Lambert, Karel and Gordon G. Brittan, Jr. An Introduction to the Philosophy of Science. Ridgeview Publishing Company, 1992. (This is a general introduction to the topics and ideas which we will cover.)
Zucker, Arthur. Introduction to the Philosophy of Science. Prentice Hall, 1996. (This is a reader containing many of the most important and/or stimulating readings in the field as well as important historical background and introduction to conte mporary issues.)
Kuhn, Thomas. The Structure of Scientific Revolutions. University of Chicago Press, 1962. (This is one of the most influential, or at least widely-quoted, books ever written in the field. We will use it as a case-study of one particular perspective on the philosophy of science. It also constitutes an excellent, if limited, source of the historical information involved in an understanding of science.)
Boyd, Richard, “Confirmation, Semantics, and the Interpretation of Scientific Theories,” in The Philosophy of Science, Richard Boyd, Philip Gaspar, and J.D. Trout (eds.), pp. 3-20.
Davidson, Donald, “Actions, Reasons, Causes.” The Journal of Philosophy, Volume LX, Number 23, pp. 685-701.
Feyerabend, Paul, “Problems of Empiricism,” in Beyond the Edge of Certainty, R. Colodny (ed.), pp. 145-218.
Friedman, Michael, “Explanation and Scientific Understanding.” The Journal of Philosophy, Volume LXXI, Number 1, pp. 5-19.
Glymour, Clark, “Relevant Evidence,” in Readings in the Philosophy of Science, Baruch A. Brody and Richard E. Grandy (eds.), pp. 328-343.
Hacking, Ian, “Do We See Through a Microscope?” in Readings in the Philosophy of Science, Baruch A. Brody and Richard E. Grandy (eds.), pp. 29-43.
Hempel, Carl. The Philosophy of Natural Science, chapter 3.
Hume, David, The Problem of Induction, from An Enquiry Concerning Human Understanding, in Classical Philosophical Questions by James A. Gould, pp. 320-330.
Maxwell, Grover, “The Ontological Status of Theoretical Entities.” in Readings in the Philosophy of Science, Baruch A. Brody and Richard E. Grandy (eds.), pp. 21-28.
Popper, Karl. The Logic of Scientific Discovery, selections, in The Philosophy of Science, Richard Boyd, Philip Gaspar, and J.D. Trout (eds.), pp. 99-119.
Putnam, Hillary, “The ‘Corroboration’ of Theories,” in The Philosophy of Science, Richard Boyd, Philip Gaspar, and J.D. Trout (eds.), pp. 121-137.
Salmon, Wesley, “Why ask Why? An Inquiry Concerning Scientific Explanation,” Proceedings and Addresses of the American Philosophical Association, 51: pp. 683-705.
Taylor, Richard, “Reality Consists of Matter,” in Classical Philosophical Questions by James A. Gould, pp. 349-363.
In brief, the criteria used to grade your papers will be these:
Papers must demonstrate a clear understanding of the course material (either that which has been specifically covered in class or drawn from independent reading of the required or recommended texts), and so, to that end, they must contain summaries of that material. There is enough material in the required and recommended readings to provide adequate cover of the topics. Thus you are neither required nor expected to use external sources, although you are certainly free to do so if you find it improves your paper. Thus your bibliography need contain no more than reference to the required texts by Lambert and Brittan and by Zucker, although references to the recommended reading on reserve is considered an improvement, and you may refer to other sources if you wish.
In order to reach a high standard papers should not be summaries only. Argument-- the combination of propositions and data in support of a conclusion--is the main tool of philosophy as well as science. Arguments can be either negative or positive, either in support of a chosen position or directed against a position, which is held to be incorrect or inadequate. You can support your own position by attacking alternative positions or by demonstrating the coherence and utility or other advantages of your position. You can attack a position by demonstrating its inadequacy, its self-contradiction, or by questioning either the truth of the premises it assumes or the structure of the argument used in its support. In order to construct such an argument, however, your own views are as essential as knowledge of your subject material.
The standard of your technical writing as well as your accuracy and argument will be taken into consideration. To assist with that end, here is a short list of common errors in writing.
attendance: possible 60 60 papers: 4 @ 30 120 midterm examination: 1 @ 70 70 Final examination: 1 @ 90 90 discussion: possible 60 60 TOTAL 400
“No number of confirming instances, no matter how great, can show that a universal generalization is true. Confirmation is inevitably indecisive. Yet a single disconfirming instance will show, in a deductively correct way, that the generalization is false. [So] to test a hypothesis is to try to find ways it might be falsified [not to find ways that it might be confirmed].” (Karel Lambert, An Introduction to the Philosophy of Science, 53.)
“the misleading distinction between theories and facts is replaced by a clear distinction between theoretical and observational sentences. The distinction between theories and facts is misleading necause it suggests that “theories” are not well-established and “facts” are. But as scientists use the word, calling a set of explanatory principles a “theory” has nothing to do with the degree to which they have been established. Some theories are very well established . . . others are not. . . . . . . any genuine scientific theory must have empirical significance and that empirical significance is gained only if a theory has testable consequences. Theories make assertions . . .about the way the world is. If these assertions are empirically significant, it must be possible to confirm or disconfirm them.” (Karel Lambert, An Introduction to the Philosophy of Science, 90, 94.)
“The sharp distinction between theoretical and observational terms . . . has been challenged on several different grounds. . . . when one presses the distinction, or tries to formulate a criterion on the basis of which to decide individual cases, one quickly runs into trouble. Is “temperature,” for instance, an observational or a theoretical term? . . . many theoretical terms . . . seem to be just as clearly observational. . . “Cell,” “charge,” and “stimulus” are examples. . . . there are in fact no observational data apart from particular “theories of observation,” sets of rules forming part of all scientific activity that tell us how to “read the data.” . . . A simple example is the apparent passage of the sun from east to west. Copernicus’ theory tells us that this is not really something we observe; what we think we see is merely illusion, to be corrected or eplained by the hypothesis that we ourselves are in motion.” (Karel Lambert, An Introduction to the Philosophy of Science, 96-7.)
“Rather than positing some goal at which all scientific activity aims or some final theory which is being more amd more closely approximated with the passage of time, the evolutionary approach sees the history of science as a series of adaptations to environmental pressures” (Lambert, 126).
“From the fact of the theory-dependence of scientific
methods and the alledged phenomenon of incommensurability . . . Kuhn and
other constructivists have drawn some striking philosophical conclusions:
"First, the pattern of theory dependence
of methods . . . precludes any account of science according to which scientists
achieve objective knowledge about a single, theory-independent world. Realism
cannot be defended. Second, the depth of the theory dependence of methods
similarly precludes any empiricist rational reconstruction: scientists
must be understood as engaged in a metaphysical project whose very rules
are irretrievably determined by theoretical conceptions regarding largely
unobservable phenomena.
“. . . the fundamental theoretical
principles that scientists accept, and the fundamental methodological principles
that those theoretical principles largely determine, are imposed on the
world by a sort of convention or social construction. But knowledge of
these principles is not to be understood as merely or trivially conventional;
instead scientific theories really do embody knowledge of unobservable
causal mechanisms, subatomic particles, etc. Socially constructed causal
and metaphysical phenomena are, according to the constructivist, real:
they are as real as anything scientists can study ever gets.” (Richard
Boyd, “Confirmation, Semantics, and the Interpretation of Scientific Theories,”
in The Philosophy of Science, Boyd, Gaspar, and Trout, (eds.) 12-13)
“Is sensory experience fixed and neutral? Are theories simply man-made interpretations of given data? The epistemological viewpoint that has most oftern guided Western philosophy for three centuries dicates an immediate and unequivocal, Yes! In the abs ence of a developed alternative, I fnd it impossible to relinquish entirely that viewpoint. Yet it no longer functions effectively, and the attempts to make it do so through the introduction of a neutral language of observation now seem to me hopeless” ( Kuhn, The Structure of Scientific Revolutions, 126).
“to explain an event or state-of-affairs scientifically is to give a correct argument, deductive or inductive, for that event. At least one of the premises of the argument must be a scientific law.” (The classical theory of scientific explanation. Eg. Carl Hempel and Oppenheim, in Lambert, 15 and in Zucker, 75-95)
Normal science means “research firmly based on one or more past scientific achievements, achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice.” (Thomas Kuhn, The Structure o f Scientific Revolutions, 10.)
“to explain all natural phenomena in terms of the properties of their least parts has been a goal of science for a very long time” (Lambert, 158)
“The scientist must . . . be concerned to understand the world and to extent the precision and scope with which it has been ordered” (Kuhn, 42).
“Science . . . is simply the most systematic and reliable way of supporting beliefs with evidence. Science commands our respect because scientific claims, as a matter of method, must be well-grounded. And this well groundedness results, in the final analysis, from the application of logic and the carrying out of experiments’ (Lambert, 123).
“According to some positivistic philosophers what science does is best seen as taking ordinary experience, subjecting it to some form of measurement so that a scale is created, then finding numerical relationships within that scale and between that scale and others” (Zucker, 54).
Vocabulary.
(The following is a list of some of the uncommon words or uses of
words encountered in the philosophy of science. Remember that these words
might have alternative, possibly more common, meanings in other contexts.)
a posteriori adj requiring empirical evidence for confirmation or falsification.
a priori adj logically verifiable without reference to empirical evidence.
ad hoc adj literally "to this." An hypothesis is ad hoc if it is improvised for the specific purpose of accounting for an existing piece of empirical evidence.
analysis n [fr. Gk analyein to break up] 1: separation of a whole into its component parts 2: examination of a complex, its elements and their relations 3: identification or separation of ingredients of a substance 4: a method in philosophy of resolving complex expressions into simpler or more basic ones.
analytic adj a statement is analytic if it is true simply by virtue of the meaning of its constituent words.
anomaly n 1: a deviation from the common rule 2: something different, abnormal, peculiar, or not easily classified 3: something not predicated by the accepted theory.
argument n a connected series of statements one of which (called the conclusion) is said to follow from the others (the premisses).
axiom n a proposition presumed true by a theory or system of logic, from which all other propositions which the system or theory endorses are deducible. See theorem.
behaviorism n a school of psychology which takes the objective evidence of behavior (as measured responses to stimuli) as the only concern of its researches and the only basis of its theory without reference to intentional explanations (reductionistic behaviorism)
contingent adj not logically necessary, a contingent proposition could be either true or false.
deductive adj a deductive argument is one in which, if the premisses are true, the conclusion must necessarily be true.
determinism n the theory that all acts of the will, occurrences of nature, social or psychological phenomena are causally determined by preceding events or natural laws. In a deterministic system the state of the system at any one time completely and invariable determines its state at all other times.
emergent adj a property of a complex system is said to be emergent when it arises out of simpler constituent properties or relations of the system, but is not predicatable from, nor reducible to those properties or relations.
empirical adj 1: relying on experience or observation alone without regard for system and theory 2: capable of being verified or falsified by experience or observation.
entelechy n [fr. Gk. telos end or goal] 1: the actualization of a cause as opposed to its potentiality 2: a hypothetical agency not demonstrable by scientific means that is sometimes considered as an inherent regulating and directing force in the developing and functioning of a living organism.
explain vb [fr. L explanere to make level] 1 a: to make known b: to make plain or understandable 2: to give the reason for or cause of 3: to show the logical development or relationships of.
falsificationism n the belief that a theory is potentially a scientific theory if and only if there are possible observations that would falsify it.
hypothesis n 1: a tentative assumption made in order to test its logical or empirical consequences 2: the antecedent clause of a conditional statement (in the conditional statement; if X then Y, X is the antecedent and Y is the consequent).
inductive adj and inductive argument is one which increases the probability of the truth of its conclusion but does not establish that truth as necessary.
inference n 1: the act of passing from one proposition or statement considered true to another whose truth is believed to follow from that of the former 2: a proposition arrived at by inference.
instrumentalism/instrumentality n the theory that theoretical scientific entities are not so much real or true as useful. Such entities are instruments of calculation.
intuition n [fr. L. intuere to look at] 1 a: immediate apprehension or cognition b: some knowledge or conviction gained by intuition c: the power or faculty of attaining to direct knowledge or cognition without evident rational thought or inference.
knowledge empiricism n the position which holds that evidence for or against a synthetic statement is provided solely by observations which confirm the truth or falsity of observational predictions deduced from it.
litmus paper n paper colored with a substance derived from lichens that turns red in acid solutions and blue in alkaline solutions.
logic n [fr. Gk. logos word, organization, arrangement fr. legein to arrange] 1 a: the science of the formal principles of reasoning b: the science of valid inference.
logical positivism n a 20th century philosophy which holds to verificationalism and knowledge empiricism. See these entries.
materialism n 1: the theory that physical matter is the fundamental or only reality 2: in philosophy the theory that the person is identical with the body.
mechanism n a doctrine that holds natural processes to be mechanically determined and capable of complete explanation by the laws of physics and chemistry. adj mechanistic
metaphysics n [fr. Gk. meta and physika beyond or after the physical] 1 a: a division of philosophy that is concerned with the fundamental nature of reality and being and that includes ontology, cosmology and often epistemology b: abstract philosophical studies: a study of what is outside objective experiece.
model n a model is a representation of a physical system such that certain relational properties of the system are preserved in the representation so that the model is structurally similar or isomorphic to the system.
objective adj 1 a: relating to or existing as an object in the realm of sensible experience independent of individual thought and being perceptible to all observers b: having reality independent of the mind
paradigm n 1: an outstandingly clear or typical example or archetype 2: as used by Thomas Kuhn in The Structure of Scientific Revolutions—an unquestioned theory or set of beliefs. These paradigms are adopted and rejected during scientific "revolutions" without strictly logical reasons.
phenomenon n [fr. Gk. phainesthai to appear] 1 a: an observable fact or event b: an object or aspect known through the senses rather than by thought or non-sensory intuition. (hence phenomenal adj. The plural is phenomena)
point mass n a purely ideal or theoretical entity: a dimensionless mass, a material point having mass but no extension in space.
pragmatic adj relating to matters of fact or practical affairs.
prima facie adj self-evident or obviously valid from its own apearance.
quaternions n 1 a: the quotient of two vectors,
or the operator which changes one vector into another, so called as depending
on four geometrical elements and capable of being expressed by the quadrinomial
formula
w + xi + yj + zk, in which w, x, y, z are scalars and
i, j, k aremutually perpendicular vectors whose squares are -1 b:
that form of the calculus of vectors in which this operator is employed
invented by Sir W. R. Hamilton in 1843.
reason n a 1: sufficient ground of explanation or of logical defense esp. something that supports a conclusion or explains a fact 2 a: the power of comprehending, inferring, or thinking esp. in orderly ways b: the proper excercise of the mind c: the sum of the intellectual powers.
reduction n one theory is said to be "reduced" to another when the theoretical principles of the first theory can be deduced from those of the second.
relativism n relativism can be epistemological, ethical, cultural, or linguistic, etc. Generally, it is the claim that what is true, right, important, or meaningful etc. is always and only true, right, etc. for some individual or society. Thus nothing is "absolutely" or "objectively" true etc. In its most extreme and unlikely form relativism holds that there is no uninterpreted, objective, independent reality. Most relativists seem to hold that "objective" reality is simply inaccessible to humanity: any comprehensible or communicable truth or value must be expressed from within a given culture and finds its precise meaning from its situation in that culture.
semantics n The general study of the interpretation of signs, the specific area of the study of language concerned with the meaning or content of linguistic expressions and their relation to nonlinguistic reality.
specific gravity n 1: the ratio of the density of a substance to the density of some other substance taken as a standard (eg. pure water, hydrogen) 2: synonymous with density.
stochastic adj any process that is not deterministic but probabilistic, eg. genetic inheritance. In a stochastic system the state at any one time determines no more than the probability of various states at other times.
subjective adj 1 a: relating to or determined by the mind as the subject of experience b: characteristic of or belonging to reality as perceived rather than as independent of mind 2 a: peculiar to a particular individual b: arising from conditions within the brain or sense organs rather than being caused by external stimuli 3: lacking in reality or substance.
synthetic adj a statement is synthetic if neither it nor its denial are analytic.
tautology n 1: a statement which is true by virtue of its logical form alone, a compound proposition which is true no matter what the truth values of its component propositions 2: a redundant or unnecessarily repetative statement.
teleological adj [fr. Gk. telos end or goal] teleological explanations attempt to account for things by appeal to their contribution to the atttainment of goals. The teleological argument appeals to those aspects of reality which appear to be designed or purposive as being analogous to cases of human design and presupposing an intelligent designer or creator with a purposeful end [telos] in mind.
theorem n 1: a formula, proposition, or statement in mathematics or logic deduced from axioms 2: an idea accepted or proposed as a demonstrable truth often as part of a general theory.
theory n [fr. Gk. theorein to look at, cf. theatre] 1: the analysis of a set of facts in their relation to one another 2: abstract thought: SPECULATION 3: a belief, policy or procedure proposed or followed as the basis of action 4: a plausible or accepted general principle of body of principles offered to explain phenomena.
verification n conclusively showing a claim to be true.
verificationalism n a theory of meaning according to which
all meaningful statements are either analytic or empirically verifiable.
Laws, Principles, and Theorems.
(The following are some of the laws, etc. which will be encountered and which should be understood in the philosophy of science.)
Bayes Theorem:
Bernoulli’s principle: when a fluid flows through a pipe of varying diameter, the ampount of energy per kilogram of liquid does not change. That is, pressure is lowest when the velocity of the flow is greatest and flow is slowest through the widest parts and fastest through the thinnest parts of the tube.
Boyle-Charles Law: (a.k.a. the ideal or classical gas law)
Boyle’s Law: At a given temperature (T)the volume occupied by a gas is inversely proportional to the pressure, or at a constant temperature the pressure (p) of a fixed mass of gas is inversely proportional to its volume (V).
Charles Law: the volume occupied by a given mass of gas at a constant pressure is directly proportional to the absolute temperature. That is, the volume increases by a constant fraction of the volume for each degree rise in temperature. So:
Dalton’s Law:
1. The Law of multiple proportions:
when two elements A and B conbine to form more than one compound, the weights of B that combine with a fixed weight of A are small whole-number ratios. For example, Carbon and oxygen can for two compounds—carbon monoxide (CO) and carbon dioxide (CO2). The former has a carbon to oxygen ratio of 1:1, the latter a ratio of 1:2.
2. Dalton’s Atomic theory: all elements are composed of atoms, all atoms of the same element are identical, atoms can be neither created nor destroyed, atoms combine to form compound atoms (molecules) in whole-number ratios.
Galileo’s law: the velocity of a falling body (discounting air resistance) can be calculated from a constant acceleration (usually given as 32 feet per-second-per-second) and the distance an object will fall is half the acceleration of the falling body multiplied by the square of the time it has fallen. Where d is the distance fallen, t is the time, v is the velocity, and g is the constant acceleration:
Kepler’s Laws of Planetary Motion:
First Law (law of elliptic orbits): each planet moves about the sun in an ellipse with the sun at one of the two foci of the ellipse.
Second Law (law of areas): an imaginary straight line joining a planet to the sun sweeps out equal areas of the ellise in equal intervals of time.
Third Law (harmonic law): the square of the period of revolution of a planet is in direct proportion to the cube of the average distance from the sun.
Mendel’s Laws:
1. The Law of Segregation:
Genes exist in pairs in individuals. In the formation of gametes (eggs or sperm), each gene separates (segregates) from the other member of the pair, passing into a different gamete. Thus each gamete has only one of each kind of gene. Which kind of gene it gets is determined by chance alone.
2. The Law of Independent Assortment:
The distribution of one pair of genes into gametes is independent from the distribution of any other pair of genes.
Rr + rR ® Rr Ú RR Ú rr Ú rR
Newton’s Laws:
First Law (law of inertia): a body at rest will remain at rest unless acted upon by an external force; a body in motion will remain in motion unless acted upon by an external force.
Second Law (law of constant acceleration): acceleration (the rate of change of velocity with respect to time) is proportional to the force acting on a body and inversly proportional to the mass of the body. It occurs in the same direction as the force.
The universal law of gravitation (the inverse square law): every body attracts every other body with a force proportional to the masses of the bodies and inversely proportional to the square of the distance between them.
or I = 
The index of refration of light in a vacuum is defined as = 1. In any other medium it is defined as the velocity of light in a vacuum divided by the velocity of light in the medium. The index of refration of light in air is very close to 1. In water it is 1.33. That is to say that light travels faster in air (almost as fast as in a vacuum) and slower in water.
Symbols needed in Introductory Philosophy of Science.
| Symbol used in class | Symbol used in Lambert | Name of symbol in class | Name of symbol in Lambert | Corresponding Verbal expressions |
| S É R | S Þ R | implication | consequence | S implies R.
R is a consequence of S. S has R as a consequence. If S then R. R given S. S only if R. S is a sufficient condition for R. R is a necessary condition for S. |
| S º R | S Û R | equivalence | equivalence | S is equivalent to R.
R is equivalent to S. S if and only if R. R if and only if S. |
| X £ Y | X £ Y | X is not more than Y.
X is less than or equal to Y. |
||
| X ³ Y | X ³ Y | X is not less than Y.
X is greater than or equal to Y. |
||
| S Ú R | S Ú R | disjunction | S or R.
Either S or R. S unless R. Note that all these can be reversed. |
|
| ~S | ~S | negation | not S It is not the case that S |
|
| S < R | S < R | S is less than R. | ||
| S > R | S > R | S is greater than R. | ||
| P(S) | P(S) | The probability of S. | ||
| P(H|E) | P(H| E) | The probability of H given E. | ||
| ¥ | ¥ | infinity | infinity | |
| H· E | H· E | conjunction | H and E
the conjunction of H and E both H and E H but E |
Probability Theory (Logical Probability)
According to certain ways of thinking new evidence for a particular hypothesis is held to confirm that hypothesis if that evidence raises the probability of the hypothesis. That is, if the probability of the hypothesis given the evidence is greater than the probability of the hypothesis alone. But what constitutes good evidence? What degree of increased probability is effected by what kind of evidence? Obviously some means are needed to calculate such probabilities.
Axioms Defining Probability.
Axiom #1: The probability of S, where S is any given statement or complex statement, is not less than zero; that is:
P(S) ³ 0
Axiom #2: Given that S is a tautological statement, that is, a statement which is true no matter what the truth values of its component statements, then:
P(S) = 1
Axiom #3: Given that S and R are mutually exclusive, that is the statement (S · R) is a self-contradictory statement, and the statement (S · ~R) is a tautology, then:
P(S Ú R) = P(S) + P(R)
Axiom #4: Conditional Probability: Where P(H| E) is the probability of the hypothesis H given the evidence E and given that P(E) ¹ 0. [because n/0 = ¥ ]
That is to say (given that the probability of E does not equal zero), the probability of hypothesis H, on the evidence E, is equal to the probability of the conjunction of hypothesis and evidence, divided by the probability of the evidence.
For example; the probability of drawing a jack of hearts from a deck of 52 cards is 1:52. The probability of drawing a heart is 1:4. The probability of drawing a jack, given that the card is a heart is the probability of drawing a jack of hearts (i.e. a card which is a jack and a heart) divided by the probability of drawing a heart. That is:
or 
So the probability of drawing a jack, given that you draw a heart, is 1:13.
Theorems deriving from the above axioms.
Negation Theorem: P(~S) = 1 - P(S)
(S · ~S) is a self-contradictory statement, so by (3) above, P(S Ú ~S) = P(S) + P(~S).
But (S Ú ~S) is tautological, it must be true, so by (2) above, P(S Ú ~S) = 1.
So P(S) + P(~S) = 1.
By substitution, P(S) = 1 - P(~S) and P(~S) = 1 - P(S)
Upper Limit Theorem: P(S) £ 1
P(S) ³ 0 [by (1) above]
P(~S) ³ 0 [by (1) above]
P(S Ú ~S) = 1 [by (2) above, tautology]
P(S) + P(~S) = 1 [by (3) above, mutually exclusive]
So P(S) £ 1
[if either S or ~S were greater than 1 and neither S nor ~S are less than zero, then their sum would be greater than 1]
Logical Consequence (implication) Theorem: (S É R) É [P(S) £ P(R)]
(Let S represent the statement "Buddy Holly died in a plane crash.")
(Let R represent the statement "Buddy Holly is dead.")
1: S É R.
2: That is, S and ~R are mutually exclusive, so the statement (S · ~R) is self-contradictory.
3: So P(S Ú ~R) = P(S) + P(~R) [by (axiom #3)].
4: P(S Ú ~R) = P(S) + 1 - P(R) [by negation, P(~R) = 1 - P(R), so we can substitute 1 - P(R) for P(~R) in 3: above].
5: But P(S Ú ~R) £ 1 [by upper limit].
6: So P(S) + 1 - P(R) £ 1 [by 4: and 5: above]
7: So P(S) £ P(R) [if P(S) were greater than P(R) then P(S) + 1 - P(R) > 1, but by 6: this is not the case]
Logical Equivalence Theorem: (S º R) É [P(S) = P(R)]
1: S É R
2: So P(S) £ P(R) [by logical consequence]
3: R É S
4: So P(R) £ P(S) [by logical consequence]
5: So P(S) = P(R) [by simple arithmetic]
Bayes Theorem:
Employing the above axioms and theorems Thomas Bayes (1702-1761) proved a theorem which allows us to calculate the adjusted probability of a hypothesis in the light of new evidence which has been predicted by that hypothesis.
Proof:
1: P(H| E) = P(H · E)¸ P(E) [Axiom #4]
2: P(H · E) = P(H| E) x P(E) [from 1: mutiplied by P(E) throughout]
3: P(E · H) = P(E| H) x P(H) [replacing H by E throughout]
4: P(H| E) x P(E) = P(E| H x P(H) [by logical equivalence P(H · E) = P(E · H)]
5: So P(H| E) = [P(E| H) x P(H)]¸ P(E) [dividing throughout by P(E)]
That is to say that the probability of a certain hypothesis, given a certain piece of evidence (the posterior probability), is the product of the prior probability of the hypothesis, P(H), and the probability of the new evidence given the hypothesis, P(E| H), divided by the probability of the evidence.
(Note that H and E themselves have no numerical value, only P(H) etc.)
Alternative more sophisticated version:
Where K is introduced as our background knowledge.
Obviously in either version, P(H| E· K) will increase the lower P(E| K) and the higher P(H| K). That is to say that the probability of the hypothesis, given the evidence will increase more the lower the probability of the evidence. This accords well with our intuitive understanding of strict scientific testing of a hypothesis. If that hypothesis predicts some unlikely event and that event indeed comes to pass, the more unexpected the event, the more the hypothesis is held to be confirmed by it.
| Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 |
The class will meet 12:30pm until 2:00 Tuesday, and Thursday
in Patterson Hall 113.
Office Hours will be Monday, Wednesday, and Friday
9:15 – 10:15; Tuesday and Thursday 9:00 – 11:00; and by appointment
Week 1. (Required reading: Lambert chapters 1 &
2, Zucker chapters 1 & 2)
Tuesday. 8/31
Introduction to the field, the class, the texts, and
the class webpage.
Thursday. 9/2
Scientific Explanation: The classical account of explanation; Explanation
and prediction; Rivals to the classical theory: the causal-statistical account
of explanation.
Week 2.
Tuesday. 9/7
Rival theories continued: the Pragmatic account of
explanation; Explanation and Laws; the question of intentional explanations.
Thursday. 9/9
Explanation as metaphor and model. Discussion on a topic
from Zucker Chapter 1 - case studies.
Thursday. 9/16
Discussion led by group #1. “What is scientific explanation?”
Thursday. 9/23
Corroboration, continued: “positive instances” and
probability theory, “Bootstrap theories” and the problem of relevance.
Thursday. 9/30
Discussion led by group #2. “How are Scientific Hypotheses Supported?
Verification, Confirmation, Corroboration, and Falsification.”
Thursday. 10/7
Scientific Theories: the semantic account and scientific
realism.
Thursday. 10/21
Realism, determinism and reduction. Science and values.
Discussion in preparation for the midterm.
Thursday. 10/28
Discussion led by group #1. “What are the Limits of Science?”
Thursday. 11/4
Crisis in science: revolution as the resolution of
incommensurable worldviews?
Thursday. 11/11
Discussion led by group #2. Thomas Kuhn.
Paper #3 due. Topics arising from Determinism and/or Reductionism in Science, Thomas Kuhn, or Zucker chapter 6, "Can there be a Science of Dreams?"
Thursday. 11/18
Conclusion: Kuhn's Postscript and the interpretation of
reality as modeling tacit knowledge
Thursday. 12/2
Discussion of Zucker chapter 7 - science and gender. Please read at least the sections by Jaggar and Ginzberg.
Thursday. 12/9
Final class. Review of the course and preparation for the
final exam. Student Assessments.
Term ends Saturday, December 18th.
