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Leibniz does not
see eye to eye with Lock on many point, even when he does he often does so with
addendum.  With this in mind, this paper
will examine the views of Locke and Leibniz in regard to their views on various
kinds of knowledge and on the degrees and extent of certainty, as well as the role of axioms in human knowledge.

views on various kinds of knowledge and on the degrees and extent of
certainty.

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Locke
and Leibiniz are among the oldest philosophies in the world of knowledge, with
a number of works published by them.  They
both establish that three kinds ok knowledge exists; intuitive knowledge,
sensitive and demonstrative knowledge.  From
the innate side of it, it has been established that every person has some
innate knowledge.  They however differ a
bit in terms of the degrees and certainty of truth.  This portion paper seeks to discuss their
differences and similarities on their views on knowledge.

Locke’s view

Locke
views knowledge as a mere perception that is wholly concerned with ideas.  The definition is however objected by
Leibiniz, arguing that the definition does not explain the differences between the
wise philosophers and the insane.  Locke
seems to have two slightly deviating views on knowledge.  He argues that the general knowledge is
generally the aspect of our ideas.  In
particulars kinds of knowledge, he states that knowledge goes a little further
than mere imagination.  He explains
habitual knowledge as that type of knowledge that is developed for learning
purposes.  General truths in the case of
habitual knowledge relies on the memories that we have mastered sometime in the
past.  An example of the habitual
knowledge application is the multiplication tables.

Locke
argues that knowledge is never innate.  He
said that the universal consent does not exist.  He further argued that if there were universal
consent, there should be universal possessions.  That if login truths were universal, is must
have been known by all human beings and they must have been universally
accepted.  That if innate existed, the
children and the insane should have been the most reliable guides to logical
truth.  The fact that they are not the
guides to logical truth, it means that innatism does not exist.

Locke
however agreed with innatists on the basis of there is a difference between the
truth we accept immediately upon receiving it, and that which we require a
significant consideration before accepting it.  He however argues that the fundamental
differences between the two kinds of knowledge do not agree with the innatist
truth ideologies.  A careful study on
knowledge and truth requires an acquisition of ideas in a particular case under
study.

On
achieving certainty, Locke argues that one must have requisite ideas and
connection between ideas.  Genuine
knowledge can only be assured by these two aspects, failure to which makes the
knowledge uncertain.  Lastly, he makes a
distinction between the four types of knowledge.  He believes that the knowledge of identity and
diversity depends on a person’s recognition of the differences between ideas.  For instance, the knowledge of real existence
acknowledges that an idea has some connection with a real-life experience.  Intuitive knowledge on the other hand is
explains our foundation on which all truths are formulated.  Demonstrative knowledge treats truth at each
step of the human process and discovers ideas through reasoning and connecting
ideas.  Lastly, the sensitive knowledge
according to Locke, provides a concrete evidence of some existence of general
truths especially on particular objects outside our lives.

Leibiniz view. 

Leibiniz
belives strongly in the idea of innate knowledge.  He uses this knowledge to distinguish between
contigent and necessary types of truths.  He argues that basically or most of the
necessary truths are innate, if not all of them.  He differs from Locke by arguing that
experience has no ability of delivering the knowledge of necessary truth to
humans. He gives various reasons for his argument.  The first one is the distinction aspect.  Leibiniz says that a proposition can only be
necessary if it is associated to some high degree of truth.  A preposition is also necessary if it is
false.  For example, mathematical
propositions such as 1 + 1=2 is necessary, because 1+1 cannot equal to any
other number but 2.  A proposition that
is contingent must be strongly false r true.  The world is however different.

Leibiniz
establishes that the experience of human sense is only helpful in specific
instances.  An example he provides is
that these two oranges plus another two oranges makes four oranges.  Most instances however confirm a general truth
according to him.  Even though they
confirm general truth, the truth is not enough to establish the universal
necessity.

The role of axioms in human knowledge.

According
to Locke, knowledge is the agreement or disagreement of ideas. This is the
definition that he uses to guide his opinions and ideas when talking of the
issue of knowledge. On the other hand, Leibniz actually disagrees with this
definition on the basis that it is actually subjective in that it is based on
the whole idea of perception. He argues that surely when this approach is used;
it may lead to refuting of the genuine knowledge just because it is about a
disagreement. Even though the basis of Locke’s argument is that all knowledge
has its own origin Leibniz’s reasoning is actually based on the fact that
knowledge is certainly not subjective instead it is able to stand on its with
its own origin but rather there is no knowledge that opposes each other.

Locke
also described it as not being peculiar to the received axiom. On this very
point he goes on to state that there are several propositions and diversity of
each of them is also self-relevant. This is evident when he actually terms the
role of perception in the maxim of knowledge. He goes on to explain that
According to him man was actually living in line with the laws guiding the
community were the very same laws that were to be used in guiding the people.
He went on to state that the best right was the right to piety. This means
according to thing the strongest and the best thing for a man was actually to
seek true happiness by bettering himself thereby making seek the perfect
himself in line with the perception of the creator. It is at this very point
that he brings in the point of existence. He also goes on to state that
according to him he is just aware that God has given him existence enough of
things without him. In that he does not have to receive something for it to be
there. Even though he cannot be able to perceive something in the background,
it does not mean that whatever he did not perceive does not exist. This means
there he is able to perceive things or not they actually exist without him.

While not supporting
axioms, he does take the time review if they hold any value, if they are innate
or how they contribute to knowledge in general, however does not draw
distinction from maxims.  Meanwhile,
Locke’s opponent on the matter, Leibniz, is a supporter of axioms and advises
Locke that axioms where defined and given meaning by those who coined the term,
axiom and are distinct from maxims.  This
vary processes deems them to valid in these regards, once we comprehend their
meaning.  Leibniz displays his knowledge
of such cases where ancient geometers made attempts to prove some axioms, while
he, himself had made effort toward signifying secondary axioms, by use of
primary axioms, as in the case of identity (Leibniz, 1996, 407).

  Axioms at this point are broken down into
five groups, those of Identity and Diversity, Coexistence and Connexion, of
relation, Real Existence, and Instances. 
Continuing along this order we see that regarding identity and
diversity, Locke contemplated the self-evident nature of ideas based on instant
perception, stating that not all obvious truth is deemed maxims, yet they are
still truths.  For example, red and blue
are not the same.  Here Leibniz points
out that identifying two different things as different is not more than
identifying them alone, however, if comparing things with similarities the
matter gets confused, such as his example of a triangle and a trilateral.  Leibniz continues that a triangle does not
carry the same meaning as trilateral geometrically as proportion is a factor
(Leibniz, 1996, 408). 

On the matter of
relation, Locke point to mathematics and principle of equals subtracted from
equals tallying equals, while one and one are equal, additionally he follows
this up with a display on one’s fingers. Leibniz counters, that one and one
providing the sum of two is not an axiom, but the definition of the number
two.  Likewise, using one’s fingers is a
demonstration of equals from equals providing equals.  Liebniz protests that axioms are always
reduced to the simplest truth formulation and examples are merely an symbolic
aid (Leibniz, 1996, 409-410). 

Moving forward Locke
questions coexistence and connexion. 
Here he views there are few self-evident propositions, such as two
bodies not occupying the same place.  Yet
again Leibniz takes the contrary pointing out Christian beliefs and Aristotle’s
belief in interpenetration regarding the density of matter.  All-be-it, defining ‘body’ as being solid and
impenetrable disallows for the later. Equally it could be argued that God could
make body that is not impenetrable, however, as this is not the case it fails
to be an axiom (Leibniz, 1996, 409). 

After looking at
coexistence and connexion, Locke moves look to real existence.  Here his stance is that there are no axioms
of real existence, while Leibniz protests that the simplicity of the statement
“I think, therefore I am” is the more than adequate proof to the contrary.  However, he continues that one may avoid
giving this axiom status since we do not need to provide that example.  Leibniz believes that the matter is above us
as God holds all truths which are necessary. 
He continues that God is the only one who can see that I and exist have
connection.  Although, if one generalizes
axioms, basic or unproved truths then the use of the words “I think, therefore
I am” provide sufficient grounds to be proclaimed an axiom.  Clearly, here we can see Leibniz’s
consideration for the metaphysical tendencies in his thought.

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