Philosophy
“Philosophy has lost all her children”
Physics
Biology
Psychology
Political Science
Economics
Social Sciences
Justice and Law
Logic
Aesthetics
Analysis of the experience of the beautiful or of art.
Metaphysics (Being)
Coined accidentally because it came “after the physics” in Aristotle’s
writings.
Many philosophers have abandoned metaphysics in favor of
epistemology, which is the theory of knowledge.
Metaphysics is concerned with principles, structures and meanings
that underlie all observable reality
Ontology, the major branch of metaphysics, examines the nature of
being and existence.
Cosmology examines origins of universe and the order of things.
Theology is usually included as a part of metaphysics.
Substance(s)
Monism
All things are made of a single substance
Materialism:” there are atoms in the void”. In monistic materialism everything
is reduced to particles in motion, which sometimes collide.
Idealism: There are only ideas, or only minds and ideas, no matter or anything
external to the mind.
Neutral Monism (matter and ideas are manifestations of a third, common
substance which is not reducible to an idea nor matter.)
Pluralism (Dualism)
More than one irreducible substance exists. (e.g. Dualism, which assumes two
substances: mind, and matter; or: spirit and matter)
Problem with dualism: If these substances are irreducible how do they affect
one another, i.e. how do they interact?
Earth, air, fire (i.e. change), water, atoms & void and the Logos. One of the
earliest recorded uses of the word Logos is in the works of the Greek
philosopher Heraclitus about 600 B.C. Our word “logic” is derived from the
Greek word Logos. Heraclitus used the word Logos to refer to the rational
principle of order in the universe. Webster’s New World Dictionary defines
Logos as “Reason, thought of as constituting the controlling principle of the
universe and as being manifested by speech.” The Logos is still thought of as a
substance. In the Gospel According to John the author begins the book with
“In the beginning was the Logos, and the Logos was with God, and the Logos
was God”. The Gospel According to John in the King James Authorized
Version of the Holy Bible translates “Logos” as “the Word”. This is, in part,
what led me to have such a great respect for language and logic. Since I have
learned a bit more about logic I have gained an appreciation of the beauty and
especially the power of logic, language, reason and rationality.
Universals vs. Particulars
Realism: relations (, :: ), concepts, and laws of nature have objective
existence.
Nominalism: relations, concepts and laws of nature exist only in our
brains or only in our minds and have no objective existence.
Cause and effect: how can we be sure such a relation has objective
existence and really holds?
Is there a necessary connection between causes and effects, or are
perceived cause-effect relations accidental? Might a law of cause and
effect someday fail or even be reversed?
Determinism – Theory assuming every event is the result of antecedent
causes.
Indeterminism – Theory assuming some or all events are not caused.
Free-will – in particular, human acts or decisions are not caused.
In either case, determinism or indeterminism, there seems to be a problem with
holding an agent responsible for their acts.
Responsibility under determinism – How can we justify punishing or rewarding,
e.g. criminals if they had no choice, as in the case of determinism where their
actions were caused and they could not have done otherwise?
Responsibility under indeterminism– If free-will holds, then the cause-effect
relation does not hold in the case of human acts, so rewards and punishments
won’t change behavior. In this case human acts are not caused, so they are
random; so, does it make sense to hold people responsible for their acts when
there is nothing we can do that will change them or their behavior in the way we
want?
Functionalist theories of consciousness (and reality)
Computational theory of mind
Mind : body :: software : hardware
Epistemology (Knowledge – justified, true belief)
Deals with problem of skepticism
Pure skepticism seems to me to be untenable. You must believe
something in order to make decisions, for instance you must believe that
the air around you is not poisoned in order to decide to take your next
breath. However, every rational decision we make is determined by our
beliefs, so it seems to be a good idea to test what you believe so you can
be relatively sure that it is true. For this reason it seems to me that
doubt can be a useful tool.
Criteria of belief
Apriori (before sense experience) (rationalism)
Before sensory experience
Rational thought, logically understood without regard to, and possibly before
sensing or experiencing the world outside our self.
Innate ideas
Certain general propositions (called necessary or apriori) are known truths in
the absence of sense data.
An example would be truths of deductive logic, like: if all men are mortal and
Socrates is a man, then Socrates is mortal. Rules of arithmetic and geometry
(and perhaps all mathematics) are apriori.
A posteriori (after sense experience) (empiricism)
After sense experience
Knowledge comes from sense experience
Tabula rasa (blank slate, we are born with no knowledge, no mental structure.
We learn everything we know from our experiences as the world impinges upon
us through our senses.
Consider the problem of the criterion of truth.
Vicious circle: if we use some criterion to test the truth of a belief, then how do
we know that our criterion is true? What criteria do we use to test our criteria?
Science seems to use the combination of the two to determine what is
true.
Theories can be tested for validity a priori.
Experiments can be done to determine if current theory matches the results our
sense experience presents to us.
Deduction vs. Induction
Deductive logic
Start from premises, which are statements previously proven true or else
assumed to be true.
Use rules of inference to argue from premises to the conclusion.
The conclusion of a valid argument is necessarily true if the premises are true.
We say the conclusions of a deductive argument hold the premises “hostage”.
We also say that a deductive argument makes explicit what was implicit in the
premises.
Deductive logic moves from the general to the specific
Inductive logic
Inductive logic is reasoning from the specific to the general. An example is the
following: because there are so many specific instances demonstrating that the
Sun rises in the East about every 24 hours, we inductively generalize to the
statement that the Sun will continue to rise in the East about every 24 hours.
The conclusions arrived at inductively are not guaranteed to be true; the
conclusions arrived at deductively are. The conclusions arrived at inductively
are said to be more or less probable.
Subjectivism vs. Objectivism
That which is objective can exist even though no one perceives it and
even though it is not in anyone’s consciousness.
The existence of that which is subjective depends on a subject which is
perceiving or is conscious of the object or event.
Ethics – Practical philosophy (Good life or Good decisions)
What is happiness?
What is a good life?
Sometimes it is phrased as “what is right?”
Compares & contrasts moral systems
Goal is good acts, based on good decisions or choices.
Deontological vs. Teleological
Deontological (Moral Realism – objective standards or principles of
value or goodness exist.)
Absolutist
Do what rules say to do without regard for consequences.
Categorical imperative: “Act on maxims which can at the same time have for
their object themselves as universal laws of nature” - Immanuel Kant
Authority’s prescription of rules to follow
Teleological - based on consequences.
Must evaluate outcome of decisions
Benefit/Cost Analysis
Subtract the value of the costs of the outcome of a decision from the value of the benefits
of the outcome of a decision to arrive at the value of the outcome of the decision
If the result of the benefit/cost analysis is positive, we might say there is some profit in
acting on this decision, or that there is some positive value associated with the outcome
of acts based on this decision.
Opportunity Cost
This is the value of the best foregone decision.
Assumes resources are limited or scarce.
Given a finite amount of resources, what is the best way to invest those resources? What
decision(s) should be made with respect to the allocation of the scarce resources? This is
a question posed in economics, but might also serve us well here in ethics.
There are mathematical algorithms which give the optimum choice or allocation of
resources. These algorithms require that you set them up with the resource constraints
The above algorithms can be incorporated into a computer program, for instance in
Decision Support Software, to help people make decisions.
Evaluation entails axiology – theory of value. What is the criterion we use to
evaluate or to decide what is true?
Hedonism: maximize pleasure or minimize pain for the individual
Utilitarianism
Maximize pleasure or minimize pain for the greatest number. “The greatest good for the
greatest number”.
Rawlsian criterion of economic justice: the worst off must be made better off than they were
before the decision was acted upon.
In economics, we often let a market function set values.
In a formal language or theory our axioms or basic beliefs determine all the conclusions of
the theory, and so are of supreme value with respect to what we believe is true or false.
Some of my students have suggested that what is true is a personal matter and that truth
may be different for each person, but how can we live together without agreements,
especially without agreements about what is true and what is false?
Theory of Obligation
Should vs. Ought
Duty (to community, self, etc.)
Morals are often normative, approbative, prescriptive
Faculties affecting decisions
Intellect
Appetites
Affections
Emotions
Reason
Will
Periods
Ancient
Thales: attempted an explanation of the world that does not depend on
gods or mythology
Medieval period, also known as the dark ages
Dominated by church in Europe
Focused on Aristotle’s theories as interpreted by St. Thomas Aquinas
Remainder of ancient philosophy science and mathematics were
preserved by Islamic philosophers
Math, Science, Platonism, Pre-Socratics
Ancient philosophers knew world is round, atomic theory, biology, math,
algebra, geometry, etc.
Modern
Breaking free of church restrictions
Free thinkers
Renaissance, humanism, enlightenment
Logic
Sometimes known as a formal system or a formal calculus.
Method used in philosophy to formally classify arguments as good or
bad, valid or invalid.
Logic is formal and can represent or symbolize any other system that
has the same form.
Example: Formal equivalence of thermodynamics and information
theory
Thermodynamics
The physical theory describing order and disorder and transformations of power from heat
into work and vice-versa,
Information theory
The theory concerned with the encoding, decoding, storage and retrieval of information and
with the transmission of a message through a given channel with a given degree of accuracy.
Both theories involve a collection of formulas used to explain, predict and
control the subject phenomena.
It turns out that the formulas of thermodynamics are equivalent to the formulas
of information theory, so one theory is formally equivalent to the other.
This suggests that information and energy (power) are formally equivalent,
because that is what these two formally equivalent theories describe. This gives
new meaning to the phrase “knowledge is power”.
We probably could not have discovered this equivalence without the tool we call
logic.
Meta-logic: system we use to talk about a logical system. It is a
“bigger” system containing the logical system we want to study. It is
bigger because we need extra symbols or letters in the alphabet of
the meta-system in order to be able to refer to the system we are
studying in an unambiguous way.
A logical system with an interpretation is a language
Interpretation: Assignment of meaning or significance to the symbols of
a formal system so that the wff have a meaning or refer to entities other
than themselves and the wff can have a truth value (true or false)
assigned to them.
Syntax: the rules of the grammar of a language
Production rules are recursive replacement rules which determine the set of
productions, starting with the axioms of the system and generating from them,
via the production rules or rules of inference, the sentences that properly belong
to the language. Formal syntax makes no reference to the meaning of the
symbols or to the sense of the expressions of the language
Given a theorem or string of symbols from the alphabet of the system, the string
can be “parsed” using the grammatical rules of the language to” recognize” the
string, i.e. to determine if the string is a proper member of the language.
Semantics: the meaning associated with the formulas of a formal system.
Consistency of a system is necessary
Contradictions
If a statement can be both true and false in the same language or logical system,
that is a contradiction
If a system contains a contradiction, it is inconsistent.
This is undesirable, because from a contradiction absolutely any statement can
be proved to be true without any restrictions on the meaning of the statement.
Axiomatic method
Axioms are statements we assume to be true, or self evident.
Different sets of axioms determine different theories.
Example: Euclidean geometry vs. hyperbolic or spherical geometry. We
use the rules of logic (rules of inference) in all three types of geometry,
but we start with slightly different sets of axioms for each system.
Originally geometry meant the study of the Earth or the study of land or the
studies of the properties of space. Geometry was used to survey real estate
property boundaries after the yearly flooding of the Nile in ancient Egypt, and
for other types of engineering. The pyramids were almost certainly built using
geometry to help design them before expending resources to cut, transport and
lift the heavy stones into place.
In Euclidean geometry, which is done in a 2-Dimensional plane, depends on an
axiom called the parallel postulate. If you are given a line and a point not on
that line, there is a unique line through the given point that is parallel to (i.e.
does not intersect) the given line.
Spherical geometry: In contrast to Euclidean geometry, which is done in the
plane (a flat space) spherical geometry is done on the surface of a sphere.
Think of a globe of the Earth with lines of latitude and longitude. Only great
circles are considered to be straight lines on a sphere. A great circle is a circle
that goes around the surface of the globe and is such that the center of the circle
is the same point as the center of the sphere. On a globe, lines of latitude other
than the equator are not great circles and so would not be considered to be
straight lines because they don’t trace out the shortest path between two points
on the surface of the sphere. There are no parallel lines in spherical geometry
because any two great circles on a sphere must intersect.
In hyperbolic geometry, which is done on a surface called a hyperbolic
paraboloid (which is, roughly speaking, a saddle-shaped surface), there are an
infinite number of lines through a point that are parallel to the given line. This
is in contrast to Euclidean geometry, which assumes only one parallel line, and
spherical geometry, which assumes no parallel lines.
So, the above shows that by including the parallel postulate (or axiom) in his
geometry, Euclid came up with only one type of geometry; when really there are
many possible geometric systems. Which geometry you end up with depends on
your selection of axioms, like the parallel postulate.
Which geometry best represents nature? It turns out that space is not flat, as it
is in Euclidean geometry; space is curved in the vicinity of strong gravitational
fields. Current theory indicates that a non-Euclidean geometry most accurately
represents the natural world we live in. This is counter-intuitive. We usually
think of space as flat; i.e. that straight lines don’t curve. Mathematics and logic,
together with the results of experiments show that our intuition is wrong. While
Euclidean geometry is adequate for measurement locally, if you are measuring a
larger area where the Earth’s curvature affects the measurements, it is more
accurate to use spherical geometry. When measuring on cosmic scales, It seems
hyperbolic geometry is may be the better choice of systems. This is mind-
boggling. How can empty space be curved? It is counter intuitive.
Example: N-dimensional Cartesian spaces or vector spaces
We have been talking about two-dimensional geometries so far, but geometry
can be done in higher dimensions.
A dimension describes a degree of freedom. It also describes how many
numbers are necessary to uniquely specify a point in the space. If you describe
a collection of points, you can describe an object in the space, or the motion of
an object in space. We can describe the relations between objects with a
mathematical function in this space. This allows us to model space, objects and
processes with a language.
Space can be two or three dimensional, which we can understand intuitively. We
can visualize and draw pictures of objects in two and three dimensional spaces;
but can also mathematically describe spaces with more than 3 dimensions. Four
dimensional spaces in Relativity theory has three space dimensions and one time
dimension. There are contemporary theories describing the universe in 10 or 26
dimensions.
We would not be able to visualize these higher dimensional spaces without the
language of science. These languages serve as a tool, metaphorically like a
telescope or a microscope which allow us to see and manipulate things we
otherwise would be unaware of.
We would not have the ability to make such precise and accurate predictions
about our world without science.
We would not have the fine detailed control over our circumstances that we do
without mathematics and science, and so would not have the ability to thrive that
science provides us.
Other examples where assumptions were made or “fictions” or
hypothetical constructs were used to explain predict and control nature.
Aristotle’s theory explaining how and why objects fall.
Galileo started observing, measuring and finding formulas and geometric explanations of
what he observed, which gave his contemporaries the ability to predict and control parts of
nature.
Newton came up with assumptions (think: axioms) which, along with the rules
of mathematics that he also extended, allowed him to explain gravity and other
observed phenomena.
Einstein changed Newton’s assumptions to come up with a theory that explains
more than Newton’s does, and explains the same things Newton’s theory does,
but with greater accuracy. We sometimes think of Newton’s theory as a “special
case” of Einstein’s theory which is valid under special circumstances, but
becomes inaccurate at speeds approach the speed of light or there are strong
gravitational fields affecting observations.
Einstein also eliminated a hypothetical construct called the luminiferous ether
which was assumed to be a medium through which light waves propagated.
Phlogiston was a hypothetical construct (assumed substance) that was used to
explain why combustion dies out. This was accepted until the discovery of
oxygen.
Caloric was assumed to be a fluid substance that was used to explain heat and
heat transfer until Brownian motion, conduction, convection and radiation were
discovered and postulated.
Wff (well formed formulas) are theorems in a given logical system (i.e.
language) which conforms to the rules of the grammar. That is to say,
they are strings in the language that have been generated by using
the inference rules. We have to have some strings or sentences to
start with, so we postulate statements or strings that we call
“axioms”, which we hope are self-evident. The axioms (e.g. the
parallel postulate) serve as a foundation for the rest of the system.
We use the inference rules of the system (or the rules of the grammar
if you think of the system as a language) to derive new formulas from
the axioms. Then we use the inference rules on the derived formulas
until the resulting wff has been reached by a step-by-step
unambiguous process that is deterministic and almost mechanical.
The advantage of this is that even a machine can understand it, and
the conclusions are guaranteed to be true if the axioms are “true”
and formulas were derived strictly by proper use of the inference
rules.
The (in)-completeness of logistic systems is an issue.
A system is complete if every true theorem can be proved from within
that system.
In any logical system rich enough to contain arithmetic, there are
theorems that are true but are not provable from within that system, so
such a system is incomplete.
For any such incomplete system, a meta-system can be constructed
which contains the original system. The un-provable statements within
the original system can be proved within the meta-system.
But now the “bigger” meta-system is a system rich enough to contain
arithmetic, so there are theorems in this system which require a
“bigger” system to prove, and so on ad infinitum.