact that it is not true. In addition, dreams seem as veridical as reality and is questionable whether we can disregard that our whole life is but a dream. These doubts raise the question whether we can trust our senses, for they are empirical and liable to change. On the other hand, Descartes correctly believed that mathematics is non-empirical and must be thusly innate. In Rule II, he asserts that we ought to study the subjects which our mind appears to know indubitably. Mathematical knowledge provides a model that discerns the modality of necessity, which is not apprehended by sense; instead, it is characterized by indubitability. Descartes believed that intuition is God-given and thus, should be the basis of knowledge; before other things can be known. Mathematics is hierarchical: some things can only be known through other things. Therefore, God gave us mathematical knowledge. It follows that on top of the hierarchy and the first step of the proof is the Axiom, which is regarded to be self-evident. For example, the equation 2+2=4, can never be false or 2 cannot change to 1 as the equation would then not be equal to 4. Therefore, the propaedeutic power of mathematics is self-evidence. In the cynic uncertainty that mathematics is equivocal, the first is inattention and the second is not understanding the subject properly. Nonetheless, Descartes identifies 2 virtues that dispel these doubts. He argues that the primal skeptical concern can be acquiesced with prudence, and through scrupulous examination of the matter in hand.
Therefore, it can be inferred that knowledge gained through sensory perception is subject to change, while mathematical knowledge is infallibly certain, indubitable and eternal. Hence, to achieve pure knowledge, the epistemological method: rationalism of mathematical model dependence must be followed.
The principal difference between the Meditations and the Principles can be explained by the fact that the first principles in metaphysics are written in conformity with the analytic method, while those of mathematics with the synthetic method. The main source of Descartes’ distinction between synthesis and analysis is cited in Replies to Objections II, where he is requested to present his argument in a geometrical fashion.
As such, from the Replies to Objection II, we know that Analysis is the method of discovery; Synthesis contrariwise is a technique which is derivative from what already exists and Mathematics is a method of synthesis.
Mathematical ideas are innate and self-evident, which produce their own axioms, whereas metaphysics is a method of analysis and it has to find its own axioms. The Axiom of equality is never in conflict with whatever the senses reveal to us. Hence, mathematical truth have nothing to do with the senses. However, metaphysical axioms are always in contradiction with the senses. We are bereft of primary notions for they are the presuppositions that harmonize with the use of our senses which we have readily accepted. We’ve accustomed ourselves to the preconceptions of our senses since our early years, that we cannot apprehend the truth. Descartes believed that the true starting point in philosophy is indifference, which is eliminating any reliance on empirical ideas. Metaphysics involves us to discredit beliefs based on senses and withdraw our minds from corporeal matters. Descartes proposed a cognitive process no less unsettling than demolishing and rebuilding a premise. In order to be sure that we acknowledge only what is unequivocal, we should deliberately repudiate all preconceived beliefs, including sensory prejudices that we have acquired through education or experience. Thus, analysis is a demonstration designed to bring the attention to the point where all prejudices have been removed and the relevant primary notions can be
intuited.
Descartes questions the reliability of mathematics: in both meditations 1 & 3 and also in Principle V, whereby his concern with mathematics stems from God’s infinite power. Now, given the Regulae accepts the certainty of mathematics, while in the meditations mathematics is subjected to doubt, it appears that Descartes has utilized a method in the meditations other than the mathematical-type method developed in the Regulae.
Reasons for why maths is dubitable are: Errors, psychological irresistibility, hypothesis of a deceiving deity and atheists/non-believers. Descartes believed that intellect can never be erroneous if it is used correctly. Reason, per se cannot be faulty, therefore errors in mathematics are human errors; inadvertence/inattentiveness or lack of attention or not properly understanding the material. In the First Meditation, Descartes considers various potential outcomes which suggest that we might be incorrect about outcomes that are most evident to us. In mathematics, there is a psychological element that makes the equations irresistible. Regardless of right or wrong, both answers are psychologically irresistible. According to the 3rd meditation, geometric-type demonstrations will always be susceptible to doubt until we know that God exists and is not a deceiver. Thus, the second reason is the deceiving deity; we have been created by a supremely good God, but for reasons unbeknownst to us, Therefore, if God is a deceiver, but also the creator of everything, then divine deception would work in such a way that God would constituted our minds that every time we add 1+1 = 2, we cannot think otherwise. On this view, there’s nothing inherently wrong with our reasoning, but, if we believed that a deceiving deity interferes with our thoughts, the results may be unreliable. The 3rd reason is skeptics and atheists; Skepticism points at the unreliability of creator’s infinite power. Non-believer who cannot accept the truth, can never achieve certainty in mathematics. Atheist must believe in the finite cause of our existence, for it decides that it’s going to create us. It is relevant and veracious. The less power you ascribe to the cause of your existence, the more likely you’re to make mistakes. Thus, Descartes concluded that Atheism is incompatible with the truth of certainty in mathematics.