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How the Growth of Success stopped Theory Change

Ludwig Fahrbach

Universität Düsseldorf

Ludwig.Fahrbach@googlemail.com

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Overview

Realist: “Successful theories are true.”

Anti-realist: “The history of science is full of counterexamples, i.e.,

successful, but false theories.”

My reply: All of these counterexamples enjoyed only comparatively

low degrees of success. Our current best theories enjoy much higher degrees of

success.

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1. The Realism Debate

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The success-to-truth principle*If a scientific theory is empirically successful, then it is approximately true.

A theory is empirically successful, iff the predictions deduced from the theory by scientists fit

with the observations gathered by scientists, and there are no serious cases of non-fit.

In what follows: “true” short for “approximately true” “successful” short for “empirically successful” best theories at some point in time = most successful

theories at that time

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The positions*

The realist endorses the success-to-truth principle therefore accepts our current best (i.e. most

successful) theories as true (e.g., theory of evolution, germ theory of disease, etc.)

The anti-realist rejects the success-to-truth principle is agnostic about or rejects (important parts of) our

current best theories

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The arguments

The realist supports the success-to-truth principle with the no-miracles argument

The anti-realist attacks the success-to-truth principle with

the argument from the underdetermination of theories by all possible evidence

the pessimistic meta-induction (PI, for short)

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The PI*

The past of science is full of once successful scientific theories that were accepted for some time, but later shown to be false.

These theories constitute counterexamples to the success-to-truth principle; they undermine it.

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Laudan’s list of successful, but refuted theories

the crystalline spheres of ancient and medieval astronomy the humoral theory of medicine the effluvial theory of static electricity the ‘catastrophist’ geology (including Noah’s deluge) the phlogiston theory of chemistry the caloric theory of heat the vibratory theory of heat the vital force theories of physiology the electromagnetic ether the optical ether the theory of circular inertia theories of spontaneous generation

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2. Degrees of success

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Grading the notion of success*

Scientific theories vary with respect to their degree of success.

The degree of success of a theory increases, iff the passed tests increase in number and quality. In general, this is the case

1. if scientists are able to derive more predictions from the theory

2. if the derived predictions become more precise3. if the derived predictions of the theory gain in variety4. if scientists gather more data5. if the gathered data are more precise6. if the gathered data gain in variety

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success

scientific fields

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success

scientific fields

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Main thesis*

Among theories with very high degrees of success (e.g., our current most successful theories) almost no refutations have occurred.

Practically all successful refuted theories enjoyed rather low degrees of success.

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Examples of theories with very high degrees of

success: the periodic system of elements the theory of evolution “Fixed stars are like our sun.” “All organisms consist of cells.“ the conservation of energy + mass “Water is H2O.“ “The brain is a net of neurons.“ And so on

*

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refuted theories

current best theories

success

scientific disciplines

realm of stability

*

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How realism is saved*

Refined success-to-truth principle: “If a theory enjoys a high degree of success, it is true.”

The refined success-to-truth principle is not undermined by counterexamples.

Refined realism:“The refined success-to-truth principle is correct.”

Refined realism is saved from the PI.

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The big boost*

Consider how the degrees of success of the best theories has increased over the history of science.

The big boost: By far most of that growth occurred in the recent past, i.e., in the last few decades.

(More generally, during the history of science the degree of success of the best theories has very roughly grown exponentially.)

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3. Five Indicators of Success

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First indicator: the exponential growth of scientific work*

Since 1700, the number of scientific publications has doubled every 15-20 years.

The same holds for the number of scientists.

1980 2000-∞ 1960

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The other four indicators

In general, the success of theories increases, when

1. the computing power increases,

2. the amount of data increases,

3. the data have more variety,

4. the data have a higher degree of precision.

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Second indicator: computing power*

Benefits of computing power: Computing power is needed to derive observable

predictions from the theory, e.g. to solve equations numerically. Predictions can then become more numerous, more varied and more precise.

Automated gathering of data Storing of data Searching in data Simulations Etc.

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Growth of computing power

growth of manpower better mathematical and computational

methods better instruments (abacus, logarithmic

tables, etc.) in the last 50 years power of computers

doubling every 2 years

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More on the benefits of computing power

„It is now possible to assign a homework problem in computational fluid dynamics, the solution of which would have represented a major breakthrough or could have formed the basis of a Ph.D. dissertation in the 1950s or 1960s.” (Tannehill et al. 1997, p. 5, quoted by Paul Humphreys 2004, Extending Ourselves, p. 49)

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Third indicator: amount of data*

The amount of data in many scientific fields grew at least proportionally to manpower.

In the last few decades, the gathering of data has become more and more automated.

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Fourth indicator: diversity of data*

100 years ago: light microscope

Today: many types of light microscopes (polarization,

fluorescence, phase contrast, ect.) many types of electron microscopes some types of scanning probe microscopes some types of acoustic microscopes Etc.

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Fifth indicator: precision of data*

In many scientific fields, every new generation of instruments has led to an (often dramatic) improvement of the precision of data.

Example: In the 1980s GPS increased the precision of distance measurements in geology 100fold.

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Unification and Success

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How precisely has the growth of the five indicators led to a big boost in success for our best theories?

Did the increase in success happen in a considerable number of big steps (e.g. by

novel predictions)? in a high number of medium-sized steps? in a very high number of small steps? all of the above?

Answer (work in progress): depends on the scientific field and theory typically all of the above, i.e., a lot of overkill

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Core theories

Many of our current best theories have strong unifying power.

This means that a lot of work in their respective fields are applications of them.

Call such a theory a “core theory in its field”.

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The accumulation of small and intermediate successes

Due to the growth of scientific work, computing power, amount of data, etc., the number of such applications of the core theories has increased enormously.

In many such applications the core theory enjoyed small or moderate successes.

These small or moderate successes accumulate to a very high overall amount of increase in success.

Examples: The periodic system of elements enjoyed small or moderate successes in millions of applications.

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How the Big Boost Supports

the Main Thesis

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refuted theories

current best theories

success

scientific fields

realm of stability

1920

big boost

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The refuted theories*

Practically all examples of successful, but refuted theories presented in the philosophical literature are older than 80 years.

If in the last 80 years there had been some refuted theories among the best theories, then they would have been sufficiently salient for philosophers to present them.

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Theories of light

19001800 20001700

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1900

1800

20001700 1980

Theories of light

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Objections

(1) Early theories with very high success

(2) Refutations of theories in the last few decades

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Conclusion*

In the last few decades there was a big boost of success.

The best theories of the recent past received that boost, while none of them was refuted.

No refuted theory received the big boost. Hence, the inference from very high

success to truth has no counterexamples.

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THE END