(Originally written April 10, 2007 in Book 25)
Class Notes
Problem of religious language
Equivocal - a term means separate things
Univocal - a term means the same thing
Problems with equivocal language is that if it means something other than what we are familiar with than we are speaking meaninglessly.
Problem with univocal language is that how can a finite term be applied to an infinite concept of God?
David Hume
How do words get their meaning?
- Sensory impression
How do I know the meaning of the word "house"? I have seen a house.
How do I know the meaning of the word "blue"? I have seen blue things.
The sensory impression gives meaning to the word describing it
Hume's Fork:
Metaphysics: any term that can not be grounded in experience is utterly meaningless and nonsense. Consign it to the flames.
In order for a word to be meaningful it must be based on an antecedent sensory impression. The problem with this thesis of Hume's is there isn't a single word in this thesis that is based on an antecedent sensory impression.
Vienna Circle
Moritz Schlick (leader): in order for philosophy to make progress it must model itself after the natural sciences and become empirically verifiable.
- Rudolf Carnap, Karl Popper, Kurt Gödel
The Vienna Circle created the philosophy of logical positivism by expanding Humean notions.
Instead of focusing on words/terms they focused on propositions.
A proposition is meaningful if it meets the principle of verifiability.
Principle of verifiability - a sentence is meaningful if they are a) not analytic and b) in principle verifiable.
Under logical positivism metaphysics was rendered (by them) as meaningless and nonsense.
Ethical language is also nonsense. It is purely emotive.
Religions or theological concepts are also nonsense.
In a sense the logical positivists are atheistic, but the atheist would deny God's existence and the logical positivist would state that any denial of the existence of God is as meaningless as any affirmation of God.
The problem with logical positivism is that its basis (the verifiability principle) is not verifiable on its own grounds.
A. J. Ayer claimed that the principle and thought structures are meaningful despite not meeting their criteria.
Strong verifiability principle: a statement is meaningful if it is derived from an observation statement.
Observation -> Proposition
Weak Verification principle: an observation statement can be inferred from a statement
Proposition -> inference -> observation
Showing posts with label Ayer. Show all posts
Showing posts with label Ayer. Show all posts
Tuesday, April 10, 2007
Monday, March 19, 2007
Allegorical & Contemporary Language Problems
(Originally written March 19, 2007 in Book 13)
Analogical Predication: The Only Alternative
If terms cannot be applied to God in a univocal or an equivocal sense, they must be applied analogically.
The analogical way of speaking about God helps to solve Parmenides' paradox because being is not taken as univocal. Being is analogical and thus things essentially differ in being.
Being cannot be univocal because it would mean that everything that hath being would be one. Being cannot be equivocal because whatever hath being hath being and what else cannot hath being or they are one. Therefore, Being must analogical.
God does not have properties at all. "God is the perfections that his creatures only have by causal participation" (263).
Univocal Concepts but Analogical Predication
Scotus was correct that any concept applied to men and God must be univocally understood. Aquinas was correct in stating that concepts must be analogically affirmed of God.
The attribute of man and God are same but the application of that attribute differs in God and man.
Whatever concept is understood of God must be understood univocally, but must be predicated (attributed to) of God must be predicated analogically.
Finite Concepts and Finite Predications
Aquinas held God is one in reality, but many things logically.
We cannot know the substance of God, but we can predicate many things about God substantively.
While there is an infinite difference in perfection between Creator and creatures, there is not a total dissimilarity. Thus, concepts are univocally understood.
A creature must bear some similarity to its creator.
The Causal Basis for Analogy Between God and Creatures
Analogy is based on intrinsic causality.
Analogy is based on efficient causality.
Analogy is based on essential causality. God is the cause of the very being of the world, not only its beginning.
Analogy is not based on material causality. God is the cause of the existence of matter, but he is not material. God is the cause of all perfections in the world, but not the imperfection resulting from the limiting conditions of a material world.
Analogy is based on principal, not instrumental causality.
God is the principal, intrinsic, essential and efficient cause of the being and perfection of the world.
Objections and Responses
1) Why select some, but not all qualities drawn from the world and apply them to God?
- Only some things flow from God's efficient, principal, essential and intrinsic causality.
2) Words are divorced from their finite mode or conditions are devoid of meaning.
- The univocal concept of the words remains the same while the way in which they are predicated charges.
-Terms applied to God are not made meaningless only extended without limitations
3) Analogy rests on the assumption that causality provides without limitations.
-If something is caused it must be caused by something. God cannot give what he does not have. Thus if God does not have existence He cannot give existence.
4) Any analogous predication of God as a "First cause" involves an infinite regress of meaning to identify the univocal element.
-The only way to predicate something of a finite being and an infinite being must be analogous because if it is univocal it predicates it equivocally. An infinite being cannot have the same mode as a finite being. It must be predicated analogously.
5) Even assuming the metaphysical assumption that there is a similarity among beings, that ontology is not univocally expressible.
-This is not a mere theistic. It is the only alternative to monism.
6) Since Wittgenstein the distinction between equivocal and univocal is obsolete, and thus, the notion of analogy is obsolete.
7) A general theory of analogy does not work.
This is not an analogical theory, but rather a metaphysical scheme in which language fits. This metaphysical scheme is rooted in reality and thus, the language is so rooted.
13. Model Religious Language
The Background of the Contemporary Language Problem
Hume is the source of the contemporary problems of religious language.
Hume: Two kinds of propositions
There are only two kinds of meaningful statements:
1. Statements expressing elation of ideas
- true by definition
- not informative about the real world
2. Statements about matters of fact
Kant called he former analytic and the latter synthetic.
Wittgenstein: Linguistic Silence
Wittgenstein held that what was mystical (religious experience) cannot be expressed in words.
He held that we are to eliminate religious language, not religious experience.
Ayer: Religious Language and Verification
In Language, Truth and Logic A. J. Ayer attempted to eliminate all metaphysics and theology.
He held that no statement can be meaningful unless it is tautological or empirically verifiable.
But Ayer's principle of verifiability is neither tautological nor verifiable and thus, meaningless on his grounds.
Ayer was neither atheistic nor agnostic. He was non-cognitivistic. He held that no cognitively meaningful statement can be made about a transcendent reality.
2/15/07 - 3/19/07
Analogical Predication: The Only Alternative
If terms cannot be applied to God in a univocal or an equivocal sense, they must be applied analogically.
The analogical way of speaking about God helps to solve Parmenides' paradox because being is not taken as univocal. Being is analogical and thus things essentially differ in being.
Being cannot be univocal because it would mean that everything that hath being would be one. Being cannot be equivocal because whatever hath being hath being and what else cannot hath being or they are one. Therefore, Being must analogical.
God does not have properties at all. "God is the perfections that his creatures only have by causal participation" (263).
Univocal Concepts but Analogical Predication
Scotus was correct that any concept applied to men and God must be univocally understood. Aquinas was correct in stating that concepts must be analogically affirmed of God.
The attribute of man and God are same but the application of that attribute differs in God and man.
Whatever concept is understood of God must be understood univocally, but must be predicated (attributed to) of God must be predicated analogically.
Finite Concepts and Finite Predications
Aquinas held God is one in reality, but many things logically.
We cannot know the substance of God, but we can predicate many things about God substantively.
While there is an infinite difference in perfection between Creator and creatures, there is not a total dissimilarity. Thus, concepts are univocally understood.
A creature must bear some similarity to its creator.
The Causal Basis for Analogy Between God and Creatures
Analogy is based on intrinsic causality.
Analogy is based on efficient causality.
Analogy is based on essential causality. God is the cause of the very being of the world, not only its beginning.
Analogy is not based on material causality. God is the cause of the existence of matter, but he is not material. God is the cause of all perfections in the world, but not the imperfection resulting from the limiting conditions of a material world.
Analogy is based on principal, not instrumental causality.
God is the principal, intrinsic, essential and efficient cause of the being and perfection of the world.
Objections and Responses
1) Why select some, but not all qualities drawn from the world and apply them to God?
- Only some things flow from God's efficient, principal, essential and intrinsic causality.
2) Words are divorced from their finite mode or conditions are devoid of meaning.
- The univocal concept of the words remains the same while the way in which they are predicated charges.
-Terms applied to God are not made meaningless only extended without limitations
3) Analogy rests on the assumption that causality provides without limitations.
-If something is caused it must be caused by something. God cannot give what he does not have. Thus if God does not have existence He cannot give existence.
4) Any analogous predication of God as a "First cause" involves an infinite regress of meaning to identify the univocal element.
-The only way to predicate something of a finite being and an infinite being must be analogous because if it is univocal it predicates it equivocally. An infinite being cannot have the same mode as a finite being. It must be predicated analogously.
5) Even assuming the metaphysical assumption that there is a similarity among beings, that ontology is not univocally expressible.
-This is not a mere theistic. It is the only alternative to monism.
6) Since Wittgenstein the distinction between equivocal and univocal is obsolete, and thus, the notion of analogy is obsolete.
7) A general theory of analogy does not work.
This is not an analogical theory, but rather a metaphysical scheme in which language fits. This metaphysical scheme is rooted in reality and thus, the language is so rooted.
13. Model Religious Language
The Background of the Contemporary Language Problem
Hume is the source of the contemporary problems of religious language.
Hume: Two kinds of propositions
There are only two kinds of meaningful statements:
1. Statements expressing elation of ideas
- true by definition
- not informative about the real world
2. Statements about matters of fact
Kant called he former analytic and the latter synthetic.
Wittgenstein: Linguistic Silence
Wittgenstein held that what was mystical (religious experience) cannot be expressed in words.
He held that we are to eliminate religious language, not religious experience.
Ayer: Religious Language and Verification
In Language, Truth and Logic A. J. Ayer attempted to eliminate all metaphysics and theology.
He held that no statement can be meaningful unless it is tautological or empirically verifiable.
But Ayer's principle of verifiability is neither tautological nor verifiable and thus, meaningless on his grounds.
Ayer was neither atheistic nor agnostic. He was non-cognitivistic. He held that no cognitively meaningful statement can be made about a transcendent reality.
2/15/07 - 3/19/07
Tuesday, February 20, 2007
Can we demonstrate the existence of God?
(Originally written February 20, 2007 in Book 13)
Can we demonstrate the existence of God?
Objections
1) Can never demonstrate an infinite cause from a finite effect.
2) God's existence is known through faith. Reason cannot prove matters of faith.
3) Even a demonstration that's logically valid may not correspond to reality.
4) We are limited by being enclosed in a finite universe, which we cannot escape. God exists outside of the universe, thus we cannot demonstrate his existence or non-existence.
5) Every argument for the existence of God must first assume His existence, thus all arguments are circular.
6) No argument for the existence of God is ever going to convince who doesn't already believe.
7) God's essence is the middle term, but we cannot comprehend God's essence.
Explanation of 7)
All birds are egg layers (major premise)
All penguins are birds (minor premise)
Therefore, all penguins are egg layers (conclusion)
"Birds" - the middle term
"egglayers" - major term, always the predicate of the conclusion
penguins - minor term, always the subject of the conclusion
The essence of God must function as the middle term, but we do not have any comprehension of the essence of God, so it cannot function that way.
8) There is no such thing as metaphysical knowledge. All knowledge is limited to experience.
9) God cannot be proven by scientific experiments.
10) The term 'God' is meaningless.
Can we demonstrate the existence of God?
Based on Summa Theologic 1, q. 2a.2
Objections revisited
1. A priori objections
2. A posteriori objections
A priori objection #1
Religious language is meaningless
- Ayer, Wittgenstein, logical positivists
- In order to be a meaningful a statement must be, in principle, verifiable
A priori objection #2
- We cannot validate religious experience empirically
- Flew
A priori objection #3
- What is rational, needn't be true
- post modernism
All dragons have wings
All monsters are dragons
Therefore, all monsters have wings
A posteriori objection #1
-Knowledge of God can only be based on faith
- Kierkegaard
A posteriori objection #2
- We cannot apprehend God's essence
A posteriori objection #3
- The finite can never extend to the infinite
- Alfred North Whitehead
A posteriori objection #4
- Presuppositionalism: Since God is first in Being, we must begin with God
- Kierkegaard, Van Til
Transcendental argumentation
Ways to draw valid logical inferences
1) Deduction - formal inferences from premises
2) Induction - probable conclusions from observations
We know there is a world
- What are the conditions that are necessary for there to be a world?
- We cannot look outside o the world to find God
- If there is a God, there could be evidence for a God in the world.
Any attempt to simply close the option of there being theistic proofs are purely arbitrary.
Can the finite attain infinity?
Georg Cantor's set theory
{1, 2, 3, 4 ... infinity}
{1, 2, 3, 4
but the set of real numbers, which is infinite is longer than the set of integers, which is also infinite.
Metaphysical infinity is more than mathematical infinite.
Important considerations
- Distinction between that something exists and comprehending its essence.
Distinction between ontology and epistemology.
-Ontology (being)
-Epistemology (knowing)
Ontologically, God exists or he doesn't.
Theistic proofs deal with the epistemological question: "Can one know that God exists".
Ontology - God exists
Epistemology - Ascertaining the ontology
Arguing in a circle.
God exists
Therefore, he has shown his effects
Therefore, he has ...
Therefore, he has ...
Therefore, God exists.
Believing the ontological statement that "God exists" and then providing an epistemological proof is not circular, so long as one does not assume it in the actual argument.
Assignment: argue for the ontological argument.
Can we demonstrate the existence of God?
Objections
1) Can never demonstrate an infinite cause from a finite effect.
2) God's existence is known through faith. Reason cannot prove matters of faith.
3) Even a demonstration that's logically valid may not correspond to reality.
4) We are limited by being enclosed in a finite universe, which we cannot escape. God exists outside of the universe, thus we cannot demonstrate his existence or non-existence.
5) Every argument for the existence of God must first assume His existence, thus all arguments are circular.
6) No argument for the existence of God is ever going to convince who doesn't already believe.
7) God's essence is the middle term, but we cannot comprehend God's essence.
Explanation of 7)
All birds are egg layers (major premise)
All penguins are birds (minor premise)
Therefore, all penguins are egg layers (conclusion)
"Birds" - the middle term
"egglayers" - major term, always the predicate of the conclusion
penguins - minor term, always the subject of the conclusion
The essence of God must function as the middle term, but we do not have any comprehension of the essence of God, so it cannot function that way.
8) There is no such thing as metaphysical knowledge. All knowledge is limited to experience.
9) God cannot be proven by scientific experiments.
10) The term 'God' is meaningless.
Can we demonstrate the existence of God?
Based on Summa Theologic 1, q. 2a.2
Objections revisited
1. A priori objections
2. A posteriori objections
A priori objection #1
Religious language is meaningless
- Ayer, Wittgenstein, logical positivists
- In order to be a meaningful a statement must be, in principle, verifiable
A priori objection #2
- We cannot validate religious experience empirically
- Flew
A priori objection #3
- What is rational, needn't be true
- post modernism
All dragons have wings
All monsters are dragons
Therefore, all monsters have wings
A posteriori objection #1
-Knowledge of God can only be based on faith
- Kierkegaard
A posteriori objection #2
- We cannot apprehend God's essence
A posteriori objection #3
- The finite can never extend to the infinite
- Alfred North Whitehead
A posteriori objection #4
- Presuppositionalism: Since God is first in Being, we must begin with God
- Kierkegaard, Van Til
Transcendental argumentation
Ways to draw valid logical inferences
1) Deduction - formal inferences from premises
2) Induction - probable conclusions from observations
We know there is a world
- What are the conditions that are necessary for there to be a world?
- We cannot look outside o the world to find God
- If there is a God, there could be evidence for a God in the world.
Any attempt to simply close the option of there being theistic proofs are purely arbitrary.
Can the finite attain infinity?
Georg Cantor's set theory
{1, 2, 3, 4 ... infinity}
{1, 2, 3, 4
but the set of real numbers, which is infinite is longer than the set of integers, which is also infinite.
Metaphysical infinity is more than mathematical infinite.
Important considerations
- Distinction between that something exists and comprehending its essence.
Distinction between ontology and epistemology.
-Ontology (being)
-Epistemology (knowing)
Ontologically, God exists or he doesn't.
Theistic proofs deal with the epistemological question: "Can one know that God exists".
Ontology - God exists
Epistemology - Ascertaining the ontology
Arguing in a circle.
God exists
Therefore, he has shown his effects
Therefore, he has ...
Therefore, he has ...
Therefore, God exists.
Believing the ontological statement that "God exists" and then providing an epistemological proof is not circular, so long as one does not assume it in the actual argument.
Assignment: argue for the ontological argument.
Saturday, December 9, 2006
Quick notes & Barebones Outline of a lost Epistemology Paper
(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).
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).
Friday, September 15, 2006
Book notes on Gettier
(Originally written September 15, 2006 in Book 8)
Part IV The Analysis of Knowledge
IV. 1 Is justified true belief knowledge?
Edmund Gettier (1927 - )
Plato:
S knows P if
1) P is true
2) S believes P
3) S is justified in believing P
Chisholm:
S knows P if
1) S accepts P
2) S has adequate evidence that P is true
3) P is true
Ayer:
S knows P if
1) P is true
2) S is sure that P is true
3) S has the right to be sure that P is true
Case I: Suppose S & J have each applied for the same position.
S has strong evidence for proposition "D".
"D" - Jones is the man who will get the job and Jones has 10 coins in his pocket.
Proposition "D" entails the man who will get the job has ten coins in his pocket.
But in fact S gets the job and buy chance he has ten coins in his pocket.
Proposition "D" turns out to be true and despite knowing with a justified belief that "D" is true he couldn't have possibly had knowledge of it.
Case II: S has strong evidence for proposition "F", Jones owns a Ford.
S has a friend named B, but has no idea where B is.
Therefore S can state
1) J owns a Ford or B is in Boston
2) J owns a Ford or B is in Barcelona
3) J owns a Ford or B is in Bologna
In fact, Jones does not own a Ford and B is in Boston. That makes proposition 1 true, but in spite of his evidence, S had no knowledge of it.
Part IV The Analysis of Knowledge
IV. 1 Is justified true belief knowledge?
Edmund Gettier (1927 - )
Plato:
S knows P if
1) P is true
2) S believes P
3) S is justified in believing P
Chisholm:
S knows P if
1) S accepts P
2) S has adequate evidence that P is true
3) P is true
Ayer:
S knows P if
1) P is true
2) S is sure that P is true
3) S has the right to be sure that P is true
Case I: Suppose S & J have each applied for the same position.
S has strong evidence for proposition "D".
"D" - Jones is the man who will get the job and Jones has 10 coins in his pocket.
Proposition "D" entails the man who will get the job has ten coins in his pocket.
But in fact S gets the job and buy chance he has ten coins in his pocket.
Proposition "D" turns out to be true and despite knowing with a justified belief that "D" is true he couldn't have possibly had knowledge of it.
Case II: S has strong evidence for proposition "F", Jones owns a Ford.
S has a friend named B, but has no idea where B is.
Therefore S can state
1) J owns a Ford or B is in Boston
2) J owns a Ford or B is in Barcelona
3) J owns a Ford or B is in Bologna
In fact, Jones does not own a Ford and B is in Boston. That makes proposition 1 true, but in spite of his evidence, S had no knowledge of it.
Monday, September 11, 2006
Book notes on Ewing (A)
(Originally written September 11, 2006 in Book 8)
VII. 3 - In Defense of A Priori Knowledge
A. C. Ewing (1899 - 1973)
-Cambridge University
Ewing argues against Ayer and states that the statement 'there is no synthetic a priori knowledge' is itself a synthetic a priori judgment.
Meaning of the Distinction, "A priori" Character of Mathematics
There is a sharp distinction betwixt a priori and empirical judgments
Most of our knowledge is empirical. This comes from two sources:
1) Sense perception
2) Introspection
Knowledge we obtained simply by thinking is a priori.
A priori knowledge is necessary truths and we know why it is true.
Empirical propositions are contingent.
Mathematics must be a priori because otherwise we could not be able to add two numbers together without counting. Since we need not count (an empirical method), knowledge of mathematics is a priori.
VII. 3 - In Defense of A Priori Knowledge
A. C. Ewing (1899 - 1973)
-Cambridge University
Ewing argues against Ayer and states that the statement 'there is no synthetic a priori knowledge' is itself a synthetic a priori judgment.
Meaning of the Distinction, "A priori" Character of Mathematics
There is a sharp distinction betwixt a priori and empirical judgments
Most of our knowledge is empirical. This comes from two sources:
1) Sense perception
2) Introspection
Knowledge we obtained simply by thinking is a priori.
A priori knowledge is necessary truths and we know why it is true.
Empirical propositions are contingent.
Mathematics must be a priori because otherwise we could not be able to add two numbers together without counting. Since we need not count (an empirical method), knowledge of mathematics is a priori.
Types of knowledge and propositions
(Originally Written September 11, 2006 in Epistemology)
A priori knowledge
Necessary truths - propositions that cannot be false
contingent truths - propositions that are true, but could be false
The distinction betwixt necessary truths and contingent truths is a metaphysical one.
Analytic propositions - true by way of their meaning
Synthetic propositions - true through their relation to the world
The distinction betwixt analytic and synthetic propositions is a semantic one.
A priori knowledge - knowledge prior to experience
A posteriori knowledge - knowledge through experience
The distinction betwixt the two is an epistemological one.
Kant:
Analytic a priori - i.e. Triangles are three sided
Synthetic a priori - i.e. 5+7=12, causality
Synthetic a posteriori - i.e. the house is brown
There is no a posteriori analytic propositions
A.J. Ayer
-a strong empiricist
-a logical positivist
-Held that in order for a statement to be cognitively meaningful it had to be either analytically true or empirically meaningful.
-Held that an en empiricists must regard analytic propositions as either:
1) Not necessary (John Stuart Mill)
2) Devoid of factual content (Ayer)
A priori knowledge
Necessary truths - propositions that cannot be false
contingent truths - propositions that are true, but could be false
The distinction betwixt necessary truths and contingent truths is a metaphysical one.
Analytic propositions - true by way of their meaning
Synthetic propositions - true through their relation to the world
The distinction betwixt analytic and synthetic propositions is a semantic one.
A priori knowledge - knowledge prior to experience
A posteriori knowledge - knowledge through experience
The distinction betwixt the two is an epistemological one.
Kant:
Analytic a priori - i.e. Triangles are three sided
Synthetic a priori - i.e. 5+7=12, causality
Synthetic a posteriori - i.e. the house is brown
There is no a posteriori analytic propositions
A.J. Ayer
-a strong empiricist
-a logical positivist
-Held that in order for a statement to be cognitively meaningful it had to be either analytically true or empirically meaningful.
-Held that an en empiricists must regard analytic propositions as either:
1) Not necessary (John Stuart Mill)
2) Devoid of factual content (Ayer)
Sunday, September 10, 2006
Book notes on Ayer
(Originally written September 10, 2006 in Book 8)
VII. 2 An Empiricist Critique of A priori Knowledge
AJ Ayer (1910 - 1989)
-Oxford University
-Argues against synthetic a priori knowledge because all supposed synthetic a priori truths are reducible to tautologies or as an analytical truths
This is a section from Ayer's early work: Language, Truth and Logic
How can empiricists account for necessary truths? Truths of empirical nature cannot ever be proven logically necessary. This, although appears to lead to utter skepticism, doesn't force one there. It is not irrational to hold beliefs that are not logical certainties; what is irrational is to search for certitude where there can be none and to demand certainty when probability will suffice.
The trouble empiricists face is dealing with necessary truths like mathematics and logic. The empiricist must deal with it in one of two ways:
1) He must state that they are not necessary truths and somehow account for their apparent universal nature.
Or, 2) He must state that they have no factual content and account for their truth, practical use, and surprising nature.
If one or two is unsatisfactory, then we are obliged to abandon empiricism and become rationalists.
Or if we opt out of rationalism we will have to adopt Kantian theory despite epistemological difficulties.
If empiricists show either 1) or 2) then, 'we shall have destroyed the foundations of rationalism'.
Mill adopted the theory that truths of logic and mathematics are not necessary truths. He held that these were inductive generalizations based on a huge amount of instances. The large number of instances was what Mill said made us think that they are necessary. He held that they were similar to empirical hypotheses, only much more probable.
Ayer does not think that this is at all acceptable. "In rejecting Mill's theory, we are obliged to be somewhat dormant" (Pojman, 371).
The Irrefutability of the Propositions of Mathematics and Logic
The truths of logic and mathematics are tautologies. If we state that any one is wrong then we contradict ourselves.
Any instance in which we think that we have an empirical situation that seems to refute a logical or mathematic truth we find error in our empirical judgment, not in the logical or mathematical truth.
The Nature of Analytic Propositions
Ayer gives an account of Kant's definitions of analytic and synthetic propositions, but contends that he does not succeed in making the distinction clear.
Kant does not give one straightforward criterion for making the distinction between Analytic propositions and synthetic propositions. He employs a psychological criterion for synthetic propositions and a logical criterion for analytic propositions and takes the criterions equivalence for granted.
Ayer defines an analytic proposition as one whose validity depends entirely on the definition of the symbols it contains; and, synthetic propositions when its validity is determined by facts of experience.
Analytic propositions never provide us any information about matters of fact. Thus, no experience can refute analytic propositions.
Analytic propositions therefore are devoid of factual content. They say nothing. "We are not suggesting they are senseless in the way that metaphysical utterances are senseless" (Jones, 382).
Linehan - Bitchsmack! Cheap shot. Though fairly strong. I admit that it stings.
Linehan - AJ Ayer has made me wary of synthetic propositions. Could I prove that there are only analytic propositions and everything is contained in the definition of the objects? i.e. The physical object 'apple'. An analytic judgment (Ayer's definition) would be that "This apple is an apple". A synthetic proposition would be "This apple is red". Could I reasonably argue (if I hold that there are forms) that the object apple in our mind is one that contains the notion of "red", "sweet/tart", "Grannysmith/other breed", etc. I don't know if I could make it plausible, but I am attracted to this theory.
Ayer - Analytic tautologies give us a way to explicitly state what we mean. It gives us clarification, but not any additional knowledge.
The Propositions of Geometry
While geometry seems the most plausible area for there to be a priori synthetic knowledge, the invention of non-Euclidean geometry has proven this wrong.
The self-evident principles of Euclidean geometry have been shown to be reducible to tautologies.
Geometry is not a study of space, though geometry can be used to reason about space.
Since geometry is analytic we can reject Kant's notion of space being synthetic a priori; since arithmetic is analytic we can reject Kant's notion of time being synthetic a priori.
We have a priori knowledge of necessary truths; they are all tautologies.
How can tautologies be surprising?
They are surprising because our intellects are not as superior as we believe they are.
Complex tautologies can easily surprise us because we are not as smart as we think.
VII. 2 An Empiricist Critique of A priori Knowledge
AJ Ayer (1910 - 1989)
-Oxford University
-Argues against synthetic a priori knowledge because all supposed synthetic a priori truths are reducible to tautologies or as an analytical truths
This is a section from Ayer's early work: Language, Truth and Logic
How can empiricists account for necessary truths? Truths of empirical nature cannot ever be proven logically necessary. This, although appears to lead to utter skepticism, doesn't force one there. It is not irrational to hold beliefs that are not logical certainties; what is irrational is to search for certitude where there can be none and to demand certainty when probability will suffice.
The trouble empiricists face is dealing with necessary truths like mathematics and logic. The empiricist must deal with it in one of two ways:
1) He must state that they are not necessary truths and somehow account for their apparent universal nature.
Or, 2) He must state that they have no factual content and account for their truth, practical use, and surprising nature.
If one or two is unsatisfactory, then we are obliged to abandon empiricism and become rationalists.
Or if we opt out of rationalism we will have to adopt Kantian theory despite epistemological difficulties.
If empiricists show either 1) or 2) then, 'we shall have destroyed the foundations of rationalism'.
Mill adopted the theory that truths of logic and mathematics are not necessary truths. He held that these were inductive generalizations based on a huge amount of instances. The large number of instances was what Mill said made us think that they are necessary. He held that they were similar to empirical hypotheses, only much more probable.
Ayer does not think that this is at all acceptable. "In rejecting Mill's theory, we are obliged to be somewhat dormant" (Pojman, 371).
The Irrefutability of the Propositions of Mathematics and Logic
The truths of logic and mathematics are tautologies. If we state that any one is wrong then we contradict ourselves.
Any instance in which we think that we have an empirical situation that seems to refute a logical or mathematic truth we find error in our empirical judgment, not in the logical or mathematical truth.
The Nature of Analytic Propositions
Ayer gives an account of Kant's definitions of analytic and synthetic propositions, but contends that he does not succeed in making the distinction clear.
Kant does not give one straightforward criterion for making the distinction between Analytic propositions and synthetic propositions. He employs a psychological criterion for synthetic propositions and a logical criterion for analytic propositions and takes the criterions equivalence for granted.
Ayer defines an analytic proposition as one whose validity depends entirely on the definition of the symbols it contains; and, synthetic propositions when its validity is determined by facts of experience.
Analytic propositions never provide us any information about matters of fact. Thus, no experience can refute analytic propositions.
Analytic propositions therefore are devoid of factual content. They say nothing. "We are not suggesting they are senseless in the way that metaphysical utterances are senseless" (Jones, 382).
Linehan - Bitchsmack! Cheap shot. Though fairly strong. I admit that it stings.
Linehan - AJ Ayer has made me wary of synthetic propositions. Could I prove that there are only analytic propositions and everything is contained in the definition of the objects? i.e. The physical object 'apple'. An analytic judgment (Ayer's definition) would be that "This apple is an apple". A synthetic proposition would be "This apple is red". Could I reasonably argue (if I hold that there are forms) that the object apple in our mind is one that contains the notion of "red", "sweet/tart", "Grannysmith/other breed", etc. I don't know if I could make it plausible, but I am attracted to this theory.
Ayer - Analytic tautologies give us a way to explicitly state what we mean. It gives us clarification, but not any additional knowledge.
The Propositions of Geometry
While geometry seems the most plausible area for there to be a priori synthetic knowledge, the invention of non-Euclidean geometry has proven this wrong.
The self-evident principles of Euclidean geometry have been shown to be reducible to tautologies.
Geometry is not a study of space, though geometry can be used to reason about space.
Since geometry is analytic we can reject Kant's notion of space being synthetic a priori; since arithmetic is analytic we can reject Kant's notion of time being synthetic a priori.
We have a priori knowledge of necessary truths; they are all tautologies.
How can tautologies be surprising?
They are surprising because our intellects are not as superior as we believe they are.
Complex tautologies can easily surprise us because we are not as smart as we think.
Class and book notes on Kant
(Originally written September 10, 2006 in Book 8)
A priori knowledge
Classifications and Definitions
"The problem of synthetic a priori knowledge involves epistemological, metaphysical and semantic considerations" (Pojman, 367).
"A priori and a posteriori are latin terms that were first developed in the Middle Ages by scholastic philosophers.
Leibniz used both to prove knowledge. Kant further developed the notions.
Is there synthetic a priori knowledge? Kant held that it was necessary from a logic standpoint.
"A. Epistemological Categories
1. A priori knowledge does not depend on evidence from sense experience. (Plato's innate ideas and Leibniz's 'truths of reason') for example, mathematics and logic.
2. A posteriori knowledge depends on evidence from Sense experience. (Plato's 'appearance' and Leibniz's 'truths of fact') - empirical knowledge.
B. Metaphysical Categories
1. Necessary truths 'are' true in all possible worlds (for example, the statement that, 'God exists' according to the ontological argument).
2. Contingent truths 'are' true in the actual world but not in all possible worlds (for example, the fact you exist and were born after January 1, 1800)
C. Semantical categories
1. Analytic-predicate is contained in the subject, explicative, not ampliative (for example, 'all mothers are women')
2. Synthetic - predicate is not contained in the subject but adds something to the subject ampliative, not explicative (for example, Mary is a mother)" (Pojman, 367-8)
Combinations
Synthetic a priori knowledge is affirmed by rationalists and denied by empiricists.
Neither believe that there are such things as analytic a posteriori knowledge because that implies a contradiction.
Kant, a radical rationalist, held that all knowledge was grounded in a priori knowledge.
"The essential claim of those who hold to synthetic a priori knowledge is that the mind can grasp connexions between ideas (concepts) that are not strictly analytical related" (Pojman, 368).
Kant's Chart of Knowledge
(clarifications are for my own sake)
Synthetic a priori knowledge
-Math, i.e. 5+7=12
-Exclusionary: i.e. nothing red is green
-Presuppositions of experience: space, time and causality
-Moral judgments - the categorical imperative
-The Laws of Logic: i.e. The principle of non-contradiction
-Metaphysical - The existence of God, Free-Will
Until Kant, people believed our knowledge must conform to objects. This had led to a failure to establish a priori knowledge. Kant switched it around so that objects conform to out knowledge, making a priori knowledge possible. This is Kant's so-called Copernican revolution.
Prolegomena: Preamble on the Peculiarities of all Metaphysical Knowledge
S1. Of the Sources of Metaphysics
Sciences differ from one another based on one or all of these:
1) object
2) sources of knowledge
3) kind of knowledge
As for metaphysics and its knowledge, it can never be, or come from things, empirical.
It can not be from external experiences because that is physics; nor can it e from internal experiences because that is psychology. Therefore, ti must come from a priori knowledge. It comes from pure understanding and pure reason.
Metaphysics is pure philosophical knowledge.
S2. Concerning the kind of knowledge which can alone be called metaphysical
Metaphysical judgments are judgments that are explicative, that is, they add nothing to their content.
Synthetical judgments are judgments that are expansive, that is, they increase the knowledge.
Analytical judgments merely analyze the subject in the predicate: 'All bodies are extended'.
Synthetical judgments add something to the subject in the predicate: 'All bodies have weight'
The common principle in all analytical judgments is the law of contradiction.
A priori knowledge
Classifications and Definitions
"The problem of synthetic a priori knowledge involves epistemological, metaphysical and semantic considerations" (Pojman, 367).
"A priori and a posteriori are latin terms that were first developed in the Middle Ages by scholastic philosophers.
Leibniz used both to prove knowledge. Kant further developed the notions.
Is there synthetic a priori knowledge? Kant held that it was necessary from a logic standpoint.
"A. Epistemological Categories
1. A priori knowledge does not depend on evidence from sense experience. (Plato's innate ideas and Leibniz's 'truths of reason') for example, mathematics and logic.
2. A posteriori knowledge depends on evidence from Sense experience. (Plato's 'appearance' and Leibniz's 'truths of fact') - empirical knowledge.
B. Metaphysical Categories
1. Necessary truths 'are' true in all possible worlds (for example, the statement that, 'God exists' according to the ontological argument).
2. Contingent truths 'are' true in the actual world but not in all possible worlds (for example, the fact you exist and were born after January 1, 1800)
C. Semantical categories
1. Analytic-predicate is contained in the subject, explicative, not ampliative (for example, 'all mothers are women')
2. Synthetic - predicate is not contained in the subject but adds something to the subject ampliative, not explicative (for example, Mary is a mother)" (Pojman, 367-8)
Combinations
Synthetic a priori knowledge is affirmed by rationalists and denied by empiricists.
Neither believe that there are such things as analytic a posteriori knowledge because that implies a contradiction.
Kant, a radical rationalist, held that all knowledge was grounded in a priori knowledge.
"The essential claim of those who hold to synthetic a priori knowledge is that the mind can grasp connexions between ideas (concepts) that are not strictly analytical related" (Pojman, 368).
Kant's Chart of Knowledge
Analytic
|
Synthetic
|
|
A Priori
|
-Entailments
-Identity Statements
-Tautologies
-Definitions
|
-Mathematics
-Exclusionary
-Presuppositions of experience
-Moral Judgments
-Laws of Logic
-Metaphysical
|
A Posteriori
|
XX
|
-Empirical
“All bodies are heavy”
“John is a bachelor”
|
The Kantian Theory About Synthetic A Priori Knowledge
The question: How are synthetic a priori judgments possible? This is Kant's primary concern in his Critique of Pure Reason.
Kant (via Ewing) makes four claims about synthetic a priori judgments
1. They are logically necessary - wholes that determine their own parts
2. They are not derivable from particular sensations (but empirical experience is the trigger to cause them to arise)
3. They are presupposed in all of our experience
4. They are contributed by our minds.
Synthetic a priori knowledge is of the conditions of experience, not of reality.
A.J. Ayer critiques the notion of the synthetic a priori knowledge from a conventionalist's point of view. He believes that all the supposed a priori knowledge can actually be reduced to analytic truths.
A.C. Ewing counters Ayer and is in favor of it. Maintaining that if nothing else, the laws of logic are a priori.
W.V. Quine denies the notion of containment being meaningful. (Containment is the notion of an idea being expressed in the definition of the word: bachelor contains the ideas 'unmarried' and 'man'). Since Quine denies containment then he makes no distinction betwixt analytic and synthetic judgments. This also rids him of a priori judgments.
H.P. Grace and P.F. Stranson disagree with Quine.
Roderick Chisholm defends a priori and analytic knowledge.
Saul Kripke throws a major curveball, contending that is possible to have a posteriori necessary truths and non-necessary a priori knowledge.
VII.1. A Priori Knowledge
Immanuel Kant
Kant (1724-1804) was born in Königsberg and never left the town.
He was deeply pious and Lutheran
He was inhuman in his orderliness. Some citizens of Königsberg set their clocks by Kant's walks.
The Critique of Pure Reason started a revolution in theory of knowledge.
He was "woke from his dogmatic slumber" by Hume.
Kant held that we have incredible structured minds that interpret and categorize all experiences that we have. This is the "Kant's Copernican Revolution"
Kant's distinctions between a priori and a posteriori knowledge is famous.
A priori knowledge is what we know prior to experience. A posteriori is knowledge we gain through experience.
Hume considered all knowledge of matters of fact a posteriori and only analytic statements a priori.
Kant rejects Hume's theory and states that it is possible to have a priori knowledge of matters of fact.
Kant holds that all knowledge begins with experience, but it does not mean that all knowledge arises out of experience.
Kant also holds that mathematical truth is synthetic (the predicate ads something to the subject) not analytical.
Other synthetic a priori knowledge is knowledge of time, of space and of causality.
A priori
|
A Posteriori
|
|
Analytic
|
Tautologies & entailments
|
None
|
Synthetic
|
Causality, Space and time, 5+7=12, and the moral law
|
Empirical judgments
|
Basically, an analytic judgment explicitly states a subject and its definition in the predicate. If an analytic statement contradicts itself it is false.
There are two types of synthetical judgments:
1) a priori
2) a posteriori
Synthetical judgments cannot be deduced solely from the Law of Contradiction, but they are still subject to it.
Judgments of experience are always synthetical by nature.
Mathematical judgments are synthetical. This is a fact that eluded people for years.
All mathematical judgments are a priori because they are necessarily true.
Arithmetic judgments like 5+7=12 are definitely true because there is nothing in the notions '5', +, '7' that demands the sum of 12.
Linehan - I think I disagree. The concept of '12', if we truly know it can be analyzed and known as, '0+12, 1+11, 2+10, 3+9, 4+8, 5+7, 6+6, and so forth, provided that we know the notion of '7".
Geometrical judgments are likewise synthetical because they require us to use intuition tadas.
"the essential and distinguishing feature of pure mathematical knolsedge among all after a priori knowledge is that it cannot proceed from concepts, but only from construction of concepts" (Pojman, 373).
Kant criticizes Hume for believing mathematics contained only analytical propositions and metaphysics having only synthetical a priori propositions. But, had Hume realized that mathematics were a priori synthetical propositions he would not have discarded metaphysics.
Metaphysical judgments are synthetical. But, judgments pertaining to metaphysics are analytical.
Definitions like a substance is that which exists as a subject is an analytical judgment pertaining to metaphysics. The concept "substance" is metaphysical but the judgment is analytical and therefore, not a metaphysical judgment.
Metaphysics is different from every other science in the way it produces its a priori cognitions.
Metaphysics receives from outside itself analytic judgments, but uses those analytic judgments to accomplish its end, which is to form a priori synthetical judgments.
"The generation of a priori knowledge by intuition as well as concepts, in fine, of synthetical propositions a priori, especially in philosophical knowledge, constitutes the essential subject of metaphysics" (Pojman, 374).
S3. A remark on the general division of judgment into analytical and synthetical:
The distinction is extremely important, but it is difficult to find in other men's work. It is obscure, and difficult to put into words. Once one discovers it though, they will be able to see the difference in places where they never saw it before.
S4. The General Question of the Prolegomena: Is Metaphysics Possible?
We cannot assume that metaphysics exists as a science, but we can confidently state that there are a priori synthetical cognitions (i.e. pure mathematics).
The question is not whether, but how is metaphysics possible?
S5. The General Problem: How is knowledge from pure reason possible?
Metaphysics stands or falls on the ability or inability to have synthetic a priori knowledge.
There can be an incredibly well put together metaphysical system with tons of truths, but if the architect of that system has not given an account to how one comes to know a priori synthetic judgments then, "to all that which thou protest me thus, I refuse to give credence, and hate"
If we did not see true synthetical a priori judgments in life then we would see that the question of how to come by that knowledge as insoluble.
To solve this we must divide it into four parts:
1) How is pure mathematics possible?
2) How is pure natural science possible?
3) How is metaphysics in general possible?
4) How is metaphysics as a science possible?
I am so irritated! Kant spends this entire last section suspending others from metaphysics but gives no definite answer. Ahh! I am thoroughly agitated right now. This is on e of the biggest disappointments in my brief (about fourteen months now) investigation into philosophy!
Metaphysical judgments are synthetical. But, judgments pertaining to metaphysics are analytical.
Definitions like a substance is that which exists as a subject is an analytical judgment pertaining to metaphysics. The concept "substance" is metaphysical but the judgment is analytical and therefore, not a metaphysical judgment.
Metaphysics is different from every other science in the way it produces its a priori cognitions.
Metaphysics receives from outside itself analytic judgments, but uses those analytic judgments to accomplish its end, which is to form a priori synthetical judgments.
"The generation of a priori knowledge by intuition as well as concepts, in fine, of synthetical propositions a priori, especially in philosophical knowledge, constitutes the essential subject of metaphysics" (Pojman, 374).
S3. A remark on the general division of judgment into analytical and synthetical:
The distinction is extremely important, but it is difficult to find in other men's work. It is obscure, and difficult to put into words. Once one discovers it though, they will be able to see the difference in places where they never saw it before.
S4. The General Question of the Prolegomena: Is Metaphysics Possible?
We cannot assume that metaphysics exists as a science, but we can confidently state that there are a priori synthetical cognitions (i.e. pure mathematics).
The question is not whether, but how is metaphysics possible?
S5. The General Problem: How is knowledge from pure reason possible?
Metaphysics stands or falls on the ability or inability to have synthetic a priori knowledge.
There can be an incredibly well put together metaphysical system with tons of truths, but if the architect of that system has not given an account to how one comes to know a priori synthetic judgments then, "to all that which thou protest me thus, I refuse to give credence, and hate"
If we did not see true synthetical a priori judgments in life then we would see that the question of how to come by that knowledge as insoluble.
To solve this we must divide it into four parts:
1) How is pure mathematics possible?
2) How is pure natural science possible?
3) How is metaphysics in general possible?
4) How is metaphysics as a science possible?
I am so irritated! Kant spends this entire last section suspending others from metaphysics but gives no definite answer. Ahh! I am thoroughly agitated right now. This is on e of the biggest disappointments in my brief (about fourteen months now) investigation into philosophy!
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