GREGORY FARNAW A. CLAVER1986-36026Feb. 27, 2014Philo 160Submitted to: Prof. Samuel Vera Cruz

1. Explain and evaluate Hempel’s logical reconstruction of theory testing. In what sense does Bayesian approach to theory testing conforms to, and improves on Hempel’s views regarding the confirmation of scientific theories.

Bayesianism is a doctrine about how a person’s degree of belief in a hypothesis should change in

the light of evidence. It therefore reflects a subjectivist approach to probability. Bayesianism is

said, by its keenest supporters, to show:

(a) how inductive practices can be rational;

(b) how inductive practices can lead to the truth;

(c) how various problems in the philosophy of science can be solved; and

(d) what the underlying structure of actual scientific reasoning is.

Bayesianism’s tool in this daunting task is surprisingly modest. In its simplest form Bayes’

theorem is where p(h) is the probability of the hypothesis h, p(e) is the probability of the

evidence e, p(e/h) is the probability of the evidence, when the hypothesis is taken as given, and

p(h/e) is the probability of the hypothesis, when the evidence is taken as given. These are all

subjective probabilities—that is, the degrees of belief we attach to the relevant propositions. The

idea is that if we put values on p(h), p(e), and p(e/h) then there is only one value we can

rationally put on p(h/e), i.e. the value computed by the theorem. Say we do this, and then we

carry out an experiment to test h. The experiment yields e as the result. According to Bayesians

we should now change our degree of belief in h from p(h) to the value we computed for p(h/e).

The idea is that if we were rationally committed to putting a value k on the probability of the

hypothesis, when the evidence e is considered as given, now the evidence e actually is given (by

the experiment) we ought now to change the probability we attach to h to k, i.e.

pafter(h)=pbefore(h/e). This is known as

conditionalization.

We can see that Bayes’ theorem has intuitive plausibility. It says that the probability of a

hypothesis, given some evidence is:

(a) proportional to the probability of the hypothesis prior to obtaining the evidence;

(b) proportional to the probability of the evidence, taking the hypothesis as given; and

(c) inversely proportional to the probability of the evidence itself prior to the test.

These relationships in turn explain the following facts about inference:

(a) If we think a hypothesis is in itself likely in the light of background knowledge, then this will

be taken in its favour when assessing its probability after a test.

(b) The degree to which the evidence supports a hypothesis depends on how closely linked they

are. If on the assumption that the hypothesis is true it would be very likely that we get the

evidence, then so much the better for the hypothesis if we do.

(c) If the evidence is not itself very likely, then it is significant when it does turn up.

Surprising evidence is good evidence.

It is perhaps best to see (b) and (c) together—that is, as the ratio of p(e/h) to p(e). This

ratio is the measure of how much more likely the evidence is given the hypothesis than it

is independent of the hypothesis. If this ratio is around 1, then Pafter(h)=Pbefbre(h), i.e. no

change is the degree of belief. This is the case where the hypothesis gives us no special

reason to expect the evidence or to think it unlikely. On the other hand, if p(e/h)>p(e),

then pafter(h)>Pbefore(h). We increase our degree of belief because the evidence we

obtained is more likely given the hypothesis than we would otherwise have thought. The

third case is p(e/h)<p(e), so that Pafter(h)<Pbefore(h). This is the case of negative evidence.

Here the evidence is supposed, according to the hypothesis, to be more unlikely than we

thought on the basis of background knowledge alone. But we obtained it nonetheless, and

accordingly we reduce the strength of our belief in the hypothesis. Imagine I have a

patient who has three symptoms: very low pulse, dilated pupils, and chest pains. I suspect

a certain virus. People infected with this virus very often have dilated pupils, more

frequently than the average patient. So this evidence favours my hypothesis. On the other

hand, we would expect someone with the virus to have a very high pulse. So the

occurrence of the low pulse, to which we would attach a low probability conditional on

the hypothesis, is contrary evidence. As regards the chest pains, there is no reason to

expect these in an infected subject. But nor is infection any reason to think chest pains

would not occur. So the chest pains are neutral as regards the hypothesis.

These very straightforward features of scientific reasoning are neatly accounted for by

Bayes’ theorem. Note what Bayes’ theorem gives us. Bayesian conditionalization tells us

how to change our degrees of belief in the light of new evidence. If conditionalization is

a priori then we have an a priori rule of inductive inference. Not surprisingly

Bayesianism has many enthusiastic supporters. However, it also has its detractors. We do

not have the space to look at all the criticisms of Bayesianism in depth, but a flavour of

the objections is given by the following considerations.

(a) Conditionalization could not be a priori because it tells us that a degree of belief at

one time (after the experiment) should depend on degree of belief at another time

(before the experiment). But a priori rules cannot be diachronic (across time), they

must be synchronic (concerning the same time).

(b) The probability we attach to a universal generalization should be no more than the

product of the probabilities of the infinitely many independent propositions it entails.

As most of these have a probability less than 1, this product is zero. Because p(h) is

zero, p(h/e) will also be zero; hence Bayes’ theorem is useless.

(c) Bayesianism does not tell us what probabilities to attach to p(h) and p(e). So, even

with the same evidence, two researchers could have widely differing degrees of belief

in a theory.

(d) As Bayesianism is subjectivist it cannot tell us whether a theory that is well supported

by the evidence is thereby more likely to be true. It only tells us that it is more rational

to believe it to be true. This, as we have seen with Strawson, is insufficient to resolve

Hume’s problem.

(e) Scientists may sometimes use Bayes’ theorem, but on the whole they do not. Indeed,

for many theories they would be hard pressed to put any value on the priors p(h) and

p(e), and even p(e/h).

Bayesians like to think they have good answers to these criticisms. Again we do not have

the space to look at all of them in detail. But let us start with one where the Bayesian

certainly has the upper hand—criticism (b) which comes from Popper. Popper argues that

the prior probability of a theory being correct is equal to the product of the probabilities

of the individual, independent basic statements it entails. In general, an infinite number of

these will remain untested. Each of these must have a prior probability of being true of

less than 1, for otherwise we could be certain of their truth in advance of testing. But as

these probabilities are less than 1 their infinite product is equal to zero, and so the prior

probability of any generalization being true is zero.

The response to this is to point out that Popper has misapplied the relevant rule of

probability. He is using a generalized version of the following truth: if C entails both A

and B, and the probabilities of A and B are independent, then p(C)<p(A)×p(B). The

important condition at work here is that the probabilities of A and B are independent—

the truth of one has no bearing on the truth of the other. A might be “I had jam for tea”

and B might be “Aldehydes are oxidized to acids by Tollen’s reagent”. Those two

propositions are clearly unrelated. But the propositions entailed by a general hypothesis

may very well be related. The hypothesis that bats have large ears entails the two

propositions that Horace has large ears and that Hildegard, his sister, has large ears. It

would be foolish to assume that these are probabilistically independent. There are many

conceivable reasons why the fact that Horace has large ears might be relevant to the

probability of Hildegard having the same feature. For instance, one might think it

plausible that siblings share many anatomical characteristics. This is a general claim and

Popper might argue that its probability of being true is therefore equal to zero, and so

cannot be used to establish a probabilistic connection between Horace and Hildegard. But

as Popper’s argument is intended to establish the conclusion that general propositions

have zero priors, it is he who cannot make use of that claim in his argument. It seems

that, by “independent”, Popper understands not probabilistically independent but

logically independent. It is true that “Horace has large ears” and “Horace’s sister

Hildegard has large ears” are logically independent. But the logical independence of A

and B does not entitle one to use the inequality p(C)<p(A)×p(B) (where C entails both A

and B). To gain that entitlement Popper would have to show that probabilistic

independence and logical independence are the same thing. But, as the example shows, to

do that would require assuming that general propositions have zero prior probabilities.

Let us now look at objection (c). The Bayesian response is taken by many Bayesians

to show the power of Bayesianism. But I think this also shows up some weaknesses of

Bayesianism. The objection is this. Say you and I both agree that a piece of possible

evidence e has a certain probability assuming the hypothesis h which we are

investigating. We agree that p(e/h) is 0.8. But you think that the hypothesis is as likely as

not (p(h)=0.5), while I am more sceptical (p(h)=0.3). You think the evidence is mildly

surprising (p(e)=0.4), while I think it mundane (p(h)=0.6). What do we now think about

the probability of the hypothesis? We both think it is more likely, but you attach a

probability of 0.875 to it, while my adjusted degree of belief is 0.35. So after

consideration of the same piece of evidence, you think the hypothesis really quite

probable while I am still sceptical. This is because the prior probabilities we each attach

to h are different. But as Bayes’ theorem does not tell us how to fix our priors it cannot be

used to say which hypothesis a person should adopt given the evidence.

The Bayesian has the following response. As the number of tests increases, opinion

will converge—and will converge on the correct hypothesis. Let us look at an illustration.

You, Lucy, and I are investigating a coin that we think might be biased. We can describe

the bias by attaching a probability to it falling heads up. For an unbiased coin this

probability is 0.5. We have different initial views on whether it is biased. You think it is

biased towards tails, Lucy thinks it is unbiased, and I think it is biased towards heads.

view of a hypothesis in the light of evidence. Whether one rejects or accepts this depends

on whether one agrees or disagrees that structural features of a hypothesis, such as

simplicity, explanatory unity, and integration with other hypotheses, can be part of the

rational evaluation of a hypothesis. I have argued that they should be, and thus that

Bayesianism is incomplete. On the other hand, Bayesians may accept that Bayesian

conditionalization is open to supplementation—for instance by a theory of how structural

features should contribute to the evaluation of the prior probability of a hypothesis. In

contrast, Inference to the Best Explanation as I have described it does give a role to the

structural features left unaccounted for by Bayesianism, and so in that regard at least

provides a better understanding of the rationality of scientific inference.

Lastly, it should not be forgotten that, as a theory of subjective probability,

Bayesianism has little to say about the propensity of inductive practices to lead to the

truth. We may well agree that someone who adjusts the credence they give to a

hypothesis in accordance with Bayesian conditionalization is thereby behaving rationally.

But nothing in Bayesianism can show that such a person is also more likely to end up

with true hypotheses than someone who infers differently. In this way, whatever the

merits of Bayesianism as either an explanatory description of our inductive practices or

an account of inductive rationality, it is in the same boat as Strawson’s account when it

comes to finding an answer to Hume’s problem. Neither shows whether rationality has a

propensity for success. Consequently, neither tells us whether inductive knowledge is

possible.

2. Defend or reject the views of Popper:

a. Criterion of demarcation between science and non-science

Popper’s criterion of science is a statement or theory’s falsifiability/refutability/testability.

Hence statements, claims or theories can be categorized only as scientific if they pass this test.

Otherwise these discarded claims properly belong to non-science or pseudo-science.

I think this Popperian test is at present necessary and can be tentatively accepted as the criterion

for screening and criticising claims and statements. This testability is not only practicable to

scientists, but also to ordinary people who are too busy to analyse and criticize volume of

information, propaganda and advertisements from multi-media especially from TV and internet.

Take for example the proliferation of herbal preparations or food supplements which claims it

can prevent and cure all kinds of diseases, from cancer to almost all illnesses imaginable. The

sale of extracts from Guyabano, mushrooms, algae etc. are making big money in the Philippines,

by posing as an alternative to established medicine which is often very expensive. Thus their

appeal come from affordability and “promise” as a cure-all medicine.

To one who is not familiar with Popper’s falsifiability criterion, one would readily accept these

kinds of “cure-all” claims by many herbal preparations which are insinuated as similarly

scientific especially when advertised by known personalities who have confirmed their potency

and effectiveness. But using Popper’s testability as a criterion for science, it is very easy to find

out that these are re-packaged myths masquerading as scientific solutions to human diseases. I

therefore support the idea of Popper because it is a practical and effective measure to discern

which ideas and claims are to be believed as reliable and scientific.

b. Falsification as the essence of scientific method

In so far as falsifiability or refutability defines what belongs to science, it is but logical that for

Popper that falsification is the essence of scientific method.

I agree with Popper that falsification is the essence of scientific method. The scientific method

that we are accustomed of, that we have known since elementary grade states that scientific

method begins with observation of facts and these observations are stated in general terms which

becomes our intelligent guess or hypothesis. This hypothesis is further confirmed and verified

by testing, either again by observation or laboratory controlled experiments until it becomes a

scientific theory.

The traditional scientific method is basically verificationist or relies on confirmation. The more

instances of confirmation, the stronger the theory is. One more thing, it always begins with

observation of facts.

On the other hand, Popper’s falsification as a method does not distinguish whether a hypothesis

or conjecture starts from observation, it is more important for Popper to evaluate this conjecture

on the basis of its testability. The method of falsification is the essence of scientific method

which we can say that it is the method itself. The shift in the method from verification to

refutation is the kernel or essence of the scientific method which I also think as more reliable

than pure verification.

c. Scientific reasoning never involves induction

For Popper, deduction has replaced induction as the true scientific method. Scientific reasoning

does not need the involvement of induction because of the limitation of verification and endless

confirmation can never establish the truth and scientific-ness of a claim or theory. Since

induction is the logic of verification and confirmation, so is deduction the logic of science

because it is open to refutation.

Scientific reasoning is therefore scientific if it involves deduction which can establish the

certainty of conclusions based on the evaluation of premises while on the other hand, induction

can only lead to inference with a more or less degree of probability which can be easily

discarded in the light of refutation.

d. Scientific objectivity, as conceived by sociologists of knowledge, is mistaken

The sociology of knowledge argues that scientific thought, and especially thought on social and

political matters, does not proceed in a vacuum, but in a socially conditioned atmosphere. It is

influenced largely by unconscious or subconscious elements. These elements remain hidden

from the thinker’s observing eye because they form, as it were, the very place which he inhabits,

his social habitat. The social habitat of the thinker determines a whole system of opinions and

theories which appear to him as unquestionably true or self-evident.

Each of these different socially determined systems of assumptions is called by the sociologists

of knowledge a total ideology.

For Popper, these sociologists of knowledge fail to understand the social aspect of knowledge,

of scientific method. It looks upon science or knowledge as a process in the mind or

consciousness of the individual scientist, scientific objectivity is founded upon the individual

scientist’s impartiality or objectivity.

I agree with Popper that scientific objectivity is not similar to the domain of social sciences

which we can be home to different individual opinions without conflict in order to arrive at the

truth. Other disciplines outside of science lets say anthropology which studies diverging

cultures, anthropologists can be influenced by the culture they are studying such that it forms

their individual prejudices, their socially determined systems of assumptions. Unlike in science,

the seeming stability of the object of science especially natural science makes it more

independent of the prejudices of the scientist.

e. Scientific objectivity as a function of the public character of the scientific method

Unlike the sociologists of knowledge who fall into the pit of individualism, Popper’s Scientific

objectivity is not a result of individual scientist to be objective but from the friendly-hostile

cooperation of many scientists, the inter-subjectivity of scientific method.

The great difference can be gleaned from the individual to the scientific community. Ideas and

theories must be subjected to test not only by the individual but of the whole scientific

community in order to cast away the prejudice of the individual scientist, to attain the level of

scientific objectivity through the method of public scrutiny.

The public character of scientific method – the openness to free criticism and the employment of

experience as the impartial arbiter of controversies, everyone who has learned the technique of

understanding and testing scientific theories can repeat the experiment and judge for himself.

This public character of scientific method ensures that subjectivity is reconciled with scientific

objectivity.

f. Scientific progress and truth as a goal of scientific enterprise

I agree with Popper that scientific progress and the eternal quest for truth is the goal of scientific

enterprise. Since theories are eternally subjected to refutation and those that can not stand it are

rejected or revised is a guarantee that we are moving towards the attainment of greater

knowledge. This trend is getting us towards scientific progress.

However, scientists do not live in a vacuum. Societies they belong to greatly determine and limit

the goal of scientific inquiry and the application of these scientific discoveries is more or less

influenced by the state of technological level in a certain country. Scientist are more often than

not contracted by big businesses either as researchers or employees. This beclouds scientific

objectivity and the scientific activity is subsumed under the lead of business and profit. The

problem here as encountered by the scientist is not about truth and scientific progress but the

goal and to whose interest would science serve. It is under the backdrop of conflicting interest

that science would be under a dilemma, the ideology of science, especially under circumstances

where such scientific activity would be turned against society. This is true to the development of

the atom bomb, the production and reproduction of genetically-modified organisms etc.

This situation forms a great barrier to the unity of science, of the scientific community, which

must serve humanity, into speaking a common language as Popper puts it.

While Practice is not the enemy of theoretical knowledge but the most valuable incentive to it,

not only be scientists, states and businesses determine the object and direction of science, but

society too as a whole, the recipient and beneficiary of scientific progress must also be involved

to ensure that science proceeds to address the short-term and long term needs of humanity.

3. Defend or reject the following views propounded by Thomas Kuhn:

a. Paradigm as the basis of well-developed or mature science

Kuhn defines paradigm as the background set of assumptions and methods. A paradigm is

developed once a general consensus among a particular scientific community had been reached,

and commonly clustered around a key text or scientist.

For me, I strongly agree with Kuhn that the development of paradigm is a sign that science has

attained a higher level, a mature level. The early days of science, if it is already proper to be

called so, individual scientists worked on their own that’s why many discoveries and theories

have been worked on simultaneously in different countries without the benefit of sharing

between and among them. During this infantile era of science, scientific community was not yet

fully developed, the community of scientists were not that developed and individual endeavour

was the rule of the game.

This completely changed as the world trade and international relations between and among

nations was developed. It was also during this era that individual discovery yielded to

innovation and reformulation of scientific theories that paved the way to the formation of a truly

scientific community, of the interconnection of scientists worldwide, not only working as

individuals but teams and groups under a more or less defined theoretical persuasion.

Thus, the development of a paradigm is not only a symptom but already became the basis of a

mature science.

b. Dogmatism is useful in scientific research

Kuhn calls dogmatism the strongly held convictions of scientists prior to research which he sees

as a precondition for success in the sciences. Dogmatism is a commitment to further research in

order to confirm and preserve normal science.

Although I disagree with Kuhn when he calls this commitment as dogmatism, I agree with him

that such commitment is necessary in scientific research whether such commitment. For me,

dogmatism is committed when there is no scientific basis but mere belief based on religious or

otherwise irrational source.

Anyway, paradigm articulation done by the scientist impelled by his commitment or dogmatism

will necessarily advance research and science itself. Given this impetus, a scientist will try his

might to extend the boundaries of his new theory or paradigm. This will eventually result to the

acknowledgement of his theory’s boundaries and limits or the extent of its validity. It may yet

result to the discovery of conflicting instances or incompatible application which may result to

its demolition by another paradigm.

c. Normal science is mainly puzzle-solving

Once a paradigm is established, it becomes a normal science not anymore concerned on

controversial discoveries but in extending paradigm as far as possible. The dogmatism or

commitment of the scientist will drive him to seek for the unknown or blind side of the theory.

Whatever is not yet explored using this theory will be a vast arena for experimentation and those

blind spots are like puzzles awaiting the scientist to solve it using the accepted paradigm.

I think this is tenable because a paradigm can not be generally accepted by a certain scientific

community however small without appealing to or even appearing to be greater than its

predecessor which was previously abandoned due to its contradiction with newly discovered

phenomena. This new scientific perspective that guides research which will become the new

theory in a dominant position will try to solve all mysteries and unknowns in its path. Once it

has illuminated such blind spots, it has entrenched itself as a strong scientific theory that can

withstand great criticism from its opponents.

d. Competing paradigms are incommensurable

Old and new or competing paradigms are incommensurable according to Kuhn.

They cannot be compared or measured. The old paradigm cannot be simply improved but must

be replaced based on a new foundation or set of assumptions, assumptions that cannot be

accommodated in the old paradigm without contradicting itself.

I think this incommensurability comes mainly from the incapacity of the old paradigm to

accommodate revisions without crumbling on its very foundation. The old paradigm is not only

insufficient but basically flawed and unable to explain or guide the explication of phenomena

that are anomalous. There is no chance of revising or modifying the paradigm in the light of

anomalous circumstances, and there is no choice left but to abandon it and be replaced by a more

dynamic and coherent paradigm, a paradigm that can shed light on these anomalous phenomena

and founded on a firmer basis.

e. Normal science always leads to crisis which in turn leads to scientific revolutions

Once a scientific system or paradigm is established and becomes the dominant one, replacing the

old one which is already abandoned and discarded, there will come a point in time where

anomalies or contradictory phenomenon will appear which can not anymore be accommodated.

The process and cycle of emergence, dominance, abandonment and replacement of one paradigm

to another will be repeated. Kuhn attributes this revolutionary situation as a result of

accumulated anomalies which brings about a crisis situation where normal science will be

replaced by revolutionary science and so on and so forth.

It think this Kuhn’s analysis of the history of the philosophy of science is similar to the historical

materialism as excerpted by Karl Marx in his studies of the development of societies, of social

revolution as a result of the insoluble conflict of diametrically opposed class interests of

economic classes.

Normal science while it can be dominant for a long time, there will come a time that it will cease

to be the guiding light in scientific endeavours. Just as societies evolve and gearing towards

progress, so is normal science.

f. Scientific revolutions are paradigm shifts, not governed by impartial, theory-

independent evidences, and neither by rational and objective rules

Far from gradual rational progress, science advanced through radical and violent upheavals or

paradigm shifts. Out of the crisis that normal science undergoes, an alternative paradigm springs

up to shed light on new phenomena never known encountered before.

It can be gleaned from the terminology of Kuhn that scientific revolutions are paradigm shifts or

abandoning the old paradigm and adopting a new one. Why not an evolutionary one? Because

changes in science does not proceed in a linear and gradual process but rather from leaps and

bounds. Paradigm shifts are characterized by the defeat of the old and the emergence of a more

stable and consistent theory, a fruit of the struggle of ideas and disentanglement of the old one

from its confusions and inconsistency.

g. Scientific objectivity is a myth

According to Kuhn, scientific objectivity is untenable because a scientist is always preoccupied

with his paradigm, a way of viewing things, that beclouds his search for the truth. Normal

science is largely paradigm-articulation and the tendency of the commitment of a scientist to his

paradigm is loyalty to it. Objectivity is therefore determined by a paradigm hence such

objectivity is a myth.