Conscious users
Mathematics is used by mathematicians , who form a global community. It is also used by students of mathematics. As mathematics is a part of primary education in almost all countries, almost all educated people have some exposure to pure mathematics. It is interesting to note that there are very few cultural dependencies or barriers in modern mathematics.
Unconscious or subconscious users
Almost every person has used mathematics for practical purposes like calculating his produce or his wage. Non-rigorous use of mathematics is used in estimating how much to eat, whether to cross a road or not etc and such activity is done not only by humans but also by other animals. The whole universe is governed by mathematical rules.
Wednesday, March 18, 2009
Monday, March 16, 2009
Is God a Concept?
A concept has two properties- it is universal i.e. it covers all elements in a set and it is abstract i.e. it obscures all differences between the different elements of a set. God is not a concept because the “set” of God has no quantifiable element and the difference between God is not obscured, every facet of God is different from others and yet it is facet of the same God.
Belief, Knowledge, and Language
Stanford Encyclopedia of Philosophy defines belief as the psychological condition in which a person holds a proposition to be true. Now, propositions of this sort can be divided into 3 categories: Necessary propositions such as 2+2=4 or all husbands are married; contingent propositions such as The moon is nearer to the earth than the sun or Madrid is the capital of Spain; or subjective such as Torture is bad or Speaking truth is good.
The definition of belief includes all three cases. If I believe Madrid is the capital of Spain, I also “believe” that the population of Madrid is less than Spain, the area of Madrid is less than that of Spain, or Madrid is a part of Spain. But we do not consider these as distinct beliefs, we consider these as logical consequences. Similarly, 2 + 2=4 0r 3 + 6= 9 is derivable from Peano’s postulates and hence they are not beliefs. If someone says that he believes 998 * 796= 7756838, this statement can be taken as a belief as due to the limited computing power of the brain such statements are not instantly derivable from Peano’s postulates. However, when we admit that they are beliefs, we consider them as falsifiable. Secondly, when we say that we say that X is my belief I admit that in other circumstances, I could have considered not X as my belief i.e. I chose what I believe. So, belief is optional- I can have belief X or belief Y or no belief about an entity A. Thirdly, a belief about something needs some awareness about that thing. A belief cannot exist in a vacuum, it needs some prior awareness. Fourthly and most trivially, belief is known i.e. I know my beliefs and X cannot be my belief if I do not know it.
The encyclopedia said that if we accept that language is necessary for belief, we have to accept that 3-year old children, who do not have the capacity to distinguish between reality and appearance have no belief. Can so-called adults distinguish between reality and appearance? As long as we believe that there is a reality outside us, we can never be sure of the reality of that reality or our knowledge about that reality. And to believe is to believe that there is a reality outside us. I think the quality of being falsifiable is a necessary condition for belief and this condition is possible only if we have the concept of belief. Hence, language is necessary for belief.
The definition of belief includes all three cases. If I believe Madrid is the capital of Spain, I also “believe” that the population of Madrid is less than Spain, the area of Madrid is less than that of Spain, or Madrid is a part of Spain. But we do not consider these as distinct beliefs, we consider these as logical consequences. Similarly, 2 + 2=4 0r 3 + 6= 9 is derivable from Peano’s postulates and hence they are not beliefs. If someone says that he believes 998 * 796= 7756838, this statement can be taken as a belief as due to the limited computing power of the brain such statements are not instantly derivable from Peano’s postulates. However, when we admit that they are beliefs, we consider them as falsifiable. Secondly, when we say that we say that X is my belief I admit that in other circumstances, I could have considered not X as my belief i.e. I chose what I believe. So, belief is optional- I can have belief X or belief Y or no belief about an entity A. Thirdly, a belief about something needs some awareness about that thing. A belief cannot exist in a vacuum, it needs some prior awareness. Fourthly and most trivially, belief is known i.e. I know my beliefs and X cannot be my belief if I do not know it.
The encyclopedia said that if we accept that language is necessary for belief, we have to accept that 3-year old children, who do not have the capacity to distinguish between reality and appearance have no belief. Can so-called adults distinguish between reality and appearance? As long as we believe that there is a reality outside us, we can never be sure of the reality of that reality or our knowledge about that reality. And to believe is to believe that there is a reality outside us. I think the quality of being falsifiable is a necessary condition for belief and this condition is possible only if we have the concept of belief. Hence, language is necessary for belief.
Sunday, March 8, 2009
Innate Knowledge
I was reading a blog which discussed the topic of innate knowledge. According to the blog, there are innate beliefs but no innate knowledge. The objection was that I know my beliefs was raised but the author did not discuss the issue satisfactorily. I believe in X if I am aware that not-X may be true and yet I believe that X and non not-X is correct. Belief implies knowledge of the belief.
It can be argued that I may have beliefs without my knowing so. Hence, I would not accept those beliefs as belief, I would accept them as knowledge. I may change my opinion on those pieces of knowledge on further inquiry but the same is possible for all scientific knowledge, individually as well as collectively.
It can be argued that I may have beliefs without my knowing so. Hence, I would not accept those beliefs as belief, I would accept them as knowledge. I may change my opinion on those pieces of knowledge on further inquiry but the same is possible for all scientific knowledge, individually as well as collectively.
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