Aristotle's Logic

The History of Western Philosophy
Bertrand Russell

Ch. XXII Aristotle's Logic

Aristotle's influence was large in general. It was largest in the field of logic. "Even
at the present day, all Catholic teachers of philosophy and many others still obstinately reject the
discoveries of modern logic, and adhere with a strange tenacity to a system which is as definitely
antiquated as Ptolemaic astronomy" (Russell, 195).

Aristotle's most important work in the field of logic is the syllogism, an argument made up of major premise, a minor premise and a conclusion.

If Aristotle's logic had been the beginning of logic and not the end, it would be easy to estimate it as historically important. But, because it was adhered to for thousands of years as the totality of logic it has some deficiencies: formal defects in the system, an over-estimation of the value of the syllogism and the over-estimation of deduction.

The formal defects in the system arise when the particulars and universals are blurred. Aristotle's system allows a lot of things to be assumed that are not necessarily true.

There are other forms of deduction and the syllogism has no priority over any other deductive argument.

All the important inferences outside logic and pure mathematics are inductive, not deductive; the only exceptions are law and theology, each of which derives its first principles from an unquestionable text, viz. the statute books or the scriptures" (Russell, 199). Even though Aristotle allowed for the importance of induction in his writing, his followers did not often mention it and thus, caused errors by accepting premises as being self-evident when they were in fact inductive in nature. Thus, if the premise is arrived at through inductive reasoning it is probably true rather than absolutely true. Two absolutely true premises lead to an absolutely true conclusion. But, if the premises are probably true than the conclusion must be probably true as well. You can see where the errors come from.

Aristotle had ten categories: substance, quantity, quality, relation, place, time, position, state, action and affection. Russell states that the definition of categories is muddy and he says that their use in philosophy is not useful.

Aristotle described a definition as a statement of a thing's essential nature, its essence. Russell argues that a thing does not have an essence, only a word can have an essence.

Russell also attacks the Aristotelian doctrine of substance, stating that a substance is merely a collective name for a number of events. By defining those events as a substance philosophy has made a bunch of metaphysical mistakes.

"I conclude that the Aristotelian doctrines with which we have been concerned in this chapter are
wholly false, with the exception of the formal theory of the syllogism, which is unimportant" (Russell, 202).

Teleological, Analogical and Models in Religious Language

(Originally written March 19, 2007 in Book 25)

Class notes

The Teleological Argument

Transcendental Logic

Given a phenomena 'X'
What are the conditions that make X possible?
Unless there is Y, there cannot be X

Given the fact that all things act for an end
What are the conditions that make it possible for all things to act for an end?
Unless there were an intelligent being that directs all things to their end, ti would not be possible.

Aristotle's Four Questions and their answers

1) What is its purpose? Final Cause (Telos)
2) What is it made of? Material Cause
3) What is its shape (form)? Formal Cause
4) Who or what made it? Efficient Cause

Substance - the total thing with all of its attributes (Aristotelian, not Cartesian)

Paley's Argument from analogy

The watch did not grow there.
It did not just happen.
Because of its complexity and purposiveness we know that it was made by a human being.

The very properties that lead us to infer that the watch was made by a watchmaker lead us to infer the universe was made by a universe-maker.

Inductive Analogy

Set A consists of member {a, b, c, d, e...}
All these members share property X
"F" is also a member of set A
Therefore, F probably has property X

In the General sample you want a "high negative analogy"

But when the General sample is extended to one particular thing you want a "high positive analogy".

The teleological argument of Paley depends on the universe being as much like a clock as possible.

Criticism of Paley's Argument

Hume:

-Even if the analogy holds, it doesn't prove the existence of God
- Even if there is a strong analogy between the watch and the universe we have not ruled out the possibility that it could have come about by chance

Post-Humean Versions

- tend to become disjunctions rather than analogy
- which is the better explanation: the universe came by chance or by purpose?

Stuart Hackett

Teleological argument from the "Macroscopic point of view"
From a conspicuous adaptation to an intelligent creator

examples:

1) The fitness of the inorganic material world to be an environment for both the production and maintenance of organic life. Chance is not a sufficient explanation because chance is tied to the consistent make-up of the inorganic material.

2) The internal adaptedness of organic beings, both in their structure of specialized functions and in their general orientation for self-maintenance or subservience to some other form of organic life. Chance is ruled out as a proximate cause. Chance would postal minute, non-advantageous changes.

3) The intelligibility of the world and its instrumentality in the realization of humanly provisioned ends. Chance ruled out because minds are not the logical outcome of our evolutionary process. Minds are so transcendent that they cannot have arisen from matter.

4) The temporal progressiveness of the cosmic progress through levels of matter, life and mind, in an order of increasing valuation significance.

Anthropic Principle

What we can expect to observe must be restricted by the condition necessary for our presence as observers. (Weak Version)

The universe would have had to passed some very tiny probabilities of window in order to be observed. (Strong version)

Generation of Carbon Post- Big Bang

- Needs to combine three helium nuclei
- May not exceed three helium nuclei
- If it becomes four it becomes oxygen and then "boom", nothing is left

The universe seems to have moved in a deliberate direction. Therefore, it seems more plausible that the universe arose from a creator and not from chance.

Ramsey: Qualified Disclosure Models

Ramsey built his religious language out of an empirical setting and tests it by its empirical adequacy.

Disclosure-Commitment Situations

There are two aspects to the kind of experiences that are religious in nature:
1) An empirical situation that evokes discernment
2) A total commitment to what is discerned

The empirical situations that evoke discernment are the experiential grounding for the meaning of religious language.

Discernment situations:

Ramsey holds that metaphors and odd words have the disclosure poor to make the "ice break" or the "light down".

The literary and logical oddity of "I-Religion" or tautologies like "I am I", "Duty for duty's sake" or "love for love's sake" do not render them meaningless.

To Ramsey there is more in empirical language and situations than meets the eye.

Commitment Situations:

Not every disclosure situation provides religious disclosure.

Religious disclosure evokes a total commitment.

Total commitment is a total commitment to the whole universe, not a total commitment to a part of the universe or a partial commitment to the whole universe.

Ramsey holds religious experience to be one in which one responds to a discernment situation with a total commitment.

Religious Language: Qualified Models

Since religious experience in and of itself is odd, religious language will in turn be odd.

The Meaning and Use of Models

A disclosure model does not seek to describe anything. It enables us to articulate what we once could not express.

Language about God is not declarative; it is evocative.

The Qualification of Models

Ramsey calls qualifiers "words which multiply models without end and with subtle changes" (279).

Models and qualifiers create what Wittgenstien calls family resemblances.

Ramsey develops three groups of qualified models:
1) The negative attributes of God - i.e. God is immutable
2) One word positive attributes of God - i.e. perfection
3) Two-word positive attributes of God - i.e. first cause or infinitely good

Ramsey holds the term "God" to be an integrative term, bringing together the separate discernment-commitment disclosures into a unified whole.

The term "God" functions like the term "I" in everyday language.

The Adequacy of Models: Empirical Fit

Models help to articulate theology in a reliable way when:
1) They arise in a moment of insight or disclosure
2) It empirically fits, it is able to incorporate diverse phenomena consistently

Evaluation of Ramsey's View

Ramsey's master model of God, a combination of many individual models, answers the problem of empirically grounded God-talk.

Without an analogy built on the ontological similarity of Creator and creature, God-talk is purely equivocal.

Only metaphysical analogy can save qualified models from equivocation.

Ferré Metaphysical Models

Ferré builds a metaphysical synthesis based on the religious model, which is subject to truth tests.

The Nature and Function of Models

To Ferré, a model y is that "which provides epistemological vividness or immediacy to a theory by offering as an interpretation of the abstract or unfamiliar theory-structure that both fits the logical form of the theory and is well-known" (283).

Models are similar to metaphors in two ways:
1) Their language is literally false
2) They have a point nonetheless

Ferré divides models threefold:
1) Type - the degree of concreteness the model has
2) Scope - degree of inclusiveness the model has
3) Status - how important the model is

Ferré holds there are three functions for models:
1) Suggest point-by-point resemblance
2) Serve heuristic value
3) Fulfill the holistic desire of man to have an explanatory model of his experience

Models in Religions Language

A scientific mode can separate reality and the observer, whereas a theological model cannot

Scientific models are judged on how helpful they are

Theological models must be judged on truth and falsity

Theological models draw upon a different set of facts than scientific models.

Ferré holds the religious imagery of the Scriptures, the creeds, and traditions of the believing community to be a "metaphysical model"

God-Language is not literal, it is anthropomorphic

The theistic model incorporates data from other areas of knowledge, but religious imagery is always the core.

Testing Religious Models

Ferré denies that religious language is purely non cognitive while admitting it serves many non-cognitive functions.

No metaphysical model (world view) should be adopted arbitrarily

There are three strata in one's total account of things:
1) Preverbal metaphysical model of symbol (taken from the imagery of Scripture)
2) Set of propositions that attempt to express this metaphysical model in a cognitive way
3) A range of functions (cognitive and non-cognitive, verbal and nonverbal) that constitute the religious language game.

Only the second strata is applicable to the truth tests

Ferry offers five truth tests for the truth of total synthesis built on religious models:
1) Consistency - it must be non-contradictory
2) Coherence - consistency must be external as well as internal
3) Applicability - masut be relatable to individual experience
4) Adequacy - must be applicable to all domains of feeling and perception
5) Effectiveness - the synthesis must be a useable instrument for coping with the total environment of human experiences

A metaphysical synthesis is adequate (according to Ferré) only if it is capable of putting all experience into a whole, pervasive and adequate pattern.

Ferré notes that nay falsification of a metaphysical position is like an erosion, not an explosion.

Ferré states that:
1) Christianity has been effective in the past, but there is doubt about its effectiveness in the present and future.
2) Few would dispute the applicability of love and reverence. But this is only a minimal test.
3) Adequacy is a complex test involving many levels that Christianity appears to meet fairly well.
4) No clear contradictions have been demonstrated in Christianity but the proposed solutions have not gained universal acceptance.
5) Christianity has a "striking internal coherence" but the external coherence is not as obvious. There are almost certainly some empirical statements in Scripture that are false (i.e. the sun standing still for Joshua)

Evaluation of Ferré's Metaphysical Model

Ferré is not in the univocal camp. No literal descriptions of God, anthropomorphic Bible, etc.

Ferré denied the analogical intrinsic causal connection of the Thomists but his concentration on truth statements suggests he does not mean to make religious language equivocal.

Ferré would need to rethink his stance on analogy to save his theory from equivocation.

Recent Trends Retreating from models

Much of contemporary religious language has been shaped by Hume, the logical positivists and young Wittgenstein

Gill: Mediation and Metaphor

Jerry H. Gill attempts to build a holistic comprehension of humanity and human knowledge, instead of a purely cognitive or empirical basis.

He held that:
1) Religious language is linguistically constituted, we cannot know religious reality apart from it being covered to us in words and concepts
2) Religious language is social activity. Many uses are more important than descriptive.
3) Religious language is meaningful with significant, not absolute precision
4) Religious language is primarily metaphorical

Gill's Proposal Evaluated

Analogy must be grounded in metaphysical reality, but Gill denies this ontological link.

Gill has made a strong analysis of the function of religious language but has forfeited any guard against it being equivocal.

Introduction to Logic: Ch. 7

(Originally written December 11, 2006 in Book 9)

Introduction to Logic
Harry J. Gensler

Chapter 7: Basic Modal Logic

Modal logic studies arguments whose validity depends on 'necessary' and 'possible' notions.

7.1 Translations

1) ◊A = it's possible that A = A is true in some possible world
2) A = It's true that A = A is true in the actual world
3)□A = It's necessary that A = A is true in all possible worlds

"Possible" is weaker then calling something true.

"Necessary" is stronger than calling something true.

Possible means logically possible (not self-contradictory).

Necessary means logically necessary (self-contradictory to deny).

A possible world is a consistent and complete description of how things might have been or might in fact be.

The actual world is the description of how things actually are.

Done' use parentheses with ◊ or □

right: ◊A □A
wrong: ◊(A) □(A) (◊A) (□A)

~◊A = A couldn't be true
□~A = A has to be false

◊(A·B) - it's possible that A and B are true. A is compatible with B.

□(A⊃B) - it's necessary that if A then B. A entails B.

"entails" is a stronger claim then an "if-then"

~◊(A·B) - A is inconsistent with B. It's not possible that A and B are both true.

~□(A⊃B) - A doesn't entail B. It's not necessary that if A then B

(◊A·~◊A) - A is a contingent statement. A is possible and not-A is possible.

(A·◊~A) - A is true but could have been false. A is a contingent truth.

Statements are necessary, impossible or contingent. Truths are only necessary or contingent.

Necessary not = □~
not necessary = ~□
necessary if = □(
if necessary = (□

English sentences can be ambiguous

"If A is true, then its necessary that B" could mean:
1) (A⊃□B) or
2) □(A⊃B)

"If A is true, then it's impossible that B" could mean:
1) (A⊃□~B) or
2) □(A⊃~B)

Inherent necessity: given that the antecedent is true it is necessarily true.

Relative necessity: given that the X is true then the relation between X and Y is true.

Inherent necessity is the "necessity of the consequent". Relative necessity is the "necessity of the consequence"

If A, then B (by itself) is necessary. (A⊃□B)
A entails B. □(A⊃B)
Necessarily, if A then B: □(A⊃B)
It's necessary that if A then B: □(A⊃B)
If A then B is a necessary truth: □(A⊃B)

7.2 Proofs

A world prefix is a string of zero or more instances of "W"

A derived step is now of a line consisting of a world prefix and then "therefore"

An assumption is now a line consisting of a world prefix and 'asm':

Therefore, A (A is true in the actual world)
asm: A (Assume A is true in world W)

WW Therefore, A (A is true in World W)
W asm: A (Assume A is true in world W)

WW therefore, A (A is true in the world WW)

WW asm: A (assume A is ture in world WW)

Reverse squiggle ~□A -> ◊~A
~◊A -> □~A

drop diamond: ◊A -> W therefore, A

drop box - □A -> W therefore, A

Class notes on Modal Logic

(Originally written December 8, 2006 in Book 9)

Class note

Modal Logic

(W⊃T) 'if today is Wednesday then I need to take out the trash
(S⊃F) 'if this figure is a square then it has four sides

The second statement is necessarily true. The first statement is contingently true.

Modal logic acknowledges that some statements are just plain true (they are actual) and that there are necessary truths.

Modal Logic
True - Actual
True - Necessary
True - Possible
False - Actual
False - impossible, necessarily false
False - possible

A statement that is necessarily rue has something in front of the well formed formula.
□(S⊃F)

But a possible truth has something in front of the well formed formula as well
◊(R⊃T)

□ - necessarily so
◊ - possibly so

~□(F⊃S) - It is not necessarily the case that a four-sided object is a square

◊~(F⊃S) - It is possible that a four-sided object is not a square

□ & ◊ are modal operators

True:
Actual - P
Necessary - □P
Possibly - ◊P

False:
Actual - ~P
Not necessarily true - ~□P
Impossible - ~◊P

Problem with modal logic is ◊□P ≡ □P

Modal logic deals with possible worlds.

Possible statements must be true in at least one possible world.

Necessary statements must be true in all possible worlds.

W.V.O. Quine flat out rejected modal logic because it entails essences.

Alvin Plantinga asserts that there are essences and therefore modal logic is a good system.

In modal logic a possible world cannot contradict the essence of the object of the actual world.

Introduction to Logic - Ch. 5b

(Originally written December 6, 2006 in Book 9)

Introduction to Logic
Harry J. Gensler

Chapter 5: Basic Quantificational Logic

Quantificational Logic concerned with arguments whose valid depends on "all", "no", "some", and similar notions.

5.1 Easier Translations

Ir - Romeo is Italian
Ix - x is Italian
(x)Ix - For all x, x is Italian
(∃x)Ix - For some x, x is Italian

Capital letters are used for general terms or categories.

Small letters are used for singular terms or specific things or particulars.

• Single capital letters denote statements = S
• Capital letters followed by a small letter denote a general term = Ir
• Capital letters followed by two or more small letters denote a relation = Lrj
• a small letter can stand as either a constant or a variable

A quantifier is a sequence in the form of either:

1) (x)

2) (∃x)

(x) is a universal quantifier. It claims that the formula that follows is true for all values of x. i.e. 

(x)Ix - for all x, x is Italian (All are Italian)

(∃x) is an existential quantifier. It claims that the formula that follows is true for at least one value of x. i.e.

(∃x)Ix - for some x, x is Italian. (Some are Italian)

English - Quantificational Language

all (every) - (x)

not all (not every) - ~(x)

some - (∃x)

no - ~(∃x)

All A is B - (x)(Ax⊃Bx)

Some A is B - (∃x)(Ax·Bx)

No A is B - ~(∃x)(Ax·Bx)

5.2 Easier Proofs

Reverse squiggle rule

~(x)Fx - (∃x)~Fx

~(∃x)Fx - (x)~Fx

Existential Instantiation 

(∃x)Fx - Fa

The variable 'x' is substituted as the constant 'a'. 'a' is a hypothetical reality.

When there is more than one existential quantifier: i.e.

(∃x)Mx

(∃x)Fx

More than one hypothetical must be used: i.e.

(∃x)Mx - Ma

(∃x)Fx - Fb

Universal Instantiation 

Since (x)Fx states all x is Fx any constant can be instantiated. Thus if a problem looks like this:

(x)Fx - Fa

(x)Rx - Ra

(x)Gx - Ga

(x)Lx - La

Since it is universal it is true (or false) for all.

In doing a proof the order now looks like this:

1. asm: the opposite of the conclusion

2. reverse squiggle

3. existential instantiation 

4. universal instantiation

Logical exercises involving Santa, Eskimos and Scarlet Fever

(Originally written on November 27, 2006 in Book 9)

Quantificational Logic

No Santas are at the North Pole
Some who live at the North Pole are eskimos
Therefore, eskimos are not Santas

Santa - major term
Eskimos - minor term
At the North Pole - Middle Term

[logical argument and proof not worth typing here]

Some Santas are red.
Some red people have scarlet fever
Therefore, some who have scarlet fever are santas.

[another logical argument, proof and refutation that are not worth typing]

An existential statement is true if it is true for at least one constant. It is false if it is false for all constants.

A universal statement is true if it is true for all constants. It is false if it is true for no constants.

Introduction to Logic - Ch. 5

(Originally written November 13, 2006 in Book 9)

x isn't evil -> ~Ex
x is either crazy or evil
(x) (Cx v Ex)
(∃x) (Cx·~(Ex·Lx)
(x) (Lx)

??

"Knowledge is meaningless without love"

Love. Joy. Happy.

Introduction to Logic
Harry Gensler

Chapter 5: Basic Quantificational Logic

Quantificational Logic - studies arguments whose validity depends on 'all', 'no', 'some' and similar words.

Easier Translations

Use capital letters for general terms: descriptive terms or categories. ex:
I - an Italian
C - charming
R - drives a Rolls Royce

Use small letters for singular terms: particulars, individuals. ex.
i - the richest Italian
c - this child
r - Romeo

A capital letter alone represents a statement.

A capital letter followed by a single small letters represents a general term -> Ir

A capital letter followed by two or more lame letters represents a relation -> Lrs

Proofs in Quantificational Logic

1. (x)(Gx⊃Wx)
2. (x)(Px⊃Gx)
Therefore, (x)(Px⊃Wx).

3. asm: ~(x)(Px⊃Wx)

Step 1. Eliminate Negated Qualifiers

4. (∃x)~(Px⊃Wx)
5. ~(Pa⊃Wa) 4 (E.I.)
6. (Ga⊃Wa) 1 (U.I)
7. (Pa⊃Ga) 2 (U.I)
8. Pa 5
9 ~Wa 5
10. Ga 8,7
11. ~Ga 9,6 and 10
12. Therefore (x)(Px⊃Wx)

Step 2. eliminate variables with U.I. and E.I.

U.I. - universal instantiation - if a universal is always true then any thing that is a member of that class will make it true

E.I. - Existential Instantiation - if there are multiple/competing (∃x) statements different variables are used. Since a (∃x) statement means 'some' there can be contradictory statements.

·⊃∃

Brief notes on Quantificational Logic

(Originally written on November 8, 2006 in Book 9)

Class Notes

Test - 11/15/06

S-Proofs
At least:

• 1 single assumption is valid
• 1 single assumption is invalid
• 1 multiple assumption is valid
• 1 multiple assumption is invalid

LogiCola!! due by 11/17/06 Friday!!!

F's & G's

[half a page of nonsense]

First-Order Logic or Quantificational Logic

Functions (Predicates)

Socrates is Mortal = Ms

M- Function (predicate)

S- Socrates

Ms= Socrates has the function of Mortality

Functions (predicates) - Capital Letters

Individual, constant - small letter

Ea - This aardvark eats ants

aardvark - individual

eats - function

Eb - This baboon eats aardvarks

baboon - individual

eats function

An individual or constant is always referring to one specific entity

1) a specific cat

2) a specific litter of cats

~(Ea⊃Uc) -> it is not the case that if this aardvark eats ants then the Colts are undefeated.

Something is rotten in Denmark

R?

There is something such that it is rotten in Denmark

R?

There is some 'x' such that Rx

x- is a variable

x- can be potentially satisfied with various constants

Variables can be fulfilled by various constants

∃ - the quantifier

The quantifier means "at least one"

There is some 'x' such that Rx = (∃x)Rx 

(∃x)Rx is a particular statement or existential statement

(∃x)Sx - something is square 

~(∃x)Sx - nothing is square

~(∃x)~Sx - something is not a square 

The bound variable (the x associated with the above S's) is governed by the quantifier

without the (∃x) or quantifier, the variables are free variables

There must be a quantifier to make a true/false statement 

(x)Cx -> for all of x, C of X

(x) is the universal qualifier

Four Causes of Aristotle and his conception of the soul

(Originally written November 2, 2006 in Book 11)

The Classical Mind
W.T. Jones

Chapter 6 - Aristotle: Metaphysics, Natural Science and Logic

Change

Change is a puzzle because it seems to involve a contradiction.

Aristotle's predecessors wrestled unsuccessfully with the paradox of change. Plato did not solve the puzzle and admitted that it was a mystery.

Aristotle's conception of form and matter made change possible to articulate through reason: form changes, but matter remains consistent.

Development in a systematic change. It is a succession of small changes following a pattern toward a specific end.

Development also solves the problem of the one and the many. The purpose or end of a thing unifies the many (stages of development) into a single thing.

Aristotle's Four Causes

The form is the end of anything. Like Plato, Aristotle believed that understand a form would shed light on a thing. But, for different reasons.

The function of a thing was its 'final cause'. It was a part of a thing's nature, but not the totality of it.

4 Causes:
1. Final Cause
2. Material Cause
3. Formal Cause
4. Efficient Cause

To understand anything, Aristotle claimed we must know four aspects of any individual thing:
1) The material it is composed of (material cause)
2) The motion or action that began it (efficient cause)
3) The function or purpose for which it exists (final cause)
4) The form it actualizes and by which it fulfills its purpose (the formal cause)

Today, scientists are only interested in one of the Aristotelian causes: The efficient cause

Aristotle agreed with Plato that the universe is a relational structure and that every individual thing it can be known only by transcending that thing and seeing its relation to everything else in the universe.

They both agreed that complete knowledge is impossible.

Natural Science

Aristotle called nature that which is sensible. Perceptible objects compose nature.

Nature is not identical with the sensible world.

Artifacts are man-man objects that are not "nature.

Nature - the totality of sensible objects capable of spontaneous change

From Book II of Physics
-Some things exist by nature, other by causes
-Nature consist of things with an innate impulse to change
-"Nature is a source or cause of being moved and being at rest in that to which it belongs primarily" (Jones, 227-228).

Natural science is concerned with the changes of natural objects. Every change is the fulfillment of some potentiality.

Types of changes:
1. Qualitative change (i.e. cold - hot)
2. Quantitative change - increase/decrease in amount
3. Locomotive change - chasing of place
4. Substantial change - substance comes into or passes out of being.

Motion is eternal

Aristotle effectively dealt with arguments that denied the eternality of motion.

Despite claiming the eternality of motion, Aristotle claims there must necessarily be an unmoved mover.

There is a first principle because the is neither an infinite series of motions or an infinite variety of kinds.

The Unmoved Mover

An eternal motion must have an eternal cause.

Original motion must be a change of place. Quantitative change (increase/decrease) involves change of place. Qualitative change also involves a change of place.

An eternal mover will cause an eternal locomotion. This motion must be circular.

The unmoved mover is pure actuality.

The unmoved mover is always thinking and understanding. The unmoved mover thinks of himself. His knowledge is immediate and complete self-consciousness.

The unmoved mover is called 'god' by Aristotle. This does not have any (or very few) religious implications.

There is no divine providence in Aristotle's conception of god.

God is a metaphysical necessity for Aristotle. This god is not an object of worship. It is transcendent and remote.

Astronomy and Physics

Geocentric, the earth is stationary.

The universe is made of concentric spheres.

Each element: fire, air, water and earth has its own natural place and natural motion.

The four elements are the material causes of physical things.

The formal cause of any particular thing is the structure into which its material factor is organized.

Biology - Psychology

Aristotle's Empiricism: Aristotle's empiricism was a correction of the rationalist tendency of the Ancient Greeks.

The Greek neglect of experimentation even in Aristotle is one of the key differences between Modern and Greek science.

Aristotle's psychology was based on biology.

The "psyche" was his word for soul. Psyche is the form of a living object.

Psychology: It's method and scope

What is soul? The body cannot be soul. The soul is the form of the body. Body = actuality; Soul = potentiality.

Powers of soul:
-nutritive
-appetitive
-sensory
-locomotive
-power of thinking

Plants have the nutritive soul. Animals have the nutritive and sensory soul.

Anything with sensory powers must have the appetitive soul. Appetite - desire, passion and wish.

The power of thinking is for man and any other being higher than man.

The Nutritive Psyche:

The Nutritive Psyche makes the potential actual. It is the simplest soul and that which all other psyches are built upon.

The function of the nutritive psyche is to sustain life, to keep the body alive.

The sensitive Psyche:

The sensitive soul is the type of the soul that exists at the animal level.

Sense experience is brought into actuality in perception.

Perception is a dual actualization
1) An actualization of the object as an object of perception
2) An actualization of the sense organ as the preceptor

The sensitive psyche involves something like consciousness

Aristotle distinguishes between:
1) Physiological change
2) Perception

Aristotle is a realist, so the difference between physiological change and perception is purely psychological consideration.

The Rational Psyche

Man has a combined soul of nutritive, sensitive and rational psyches.

Man's perception is different than animals because of the involvement of the rational psyche.

Memory and the nursing of it to the here-and-now experience allows man's cognition to take place. It allows men to recognize universals from particulars.

Thought is rooted in experience for Aristotle.

Thought is the form of forms, as the tool  of tools is the hand.

Thought is divided into two categories:
1. Unanalyzable wholes
2. Prior Synthesis

Logic

Aristotle invented formal logic.

Aristotle distinguished between truth and validity.

Truth is a characteristic of individual propositions.

Validity is the logical relationship between multiple propositions.

A syllogism is two premises and a logically derived conclusion.

Limitations of Aristotle's logic

Aristotle's logic covers a relatively small part of reasoning

Logic class notes 11/1/06

(Originally written November 1, 2006 in Book 9)

Refute me please...

X≡Y
(Y·~Y)
Therefore, (X·~X)

X-God
Y- Man

Jesus Christ?

anyway, enough nonsense... (logical game, not JC)

[Another jumble of letters, numbers and symbols in increasingly worse penmanship]

What is this thing called science? Ch. 4 (B)

(Originally written October 30, 2006 in Book 8)

What is this thing called science? Ch. 4
A. Chalmers

To avoid the problem of induction one can weaken the demand that scientific knowledge be proven true. Instead, scientific knowledge would be probably true.

Thus, under this assumption the principle of induction would be as follows: "if a large number of A's have been observed under a wide variety of conditions, and if all these observed A's have the property B, then all A's probably have the property B" (Chalmers, 51-52).

Unfortunately, this reformulation does not solve the problem of induction, It is still a universal statement; it still relies on a number of particulars producing a universal.

Another major problem faced by the inductivist is that how probable is probably true?

"We are bound to run into trouble if we seek rational justifications of every principle we use, for we cannot provide a rational argument for rational argument itself without assuming what we are arguing for" (Chalmers, 53).

Logic cannot even be argued for in a way that doesn't beg the question a little bit.

The appeal of inductivism

Facts acquired through observation --> Induction --> Laws and theories --> Deduction --> Predictions and explanations

Inductivism does not search for truth of premises in a deductive argument in logic. The source of the premises' truth is in experience.

The general form of all scientific explanation and predictions can be summarized this way:

1. Laws and theories
2. Initial conditions
3. Predictions and explanations

The attraction of inductivism lies in the fact that it seems to capture some of the commonly held intuitions about the special characteristics of scientific knowledge, including:

1. Objectivity
2. Reliability
3. Usefulness

The objectivity of science from the inductivist point of view is derived from the objectivity of observation, induction, and deduction process.

Observation is objective if and only if they are established by an unprejudiced use of the sense in such a way that leaves no room for intrusion by subjective opinion.

Induction and deduction are objective so long as they conform to a publicly formulated set of criterion. If this is done then subjective opinion is again left out of the equation.

"Inferences either conform to the objective standards or they don't" (Chalmers, 57).

The reliability of science in the inductivist point of view comes from inductivism's claims about observation, induction and deduction.

The careful use of the senses can lead to a secure factual basis for science according to the inductivist.

By presuming the principle of induction to be the basis of science, the laws and theories derived inductively from the factual basis of science, the laws and theories derived inductively from the factual basis of science can be held as reliable. (This is the circular problem of inductivism).

Chalmers: At best, inductivism is in dire need of sever qualification. At worst, inductivism is wholly inadequate.

Ben Stein's voice got inside my head in Logic Class

(Originally written October 30, 2006 in Book 9)

Class Notes

[A logical proof consisting of letters, symbols, numbers, and starred lines]

Oh my goodness! I'm actually excited to be here sitting in Logic class because I actually understand it! Woo Hoo (Ben Stein's voice)!

[A three page Multiple Assumption Propositional Proof that I have no intention of ever rewriting]

Introduction to Logic - Ch. 4

(Originally written October 29, 2006 in Book 9)

Introduction to Logic
Harry J. Gensler

Chapter 4: Propositional Proofs

The way to start a proof is to assume the opposite of the conclusion. Then you must attempt to prove a contradiction in the assumption. If a contradiction is found then the argument is valid. If no contradiction is found then the argument is invalid.

More S-Rules and I-Rules...

• A premise is a line consisting of a well formed formula by itself
• An assomption is a line with "asm" in front of it
• A derived step is a line with the "therefore symbol" in front of it
• A formal proof is a vertical sequence of zero or more premises followed by one or more assumptions or derived steps, where each derive step follows from previously unblocked lines by RAA or one of the inference rules, and each assumption is blocked off using RAA
• Two well formed formulas are contradictory if they are exactly alike except that one is negated
• A simple well formed formula is a letter or its negation. All others are complex well formed formulas

[About three pages of logic problems/proofs]

S-Rules, I-Rules and some extended inferences

(Originally written October 29, 2006 in Book 9)

[5 logic problems and answers that may or may not be right]

S-Rules (simplifying)
P·Q --> P, Q
~(P∨Q) --> ~P, ~Q
~(P⊃Q) --> P, ~Q

I-Rules (inferring)

~(P·Q), P --> ~Q
~(P·Q), Q --> ~P
(P∨Q), ~P --> Q
(P∨Q), ~Q --> P
(P⊃Q), P --> Q
(P⊃Q), ~Q --> ~P

[5 more logic problems. Same caveat as above]

Extended inferences

~((C·D)⊃(E⊃F)) --> (C·D), ~(E⊃F)
((X⊃Y)·(F≡R)) --> (X⊃Y), (F≡R)

[5 more logical problems]

What is this thing called science? Ch. 4 (A)

(Originally written October 28, 2006 in Book 8)

What is this thing called Science?
Alan Chalmers

Ch. 4 - Deriving theories from the facts: induction

Introduction

How can scientific knowledge be derived from the facts established (if they can be established by science) by science?

If we take "science is derived from the facts" in a logical and not a temporal sense we can call science: theories derived logically from the facts. (But this strong claim cannot be substantiated.

Baby Logic

Logic is basically concerned with deriving a conclusion from premises.

Valid logical argument:
All A is B
t is A
Therefore, t is B.

Logical validity means that a conclusion is derived from the premises.

Logical deduction does not establish any bit of truth or falsity, even if the argument is valid.

Valid does not equal truth. Invalid does not equal false.

Logic alone is not the source of new truths.

Can Scientific laws be derived from the facts?

Scientific knowledge cannot be derived from the facts if derivation is taken as logical deduction.

Deductive arguments cannot establish scientific laws.

Any number of observed facts cannot create a universal fact through deduction.

Inductive arguments, as opposed to deductive arguments however, can produce scientific laws.

What constitutes a good inductive argument?

Derivation in the statement "science is derived from the facts" must be understood in an inductive sense.

Not all generalization from observable facts warrant an inductive qualification.

If an inductive inference from observable facts to laws is to be justified then some conditions must be satisfied:
1. The number of observations forming any generalization must be large
2. The observations must be repeated under a wide variety of conditions.
3. No accepted observation should conflict with the derived law.

A good inductive argument does not jump to conclusions.

The principle of induction:

"If a large number of A's have been observed under a wide variety of conditions, and if all those A's without exception posses the property B, then all A's have the property B" (Chalmers, 47).

The vagueness of the word "large" is problematic for induction.

What is a variety of conditions? The ambiguity of the second condition of a good inductive argument is problematic.

Inductive arguments also pose an infinite regress problem. If knowledge is based on inductive arguments then those inductive arguments are based on other inductive arguments, etc., etc., etc.

No exceptions (condition 3) is also problematic because there is rarely ever a complete lack of anomalies.

Further problems with inductivism

Inductivism is the school of thought that holds scientific knowledge is derived from observable facts through some form of inductive derivation.

It is not clear what exactly induction entails because of the ambiguity of its criteria.

Science refers to many things that are unobservable (i.e. DNA, electrons, protons, etc.)

If induction is deriving something from observable facts, how can inductivism say anything about unobservable things?

True inductivists would have to reject much of contemporary science if they strictly adhered to the inductivist handbook.

Inductivism faces the problem of induction. How is the principle of induction itself to be justified?
1. Logic?
2. Experience?

Logic is wholly inadequate for inductivism. Inductive inferences are not (by design) subject to deductive logical rules. Hence, inductivism cannot be justified by logic.

If inductivism is to be justified by experience the argument would be as follows:
1. Induction worked in case "X"
2. Induction worked in case "Y"
3. Induction worked in case "Z"
4,5,6...
Therefore, Induction always works.

This is also unacceptable. Inductivism cannot find its justification in logic or experience.

The attempt to justify induction via experience involves assuming what one is trying to prove.

Elephant Tyranny

(Originally written October 27, 2006 in Book 9)

Introduction to Logic
Harry J. Gensler

S-Rules pg. 61

~(I∨~V) = ~I, V
(~O∨~X) = No Conclusion
(F⊃~G) = No Conclusion
~(F⊃M) = F, ~M
(~D·~Z) = ~D, ~Z
(~K∨B) = No Conclusion

I-Rules
~(P·Q)
P
Therefore, ~Q

~(P·Q)
Q
Therefore, ~P

 (P∨Q)
~Q
Therefore, Q

(P∨Q)
~Q
Therefore, P

(P⊃Q)
P
Therefore, Q

(P⊃Q)
~Q
Therefore, ~P

Class Notes (RAA Proofs)

[Editor's note: There are a whole lot of letters and symbols that I simply don't feel like typing. They made little sense to me in 2006 and even less in 2017. The gibberish goes on for two and a half pages until the heading "Trees Method". Under this heading I wrote (A⊃B), (B⊃C), ~(A⊃C) and drew a picture. Here is that picture and hence, the title of this particular post.]

Simple Truth Tables and some Harder Translations

(Originally written October 26, 2006 in Book 9)

Introduction to Logic
Harry J. Gensler

Simple Truth Tables (pg. 38)

Married in nine days! Stress, excitement, exhaustion. My studies have been suffering immensely; I hope to catch up a bit today though.

There are two possible truth values:
True
False

True is represented by '1'.
False is represented by '0'.

A truth table is a logical diagram for a Well-Formed Formula (WFF).

I went to Paris and Quebec = (P · Q)

P  Q  = (P · Q)
0   0      0
0   1      0
1   0      0
1   1      1

(P · Q) can only be true when both 'P' and 'Q' are true, as represented by the '1'.

A conjunction ("·") claims that both are true.

A disjunction claims that at least one is true. ("∨")

An inclusive disjunction = (P∨Q), meaning that at least one is true; but, both can be true.

An exclusive disjunction = (P∨Q)·~(P·Q), meaning that P or Q is true, but not both P and Q are true.

Inclusive Disjunction Truth Table
P  Q  = (P∨Q)
0  0      0
0  1      1
1  0      1
1  1      1

Exclusive Disjunction
P  Q  (P∨Q) = (P∨Q)·~(P·Q)
0  0      0                 0
0  1      1                 1
1  0      1                 1
1  1      1                 0

[There are many more truth tables confirming various propositional logic well formed formulas. I'll simply type the type of propositional well-formed formula and omit the truth table from here on out]

If-then statements are called a conditional.

If P then Q
P- the antecedent
Q- the consequent

The antecedent does not need to be true for the consequent to be true.

≡ is a biconditional.

[5 pages of truth values and truth tables omitted]

Contingent statements are true in some cases and false in others.

A tautology is true in all cases.

A self-contradiction ( P and not-P) is never true.

[1.5 pages of truth tables omitted]

The Truth Table Test (pg. 46)

The truth table test tests the validity of an argument. The argument is valid if and only if no line has all true premises and a false conclusion.

The Truth Assignment Test

PAY ATTENTION! This is why I failed the Logic Test!

"Take a propositional argument. Set each premise to 1 and the conclusion to 0. The argument is Valid if and only if no consistent way of assigning 1 and 0 to the letters will make this work - so we can't make the premises all true and conclusion false" (Gensler, 50).

[...more truth tests]

So the premises are true and the conclusion is false; thus, the argument is invalid.

[...even more truth tests]

The argument is invalid because of a true premise and a false conclusion.

Linehan - I think I get it! :)

[... yet more truth tests, 11.5 pages]

Harder Translations:

• Translate "yet", "however", "although" into "and" (·)
• Translate "unless" into "or" (∨)
• Translate "just if" into "iff" (if and only if) (≡)
• Translate "only if" into "if...then" (⊃)
• A is sufficient for B = If A then B
• A is necessary for B = If not-A then not-B
• A is necessary and sufficient for B = A if and only if B

[half a page of symbols and letters representing some answers to some questions from somewhere]

Introduction to Logic - Ch. 3

(Originally written October 24, 2006 in Book 9)

Well. I did very poorly on my first logic test and I am flunking this class right now. I need to hit this harder and get it. Let's go. Ok, the biggest problem was the Truth-assignment test of basic propositional logic so I'm going to start just prior to that. Let's go back to the beginning of Chapter 3.

Introduction to Logic
Harry J. Gensler

Propositional logic is composed of arguments whose validity is based on 'if-then', 'and', 'or' and 'not' notions.

[The rest of this entry is my notes on how to write in propositional logic language. It's rather dry stuff and I didn't include any pithy anecdotes or self-criticizism]

LogiCola Exercises and my thoughts on them

(Originally written October 8, 2006 in Book 9)

LogiCola Exercises

1. u is t
t is E
no E is P
Therefore, u is not P.
valid

Got it right

2. all C is T
no C is V
therefore, no T is V
invalid

Got it wrong

3. all D is T
therefore all T is D
invalid

Got it right

4. all B is F
some S is not F
therefore, some S is not B
valid

Got it right

5. Some F is C
some C is R
therefore, some F is R
invalid

Got it right

6. all C is M
no M is D
some D is N
therefore, some N is not C
valid

Got it right

7. all D is F
some R is not F
Therefore, some D is not R
valid

Got it wrong

8. some C is not B
therefore some B is not C
valid

Got it wrong

(Editor's note from February 5, 2017. This exercise goes on for another thirteen and a half pages in my composition book and really isn't anything more than just logical exercises, the majority of which I apparently marked myself wrong on. Aside from the logical problems there are two little sentences that I wrote regarding my feelings at the time. They occur on pages 13 (backside) and 23 (backside), respectively in my notebook number 9. These feelings are the only thing worth recording here, but you are more than welcome to go back and see the problems written out if you wish).

"This makes absolutely no sense!" - pg. 13b
"This is absolutely fucking pointless. Logic is the worst class ever." - pg. 23b

Book Notes on Ewing (B)

(Originally written September 12, 2006 in Book 8)

Geometry is likewise necessarily a priori. If it were empirical, then we would have to draw figures for every proof and make a very unscientific and hazardous speculation that the single figure drawn can represent all the figures.

The "a priori" in logic

"The laws of logic must be known a priori or not at all" (Pojman, 386).

A syllogism is an important form of a priori knowledge. It consists of three propositions: two are premises, one is the conclusion.

Other cases of the "A priori"

A priori knowledge is most prevalent in mathematics and logic, although it is not limited to these fields.

Philosophers have been divided into two major classes (rationalists and empiricists) based on their stressing of a priori knowledge.

The possibilities of metaphysics is based on a priori knowledge.

A priori knowledge comes from self-evident truths and truth derived by inferences from self-evident principles.

The Linguistic theory of the "A priori" and the denial that "a priori" propositions or inferences can give new knowledge

Empiricists are not in the business of explaining away a priori propositions as merely empirical generalizations. They have adopted the view that a priori cannot tell us anything new about the real world.

They have decided that a prior is simply clarifying language.

Empiricists often admit that there are a priori analytic truths, but deny a priori synthetic truths.

The proposition "there are no synthetic a priori propositions" cannot be verified by experience. Thus, to justify it would prove that there are synthetic a priori propositions./

Many people have denied synthetic a priori knowledge due to the reduction of Euclidean geometry's axioms to analytic propositions. While this may show that the axioms are not synthetic a priori, it does not show that the steps taken after the axioms are not synthetic a priori.

Empiricists play with language to deny synthetic a priori propositions.

"An a priori proposition cannot fully be understood without being seen to be true" (Pojman, 390).

The existence of a priori judgments must be taken as an ultimate fact. We cannot explain their existence any more than we can explain the existence of man's ability to make empirical judgments.

"Human beings certainly cannot explain everything, whether there is ultimately an explanation for it or not" (Pojman, 390).