(Originally written December 9, 2006 in Book 12)
Ok, it's Saturday about 1:00 pm. I have a major epistemology paper due at 9:00 am on Monday, which I have not ben diligent in working on. So, it's research time!
Thesis (preliminary) all knowledge is analytic in nature. Synthetic nature is artificial.
Louis Pojman
The Theory of Knowledge 3rd Edition
VII.2 An Empiricist Critique of A priori knowledge - A.J. Ayer
No matter of fact can be shown to be logically necessarily or universally true (Hume).
Ayer states that no proposition with factual content is necessarily true.
Every empiricist must accept the thesis that no factual propositions can be necessary truths.
Empiricism faces difficulties with this thesis in dealing with mathematics and logical truths. There are two ways of dealing with this:
1) They are not necessary truths (in this case their universalness must be somehow explained).
2) They have no factual content (in this case they must be able to explain why a proposition without factual content can be true and useful and surprising).
If both of these prove unsatisfactory, empiricism is proven wrong and rationalism is vindicated.
Rationalism states that thought, independent of experience is a more reliable source of knowledge than experience.
John Stuart Mill adopted the thesis that mathematic and logical truths are not necessary. He maintained that they were merely inductive generalizations based on a very large number of experiences. Thus, these mathematical and logical truths were very probable, but not certain.
The difference between Mathematical and logical truths and scientific generalizations was a difference of degree, not kind.
Ayer admits that by rejecting Mill's approach, empiricists are obliged to be somewhat dogmatic.
The Irrefutability of the Propositions of Mathematics and Logic
In every instance when a mathematical or logical truth appears to be refuted we can easily find a way to show that it has not. Truths of logic and mathematics are analytic propositions or tautologies.
The Nature of Analytic Propositions
Kant's definition of an analytic proposition, "one in which the predicate B belonged to the subject A as something which was covertly contained in the concept of A" (Pojman, 381).
Analytic judgments add nothing to the subject; whereas synthetic judgments do.
Analytic judgments provide no factual content and it is for this reason no experience can refute them.
Because analytic judgments provide no factual content it does not follow that they are senseless.
Analytic propositions provide us with some new knowledge. They clarify. They show new linguistic usages.
Analytic judgments allow us to make explicit what was implicit.
The Propositions of Geometry
Kant believed that geometry was the study of the properties of physical space.
Non-Euclidean Geometry has proven that geometry is not the study of physical space. We merely use geometry to reason about physical space.
Necessary truths are devoid of factual content. A priori truths are always analytic. They are always tautologies.
How can Tautologies be surprising?
The power of logic or mathematics to surprise us has its origin solely in the limitedness of our minds, not in their content.
All a priori truths are tautologies. Tautologies serve to guide us in our empirical search for knowledge, they do not contain any information about any matter of fact.
Monadology and Other Philosophical Essays
Gottfried Wilhelm von Leibniz
translated by: Paul Schrecken and Anne Martin Schrecker
The Unity of Leibniz's philosophic thought
There is a pervasive inner unity that flows through all of Leibniz's work.
Leibniz held a belief in a universal language.
Reflections on knowledge, truth, and ideas
All knowledge is either obscure or clear. Clear knowledge is either confused or distinct. Distinct knowledge is either adequate or inadequate. Distinct knowledge is either symbolic or intuitive.
"The most perfect knowledge is that which is both adequate and intuitive" (Leibniz, 3).
Knowledge is obscure when it is insufficient to recognize what it represents.
Knowledge is clear when it is sufficient to recognize the object it represents.
Clear knowledge is confused when it cannot be distinguished from other objects in description. It is recognizable, but only to me.
Distinct knowledge is distinguishable and explicable knowledge. It is distinct when we can explain it to others.
Perfect knowledge is both adequate and distinct, but Leibniz doubts whether or not man can give a true account of this, but numbers come close.
Intuitive knowledge occurs when the whole of simple idea is known at once. Symbolic knowledge is knowledge o highly complex notions where the whole is known without full knowledge of all the parts.
There is a difference in definitions:
1) Nominal definitions - contain only marks to distinguish the defined thing from other things
2) Real definitions - actually describing the object in its fullest
By distinguishing these definitions we refute Hobbes' notion that all truths are arbitrary. (Hobbes' assumption rests on all definitions being nominal ones).
An idea is true when it is possible (it is false when it involves a contradiction).
Possibility is known either a priori or a posteriori
Causal definitions are known a priori.
A posteriori possibility is known when we experience a thing in reality.
When we have adequate knowledge we also possess a priori knowledge of a possibility.
Thought experiment - when we perceive green we are unaware that we are actually perceiving blue + yellow. Thus, what is green is known, analytically, as yellow+blue.
On the Universal Science: Characteristic XIV
All certain knowledge is established through demonstration or experiments.
Science is based on reason.
We need some exact language, or a form of truly philosophical writing in which ideas are reducible to a kind of "alphabet of human thought"
Leibnizian demonstrations involve two principles:
1) What implies contradiction is false
**2) Reason can be given for any truth, the predicate concept always inheres in its subject concept, either explicitly or implicitly
Necessary truths can be reduced to identical propositions
Contingent truths require an infinite analysis which can be performed solely by God. Only God can know contingent truths a priori.
Contingent truths are truths of fact.
XV
"All human reasoning uses certain signs or character" (Leibniz, 17).
Knowledge is symbolic.
All human ideas can be reduced into a few primitives. (cogitationes -> primitivas)
Critical remarks concerning the General Part of Descartes' principles
One must, in searching for truth, doubt everyone at some point in one's lifetime.
2. That what is doubtful should be considered false.
-There is no advantage to this.
4. Why one can place in doubt the truth of sensible things.
-All we need to know is that they are consistent among themselves.
Linehan - This is interesting, but unhelpful to my research. I'm skipping it.
On the Improvement of Metaphysics and on the concept of substance
Mathematics possesses clarity; metaphysics possesses obscurity.
The cause of metaphysical obscurity is that the general concepts of metaphysics are ambiguous.
Metaphysics needs clarity and clearness and certitude even more than mathematics.
Force is inherent in substance. Force is the faculty to act, action itself and requires effort.
What is nature? Reflections on the force inherent in created things and on their actions
What does nature consist of?
Do created things posses an energy?
The whole of nature is the perfect work of God's making.
Robert Boyle states that nature is the mechanism of bodies.
Linehan - I think I have exhausted my resources in this book for my epistemology paper. But, just reading a little bit of Leibniz has restored my love and respect for him and rationalism in general.
So now it is time for the paper!
Paper Structure:
I. Thesis
II. Definitions
A. Historical
i. epistemological/metaphysical/semantical categories
1. Kant's 4 Quadrants
2. A.J. Ayer's a priori
3. Leibniz divisions of knowledge
B. Personal
III. Thought Experiments (proofs of I)
1. Logical
2. Mathematical
3. Propositional
IV. Objections and responses
V. Closing
Thesis: Knowledge is...
1) Analytic (semantical)
2) Tautological (semantical)
3) A Priori (epistemological)
4) Necessary (metaphysical)
Knowledge has three major components
1) Epistemological
2) Semantical
3) Metaphysical
Epistemological and semantical knowledge are closely related and focused on together, mainly because of Kant. Metaphysical knowledge has been intertwined with epistemological and semantical, though less explicit.
Definitions of Knowledge
Leibnizian distinctions lead to my definition.
First of the three components: Epistemological
definition of a priori (Pojman, 367)
definition of a posteriori (Pojman, 367)
Kantian definition of analytic propositions
Ayer definition of a priori truths
2nd of the 3 components: Semantical
definition of analytic
definition of synthetic
Ayer's distinction
Leibnizian definition/personal additions
Ayer's truth of logic (mathematics)
Thought experiments
1) Logic
2) Mathematics
3) Empirical (most controversial)
3rd of 3 Components: Metaphysical
definition of necessary truths
definition of contingent truths
Hume's objection (needs more research)
Ayer's factual content necessary truth?
Metaphysical difficulties for the empiricist
Ayer has satisfactory proved factual content but he has not eliminated rationalism. Explain why and you'll be able to demonstrate all three parts of your thesis and vindicate your definition of knowledge (conclusion).
No comments:
Post a Comment