“Present knowledge is wholly dependent on past knowledge.” Discuss this claim with reference to two
areas of knowledge.
Word Count: 1598
It is uncertain where knowledge originates from. Some philosophers claim that knowledge is
innate, while others claim that knowledge is a priori; built upon knowledge. Yet others claim that
knowledge is a posteriori, meaning that it is based on the perception of our surroundings. “Past
knowledge” refers to the state of knowledge that has existed at some point in the past, while “present
knowledge” refers to what is known in the immediate present moment. As time is relative to an
individual, present knowledge is strictly personal, as in the beetle in a box analogy. By the time
personal knowledge becomes shared knowledge - assuming telepathy does not exist - it becomes past
knowledge. While past knowledge may influence present knowledge, the phrase “wholly dependent”
implies that present knowledge is contingent on past knowledge; it cannot exist without past
knowledge. To determine whether present knowledge is wholly dependent on past knowledge, it is
important to analyse where present knowledge originates from. This essay considers only knowledge
of humans, excluding knowledge of god which is believed to be transcendent and omniscient, where
knowledge past, present, and future are all interdependent on each other. In Mathematics, one could
argue that present knowledge is wholly dependent on (a priori) past knowledge, because it relies
heavily on reasoning as a Way of Knowing (WOK). However, it can also be said that mathematical
knowledge originates from intuition and perception, which suggests that it is independent of past
knowledge. In Arts, it is widely accepted that artistic knowledge relies on the WOK of intuition,
suggesting that it does not depend on the past. It also relies on the emotions which may be affected by
outside factors. At the same time, however, it relies on the existing conventions within art which
implies reason is used, showing that present knowledge is dependent on past knowledge. Perspectives
in relation to the AOK of mathematics and art will be discussed in this essay.
1
, Mathematical knowledge can be shown to be independent of past knowledge. Mathematical
realism states that mathematics exists objectively, and that mathematical knowledge is a posteriori. It
states that knowledge is gained primarily through the WOK of sensory perception. Quines’
contemporary mathematical empiricism is based on the indispensability argument, that mathematics is
indispensable to reality. Some people may find it hard to notice mathematics as a fundamental unit of
the universe as a result of availability heuristics. With sense perception, we can see physical objects,
yet we cannot see mathematics. With scientific knowledge, we know that everything is made up of
atoms, which, is made up of elementary particles such as quarks. Mathematical descriptions of these
elementary particles such as the Dirac equations and Newtonian mechanics are said to be
“fantastically accurate” (Roger Penrose). Furthermore, each of the elementary particles correlate to
its own “Lie group,” a set of mathematical functions that connects particle physics and
representation theory. This is congruent with the Platonist view on mathematics; in which
mathematics is “independent of intelligent agents and their language, thought, and practices,”
providing further evidence that preset knowledge is independent of past knowledge. Realists argue
that because of this, mathematics was discovered via observation. Sensory perception is a WOK that
forms a connection between knowledge and the present reality, which shows that present knowledge
is therefore independent of past knowledge. An example can be seen from the first origins of
mathematics. The first system of numbers was found as tally marks from cuts on bones from the
palaeolithic age. Through abductive reasoning, it can be said that these were observations of maths in
nature. Realists also believe that mathematics, like the objective universe, is infinite in the sense that
an external mathematical universe exists beyond human knowledge. Mathematical realism shows that
present knowledge is not wholly dependent on past knowledge, therefore the knowledge claim may be
falsified. Yet, mathematical realism is not a universal truth; there is no certain way to verify this
perspective and there are other equally compelling perspectives. Therefore the knowledge claim is not
falsified.
2
areas of knowledge.
Word Count: 1598
It is uncertain where knowledge originates from. Some philosophers claim that knowledge is
innate, while others claim that knowledge is a priori; built upon knowledge. Yet others claim that
knowledge is a posteriori, meaning that it is based on the perception of our surroundings. “Past
knowledge” refers to the state of knowledge that has existed at some point in the past, while “present
knowledge” refers to what is known in the immediate present moment. As time is relative to an
individual, present knowledge is strictly personal, as in the beetle in a box analogy. By the time
personal knowledge becomes shared knowledge - assuming telepathy does not exist - it becomes past
knowledge. While past knowledge may influence present knowledge, the phrase “wholly dependent”
implies that present knowledge is contingent on past knowledge; it cannot exist without past
knowledge. To determine whether present knowledge is wholly dependent on past knowledge, it is
important to analyse where present knowledge originates from. This essay considers only knowledge
of humans, excluding knowledge of god which is believed to be transcendent and omniscient, where
knowledge past, present, and future are all interdependent on each other. In Mathematics, one could
argue that present knowledge is wholly dependent on (a priori) past knowledge, because it relies
heavily on reasoning as a Way of Knowing (WOK). However, it can also be said that mathematical
knowledge originates from intuition and perception, which suggests that it is independent of past
knowledge. In Arts, it is widely accepted that artistic knowledge relies on the WOK of intuition,
suggesting that it does not depend on the past. It also relies on the emotions which may be affected by
outside factors. At the same time, however, it relies on the existing conventions within art which
implies reason is used, showing that present knowledge is dependent on past knowledge. Perspectives
in relation to the AOK of mathematics and art will be discussed in this essay.
1
, Mathematical knowledge can be shown to be independent of past knowledge. Mathematical
realism states that mathematics exists objectively, and that mathematical knowledge is a posteriori. It
states that knowledge is gained primarily through the WOK of sensory perception. Quines’
contemporary mathematical empiricism is based on the indispensability argument, that mathematics is
indispensable to reality. Some people may find it hard to notice mathematics as a fundamental unit of
the universe as a result of availability heuristics. With sense perception, we can see physical objects,
yet we cannot see mathematics. With scientific knowledge, we know that everything is made up of
atoms, which, is made up of elementary particles such as quarks. Mathematical descriptions of these
elementary particles such as the Dirac equations and Newtonian mechanics are said to be
“fantastically accurate” (Roger Penrose). Furthermore, each of the elementary particles correlate to
its own “Lie group,” a set of mathematical functions that connects particle physics and
representation theory. This is congruent with the Platonist view on mathematics; in which
mathematics is “independent of intelligent agents and their language, thought, and practices,”
providing further evidence that preset knowledge is independent of past knowledge. Realists argue
that because of this, mathematics was discovered via observation. Sensory perception is a WOK that
forms a connection between knowledge and the present reality, which shows that present knowledge
is therefore independent of past knowledge. An example can be seen from the first origins of
mathematics. The first system of numbers was found as tally marks from cuts on bones from the
palaeolithic age. Through abductive reasoning, it can be said that these were observations of maths in
nature. Realists also believe that mathematics, like the objective universe, is infinite in the sense that
an external mathematical universe exists beyond human knowledge. Mathematical realism shows that
present knowledge is not wholly dependent on past knowledge, therefore the knowledge claim may be
falsified. Yet, mathematical realism is not a universal truth; there is no certain way to verify this
perspective and there are other equally compelling perspectives. Therefore the knowledge claim is not
falsified.
2
