The scientific method

This outline discusses the history of science, the definition of the scientific method, its central role in founding a scientific epistemology, the demarcation of science from pseudoscience, and other epistemological topics concerning the methods and philosophy of science. The metaphysical implications of science are discussed in the Outline on scientific realism.

This could have been called the outline of “Epistemology.”


  1. History of science
    1. Antiquity
    2. The Middle Ages
    3. Early Modern Period
    4. The Age of Enlightenment
    5. Canonical classical physics
    6. “Scientists”
    7. Biological evolution
    8. Modern physics
    9. Modern statistics
    10. Computer science
  2. Rationalism vs empiricism
    1. Introduction
    2. Early empiricists
    3. Rationalists
    4. British empiricists
    5. Important synthesizers
  3. Knowledge
    1. Definining knowledge
    2. Epistemic errors
    3. Scientific knowledge
  4. Analytic/synthetic distinction
    1. Introduction
    2. Formal epistemology
    3. Criticisms
    4. Discussion
  5. Induction
    1. Problem of induction
    2. Causation
    3. Uniformity of nature
    4. Inductive logic
    5. Challenges
    6. Abduction
    7. Statistics as a solution to the problem of induction
    8. Meta-induction as a solution to the problem of induction
  6. Is there a universal scientific method?
    1. First pass
    2. Yes: Models of science
    3. No: There is no unified “scientific method”
    4. Yes: Rebuttals in favor of scientific method
    5. Anthropology of science
  7. Models in science
    1. What’s a model?
    2. Models represent theories
    3. Digression: Some physicists have semantic differences
  8. Pseudoscience
    1. The demarcation problem
    2. Bullshit
  9. My thoughts
  10. Annotated bibliography
    1. Hume, D. (1748). An Enquiry Concerning Human Understanding.
    2. Pigliucci, M. (2010). Nonsense on Stilts: How to Tell Science From Bunk.
    3. French, S. (2007). Science: Key Concepts in Philosophy.
    4. More articles to do
  11. Links and encyclopedia articles
    1. SEP
    2. IEP
    3. Wikipedia
    4. Others
  12. References

History of science

In this first section, we briefly outline chronologically highlights in the development of science, after which there are sections focusing on topics in the epistemology of science, starting with rationalism vs empiricism.

Figure 1: Timeline of some major philosophers in history.

This section is collapsed:



See also:

Industrial revolution


  • Ionian Enlightenment
    • “Ionian enchantment: A brief history of scientific naturalism”1
  • Thales of Miletus (c. 624/623-548/545 BCE)
    • “first philosopher”
    • predicted a solar eclipse in 585 BCE
  • Anaximander (c. 610-546 BCE)
    • Carlo Rovelli argues that Anaximander is the first scientist.2
    • speculated that humans evolved from fish?
    • first to make a map?
  • Anaximenes (c. 586-526 BCE)
  • Xenophanes (c. 570-478 BCE)
  • Pythagoras (570-495 BCE)
    • radical mathematical realist
  • Heraclitus (c. 535-475 BCE)
  • Parmenides (b. c. 515 BCE)
  • Anaxagoras (c. 510-428 BCE)
  • Zeno of Elea (c. 495-430 BCE)
  • Empedocles (c. 494-434 BCE)
    • theory of the four elements
  • Protagoras (c. 490-420 BCE)
    • major Sophist - professional tutor, especially in rhetoric.
  • Herodotus (c. 484-425 BCE)
    • “Father of history”
  • Socrates (c. 470-399 BCE)
    • First moral philosopher
    • Socratic method
    • Teacher of Plato and Xenophon
  • Thucydides (c. 460-400 BCE)
    • “Father of scientific history”
  • Democritus (460-370 BCE)
    • atomic theory
  • Hippocrates (c. 460-370 BCE)
    • “Father of medicine”
  • Xenophon (c. 431-354 BCE)
  • Plato (428/7 or 424/3 - 348/7 BCE)
    • revolutionized western thought
    • epistemology
    • abstract Platonism
    • Platonic Academy (387 BCE - 529 CE) from which we derive academia
    • “the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.”3
  • Aristotle (384-322 BCE)
    • His writings cover many subjects and have influenced the intellectual lexicon of virtually every field of study.
    • Riddled with teleological explanation: things have “natural” purposes or tendencies.
    • Founded the Lyceum (334-86 BCE)
    • Tutored Alexander the Great ages 13-16 beginning in 343 BC.
    • Prior Analytics (c. 350 BCE) - book that founded formal logic
    • Peripatetic school
  • Theophrastus (c. 371-287 BCE)
  • Strato of Lampsacus (c. 335-269 BCE)
  • Epicurus (341-270 BCE)
    • Emphasized skepticism until something can be demonstrated
    • Principle of Multiple Explanations: “if several theories are consistent with the observed data, retain them all”
  • Zeno of Citium (c. 334-262 BCE)
  • Euclid (fl. 300 BCE)
    • logico-deductive method founded by Euclid’s Elements
  • Aristarchus of Samos (310-230 BCE)
  • Archimedes (c. 287-212 BCE)
    • The Method
  • Chrysippus (c. 279-206 BCE)
  • Eratosthenes (276-195/194 BCE)
    • Estimated the circumference of the Earth to be 50 times the distance between Alexandria and Syene, which was pretty acurate as it is actually 47.9 times!4
  • Library of Alexandria
  • Library of Pergamum
  • Hipparchus (c. 190-120 BCE)
  • Antikythera mechanism (between c. 200 and 100 BCE)
  • Lucretius (99-55 BCE)
  • Ptolemy (c. 100-170 CE)
    • Almagest


The Greeks contributed, it is true, something else which proved of more permanent value to abstract thought: they discovered mathematics and the art of deductive reasoning. Geometry, in particular, is a Greek invention, without which modern science would have been impossible. But in connection with mathematics the one-sidedness of the Greek genius appears: it reasoned deductively from what appeared self-evident, not inductively from what had been observed. Its amazing successes in the employment of this method misled not only the ancient world, but the greater part of the modern world also. It has only been very slowly that scientific method, which seeks to reach principles inductively from observations of particular facts, has replaced the Hellenic belief in deduction from luminous axioms derived from the mind of the philosopher. For this reason, apart from others, it is a mistake to treat the Greeks with superstitious reverence. Scientific method, though some few among them were the first men who had an inkling of it, is, on the whole, alien to their temper of mind, and the attempt to glorify them by belittling the intellectual progress of the last four centuries has a cramping effect upon modern thought.

There is however, a more general argument against reverence, whether for the Greeks or for anyone else. In studying a philosopher, the right attitude is neither reverence nor contempt, but first a kind of hypothetical sympathy, until it is possible to know what it feels like to believe in his theories, and only then a revival of the critical attitude, which should resemble, as far as possible, the state of mind of a person abandoning opinions which he has hitherto held. Contempt interferes with the first part of this process, and reverence with the second.5


Like modern scientists, these early Greeks were willing to look beneath the surface appearance of the world, pursuing knowledge about a deeper level of reality. The matter of the world does not appear at first glance as if it is all made of water, or air, or earth, or fire, or all four together, or even atoms.6

Nevertheless, I think one should not overemphasize the modern aspects of Archaic or Greek science. There is an important feature of modern science that is almost completely missing in all the thinkers I have mentioned, from Thales to Plato: none of them attempted to verify or even (aside perhaps from Zeno) seriously to justify their speculations. In reading their writings, one continually wants to ask, “How do you know?” This is just as true of Democritus as of others. Nowhere in the fragments of his books that survive do we see any effort to show that matter really is composed of atoms.7

This did not occur to the early Greeks, or to many of their successors, for a very simple reason: they had never seen it done.8



See also:

The Middle Ages

  • Islamic Golden Age
  • Academy of Gondishapur
    • in what is now Khuzestan Province, Iran
  • House of Wisdom
    • in Abbasid-era Baghdad, Iraq
  • Muhammad ibn Musa al-Khwarizmi (c. 780-850)
  • Ibn al-Haytham (965-1040) AKA “Alhazen”
    • Book of Optics
    • First to demonstrate the success of the intromission theory over the extramission theory of vision.
    • Doubts Concerning Ptolemy
    • “But for a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet’s motion… And therefore the arrangements assumed by Ptolemy for the five planets are false, and he asserted them knowing them to be false, and there exists for the planets a true arrangement in existing bodies which Ptolemy failed to grasp.”11
    • “Ibn al-Haytham was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical evidence—an early pioneer in the scientific method five centuries before Renaissance scientists.” - Wikipedia
    • The first true scientist - By Jim Al-Khalili
  • Ibn Sina (980-1037) AKA “Avicenna”
  • Shen Kuo AKA Shen Gua (1031-1095)
  • Reconquest of Toledo (1085)
  • Scholasticism
  • Robert Grosseteste (ca. 1168-1253)
  • Roger Bacon (1214-1292)
  • William of Ockham (1287-1347)
    • Ockham’s razor as a hint at parsimony and abduction

Early Modern Period

The Age of Enlightenment

Canonical classical physics


Biological evolution

Modern physics

Modern statistics

Computer science

Rationalism vs empiricism


See also:

Early empiricists


The things that can be seen, heard, and learned are what I prize the most.12


Figure 2: Mind Chunks by Pete Mandik (Nov 1, 2016).

British empiricists


[S]cepticism, when more moderate, may be understood in a very reasonable sense, and is a necessary preparative to the study of philosophy, by preserving a proper impartiality in our judgments, and weaning our mind from all those prejudices, which we may have imbibed from education or rash opinion. To begin with clear and self-evident principles, to advance by timorous and sure steps, to review frequently our conclusions, and examine accurately all their consequences; though by these means we shall make both a slow and a short progress in our systems; are the only methods, by which we can ever hope to reach truth, and attain a proper stability and certainty in our determinations.16

Important synthesizers


Definining knowledge


I myself do not have the answer when I perplex others, but I am more perplexed than anyone when I cause perplexity in others. So now I do not know what virtue is; perhaps you knew before you contacted me, but now you are certainly like one who does not know. Nevertheless, I want to examine and seek together with you what it may be.21

SOCRATES: Then suppose a jury has been justly persuaded of some matter which only an eye-witness could know, and which cannot otherwise be known; suppose they come to their decision upon hearsay, forming a true judgment: then they have decided the case without knowledge, but, granted they did their job well, being correctly persuaded?

THEAETETUS: Yes, certainly.

SOCRATES: But, my dear lad, they couldn’t have done that if true judgment is the same thing as knowledge; in that case the best juryman in the world couldn’t form a correct judgment without knowledge. So it seems they must be different things.

THEAETETUS: Oh, yes, Socrates, that’s just what I once heard a man say; I had forgotten, but now it’s coming back to me. He said that it is true judgment with an account that is knowledge; true judgment without an account falls outside of knowledge. And he said that the things of which there is no account are not knowable (yes, he actually called them that), while those which have an account are knowable.

SOCRATES: Very good indeed.22

Figure 3: Knowledge = JTB - G (, 2014).

In his unfinished work, Rules,23 Descartes defines “science” (scientia) in Rule 2 as

Omnis scientia est cognitio certa et evidens.
All (scientific) knowledge is certain and evident cognition.

In the same section, Descartes’ boldly declares to reject probable knowledge for only what is perfectly certain:

we reject all […] merely probable cognition and resolve to believe only what is perfectly known and incapable of being doubted.

Ichikawa & Jenkins:

The standard analysis of knowledge says that for any subject \(S\) and any proposition \(p\), the following are individually necessary and jointly sufficient conditions for \(S\) knows that \(p\):

  1. \(p\)
  2. \(S\) believes that \(p\)
  3. \(S\) is justified in believing that \(p\).

Precursors of this view are sometimes attributed to Plato, who says in the Meno that knowledge is distinguished from mere true belief in being ‘tied down,’ so that it cannot easily escape or be lost as mere true belief can. Views more closely resembling the above formulation of the JTB analysis are attributed by Edmund Gettier to Roderick Chisholm and A. J. Ayer. Neither of those authors phrased their conditions for knowledge exactly this way. The now-usual formulation, in terms of justification, is so in large part because of Gettier (1963).26

Epistemic errors



One must learn by doing the thing; though you think you know it, you have no certainty until you try.


All scientific knowledge is uncertain… [W]hat we call scientific knowledge today is a body of statements of varying degrees of certainty. Some of them are most unsure. Some of them nearly sure; but none of them is certain.27

The stopped clock from Russell’s Human Knowledge: Its Scope and Limits. Russell:

You’re walking by a clock that you’ve always known to be accurate in the past. You glance up at it and see that it reads five o’clock; on the basis of this you believe that it’s five o’clock. Your belief is justified, and as it happens it is five o’clock. But unbeknownst to you, the clock stopped exactly twelve hours ago.28

Gettier cases

Systematic uncertainties

See also:

Internalism vs externalism

Scientific knowledge

From Aristotle’s Posterior Analytics:

We suppose ourselves to possess unqualified scientific knowledge of a thing, as opposed to knowing it in the accidental way in which the sophist knows, when we think that we know the cause on which the fact depends, as the cause of that fact and of no other, and, further, that the fact could not be other than it is.32

another translation:

We think we understand something simpliciter (and not in the sophistical way, incidentally) when we think we know of the explanation because of which the object holds that it is its explanation, and also that it is not possible for it to be otherwise. It is plain, then, that to understand is something of this sort.33

See also:

Analytic/synthetic distinction



When we run over libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.35

Table 1: Kant’s division of judgments.
analytic synthetic
a priori True by definition, Kant: Arithmetic propositions?
Hume’s relations of ideas Kant: Transcendental deduction?
a posteriori Impossible? Empirical,
Hume’s matters of fact

Kant in his Critique of Pure Reason (1787):

In all judgments in which we think the relation of a subject to the predicate… this relation is possible in two ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B, though connected with concept A, lies quite outside it. In the first case I call the judgment analytic; in the second, synthetic. Hence (affirmative) analytic judgments are those in which the predicate’s connection with the subject is thought by [thinking] identity, whereas those judgments in which this connection is thought without [thinking] identity are to be called synthetic. Analytic judgments could also be called elucidatory. For they do not through the predicate add anything to the concept of the subject; rather, they only dissect the concept, breaking it up into its component concepts which had already been thought in it (although thought confusedly). Synthetic judgments, on the other hand, could also be called expansive. For they do add to the concept of the subject a predicate that had not been thought in that concept at all and could not have been extracted from it by any dissection.37


logic is a science that provides nothing but a comprehensive exposition.38


Now the proper problem of pure reason is contained in this question:
How are synthetic judgments possible a priori?39


It is a well-known fact in the history of philosophy that necessary truths in general, but especially those of which it is said that the opposite is inconceivable, have been commonly supposed to be analytic, in the sense that the proposition denying them was self-contradictory. It was in this way, commonly supposed, before Kant, that many truths could be proved by the law of contradiction alone.40

Vienna Circle manifesto:

In such a way logical analysis overcomes not only metaphysics in the proper, classical sense of the word, especially scholastic metaphysics and that of the systems of German idealism, but also the hidden metaphysics of Kantian and modern apriorism. The scientific world-conception knows no unconditionally valid knowledge derived from pure reason, no ‘synthetic judgments a priori’ of the kind that lie at the basis of Kantian epistemology and even more of all pre- and post-Kantian ontology and metaphysics. The judgments of arithmetic, geometry, and certain fundamental principles of physics, that Kant took as examples of a priori knowledge will be discussed later. It is precisely in the rejection of the possibility of synthetic knowledge a priori that the basic thesis of modern empiricism lies. The scientific world-conception knows only empirical statements about things of all kinds, and analytic statements of logic and mathematics.41

See also:

Formal epistemology


Theorem 52.3. Every logical sentence is \(L\)-determinate; there are no synthetic logical sentences.46



See also:



As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.51


I am even of the opinion that this standpoint [Kant’s system of a priori concepts and norms] cannot be strictly refuted by any scientific development. For, one will always be able to say that critical philosophers had hitherto erred in setting up the a priori elements and one will always be able to set up a system of a priori elements that does not conflict with a given physical system. I surely may briefly indicate why I do not find this standpoint natural. Let a physical theory consist of the parts (elements) \(A\), \(B\), \(C\), \(D\), which together form a logical whole that correctly connects the pertinent experiments (sensory experiences). Then the tendency is that less than all four elements, e.g., \(A\), \(B\), \(D\), still say nothing about the experiences, without \(C\); no more so \(A\), \(B\), \(C\), without \(D\). One is then free to regard three of these elements, e.g., \(A\), \(B\), \(C\), as a priori and only \(D\) as empirically determined. What always remains unsatisfactory in this is the arbitrariness of the choice of elements to be designated as a priori, even disregarding that the theory could be replaced at some point by another theory that substitutes some of these elements (or all four of them) with others. One could be of the view, though, that through direct analysis of human reason, or thought, we would be in a position to recognize elements that would have to be present in any theory. But most researchers would probably agree that we lack a method for recognizing such elements, even if one were inclined to believe in their existence. Or should one imagine that the search for a priori elements was a kind of asymptotic process that advances along with the development of science?52

See also:


de Swart:

Sometimes one speaks of logically necessary truths instead of analytic truths and of logically contingent truths instead of synthetic truths, to be distinguished from physically necessary truths (truths which physically could not be otherwise, true in all physically possible worlds). The distinction between necessary and contingent truth is a metaphysical one, to be distinguished from the epistemological distinction between a priori and a posteriori truths. Although these—the metaphysical and the epistemological—are certainly different distinctions, it was controversial whether they coincide in extension, that is, whether all and only necessary truths are a priori and all and only contingent truths are a posteriori.59

Gillian Russell:

[O]ur old view of analyticity was based on a naive theory of meaning, and some Quinean challenges to it were basically right. But our new theories of meaning will support a new picture of analyticity, one which—being based on a better theory of meaning—admits of a more robust defence.60


Problem of induction

Sextus Empiricus:

When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite.61


The senses, although they are necessary for all our actual knowledge, are not sufficient to give us the whole of it, since the senses never give anything but instances, that is to say particular or individual truths. Now all the instances which confirm a general truth, however numerous they may be, are not sufficient to establish the universal necessity of this same truth, for it does not follow that what happened before will happen in the same way again… And any one who believed that [day must follow night] is a necessary and eternal truth which will last for ever, would likewise be wrong, since we must hold that the earth and even the sun do not exist of necessity, and that there may perhaps come a time when that beautiful star and its whole system will exist no longer, at least in its present form. From which it appears that necessary truths, such as we find in pure mathematics, and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances, nor consequently on the testimony of the senses, although without the senses it would never have occurred to us to think of them.62


Locke divides all arguments into demonstrative and probable. In this view, we must say, that it is only probable that all men must die, or that the sun will rise tomorrow. But to conform our language more to common use, we ought to divide arguments into demonstrations, proofs, and probabilities—by proofs meaning such arguments from experience as leave no room for doubt or opposition.63


The methods by which generalizations are arrived at have received the name “induction”; the methods by which already existing generalizations are employed have received the name “deduction.”66



Even after the observation of the frequent conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience.

– David Hume, in A Treatise of Human Nature, Book I, part 3, §12.

See also:

Uniformity of nature

See also:

Inductive logic


In experimental philosophy, propositions gathered from phenomena by induction should be considered exactly or very nearly true not withstanding any contrary hypothesis, until yet other phenomena make such propositions either more exact or liable to exceptions.69

Price knew the work of Bayes well. Concerning Bayes’ “An Essay towards Solving a Problem in the Doctrine of Chances” (1763),

It was on this essay, and on an Appendix which Price himself authored, that Price drew in fashioning his critique of Hume’s “Of Miracles.” In Four Dissertations, Price gives a reference to Bayes’ paper. But it is doubtful that Hume read the paper, and even if he had it is even more doubtful that Hume would have understood it because he was unfamiliar with the technical developments in the probability calculus.

Is it then fair to use this apparatus as part of a critique of Hume’s argument against miracles? My answer is an unqualified yes. In the Abstract to the Treatise, Hume endorses Leibniz’s complaint that various authors, including Locke, are “too concise when they treat of probabilities, and those other measures of evidence on which life and action intirely depend, and which are our guides even in most of our philosophical speculations.” The Abstract announces that “The author of the treatise of human nature seems to have been sensible of this defect in these philosophers, and has endeavoured, as much as he can, to supply it” (T 647). Of course, by “probabilities” Hume did not have in mind reasoning that proceeds by proving and applying theorems of the probability calculus. But ignorance of the apparatus is no excuse since, for example, before the end of the seventeenth century, there were published attempts to apply the probability calculus to some of the questions at issue in Hume’s essay, such as the effect of multiple witnesses. A number of Hume’s contemporaries, such as Price, understood Hume’s claims as being about quantifiable degrees of belief or credibility, the quantification being subject to the constraints of the probability calculus.72


[I]n Peirce’s phrase, inductions are ampliative. Induction can amplify and generalize our experience, broaden and deepen our empirical knowledge. Deduction on the other hand is explicative. Deduction orders and rearranges our knowledge without adding to its content.73

Peirce on merely the denial of any major failures of induction and the wonderful self-correcting nature of ampliative inference:


I maintain that it has been shown that the modes of inference in question are necessarily valid, whatever the constitution of the universe, so long as it admits of the premises being true. Yet I am willing to concede, in order to concede as much as possible, that when a man draws instances at random, all that he knows is that he tries to follow a certain precept; so that the sampling process might be rendered generally fallacious by the existence of a mysterious and malign connection between the mind and the universe, such that the possession by an object of an unperceived character might influence the will toward choosing it or rejecting it. Such a circumstance would, however, be as fatal to deductive as to ampliative inference. Suppose, for example, that I were to enter a great hall where people were playing rouge et noir at many tables; and suppose that I knew that the red and black were turned up with equal frequency. Then, if I were to make a large number of mental bets with myself, at this table and at that, I might, by statistical deduction, expect to win about half of them, —precisely as I might expect, from the results of these samples, to infer by induction the probable ratio of frequency of the turnings of red and black in the long run, if I did not know it. But could some devil look at each card before it was turned, and then influence me mentally to bet upon it or to refrain therefrom, the observed ratio in the cases upon which I had bet might be quite different from the observed ratio in those cases upon which I had not bet. I grant, then, that even upon my theory some fact has to be supposed to make induction and hypothesis valid processes; namely, it is supposed that the supernal powers withhold their hands and let me alone, and that no mysterious uniformity or adaptation interferes with the action of chance. But then this negative fact supposed by my theory plays a totally different part from the facts supposed to be requisite by the logicians of whom I have been speaking. So far as facts like those they suppose can have any bearing, they serve as major premises from which the fact inferred by induction or hypothesis might be deduced; while the negative fact supposed by me is merely the denial of any major premise from which the falsity of the inductive or hypothetic conclusion could in general be deduced. Nor is it necessary to deny altogether the existence of mysterious influences adverse to the validity of the inductive and hypothetic processes. So long as their influence were not too over whelming, the wonderful self-correcting nature of the ampliative inference would enable us, even if they did exist, to detect and make allowance for them.74


It will appear plausible that this answer was given in the frame of a theory of probability, though the form of this theory is very different from what might be expected. To say that observations of the past are certain, whereas predictions are merely probable, is not the ultimate answer to the question of induction; it is only a sort of intermediate answer, which is incomplete unless a theory of probability is developed that explains what we should mean by “probable” and on what ground we can assert probabilities.82

See also:


See also:



Bhaskar also offers a practical solution to the problem. He argues that the problem of induction only arises if we deny the possibility of a reason for the predicate, located in the enduring nature of something. For example, we know that all emeralds are green, not because we have only ever seen green emeralds, but because the chemical make-up of emeralds insists that they must be green. If we were to change that structure, they would not be green. For instance, emeralds are a kind of green beryl, made green by trace amounts of chromium and sometimes vanadium. Without these trace elements, the gems would be colourless.90


Today abduction remains most commonly understood as induction from characters and extension of a known rule to cover unexplained circumstances.91


The surprising fact, C, is observed;

But if A were true, C would be a matter of course,
Hence, there is reason to suspect that A is true.92


General schema of abduction (or inference to the best explanation, IBE)
Premise 1: A (singular or general) fact E, in need of explanation.
Premise 2: Background knowledge K, which implies for some hypothesis H that H is a sufficiently plausible explanation for E.

Abductive conjecture: H is true.93

Arthur Conan Doyle:

[W]hen you have eliminated the impossible, whatever remains, however improbable, must be the truth.94

See also:

Statistics as a solution to the problem of induction

See also:

Meta-induction as a solution to the problem of induction

Is there a universal scientific method?

First pass


[S]cience is a method of finding things out. This method is based on the principle that observation is the judge of whether something is so or not. All other aspects and characteristics of science can be understood directly when we understand that observation is the ultimate and final judge of the truth of an idea… That is the principle of science. If there is an exception to any rule, and it can be proved by observation, that rule is wrong.105


There are in science a number of technical consequences that follow from the principle of observation as judge. For example, the observation cannot be rough. You have to be very careful. There may have been a piece of dirt in the apparatus that made the color change; it was not what you thought. You have to check the observations very carefully, and then recheck them, to be sure that you understand what all the conditions are and that you did not misinterpret what you did.106


Spin more than one hypothesis, think of all the different ways in which it could be explained. Then think of tests by which you might systematically disprove each of the alternatives. What survives, the hypothesis that resists disproof in this Darwinian selection among ‘multiple working hypotheses,’ has a much better chance of being the right answer than if you had simply run with the first idea that caught your fancy.107

Yes: Models of science


Grosseteste was the first of the Scholastics to fully understand Aristotle’s vision of the dual path of scientific reasoning: generalising from particular observations into a universal law, and then back again from universal laws to prediction of particulars. Grosseteste called this “resolution and composition.” So, for example, looking at the particulars of the moon, it is possible to arrive at universal laws about nature. Conversely once these universal laws are understood, it is possible to make predictions and observations about other objects besides the moon. Grosseteste said further that both paths should be verified through experimentation to verify the principles involved.


Whether someone’s treatment of the cognitions pertaining to reason’s business does or does not follow the secure path of a science—this we can soon judge from the result. If, after many preparations and arrangements have been made, the treatment falters as soon as it turns to its purpose; or if, in order to reach that purpose, it repeatedly has to retrace its steps and enter upon a different path; or, again, if the various collaborators cannot be brought to agree on the manner in which their common aim is to be achieved—then we may rest assured that such an endeavor is still far from having entered upon the secure path of a science, but is a mere groping about. We shall indeed be rendering a service to reason if we can possibly discover that path, even if we should have to give up as futile much that was included in the purpose which we had previously adopted without deliberation.119

Figure 4: Spivak’s figure “intended to evoke thoughts of the scientific method.”

See also:

No: There is no unified “scientific method”

Yes: Rebuttals in favor of scientific method

Anthropology of science

Models in science

What’s a model?


[S]cientist don’t simply deduce experimental/observational consequences; they construct models that ‘mediate’ between theories and the observations. There are a number of reasons why scientists will proceed in this way but one is that theories are often quite complex and difficult to work with. So a scientist may build a simplified model, containing significant idealizations that allow the scientist to ignore certain factors, for example, and [more] easily relate the theory to observations.136


Fermat’s principle (that the light ray passing from one point to another in an optical medium takes the path of stationary optical length) is complementary to Huygens’ principle (that a later wave front emerges as the envelope of wavelets emitted from the present wave front). Both principles are only models of reality, but they are models in the best sense. Both are transcendent fabrications that intuited the results of a later, more fundamental principle (Maxwell’s equations) and gave accurate predictions at the level of physical perception in their time. Without being the full truth by being physically tenable themselves, they fulfilled the tasks for which they were developed and they laid the foundations for more fundamental theories. Light rays do not exist and points along a light wave do not emit light. However, both principles work quite well in the design of optical instruments! In addition, both principles are still interesting now as the mathematical definitions of rays and wave fronts, respectively, although neither fully represents the physical principles of optics.137

Model the theory:

\[ \text{Theory} + \text{Modeling} \longrightarrow \text{Model} \]

Fit the model to the data to make inferences on the theory:

\[ \text{Model} + \text{Data} + \text{Statistical Analysis} \longrightarrow \text{Model(improved)} \longrightarrow \text{Theory(improved)} \]

Models represent theories

Model the theory:

\[ T(\theta_k, \psi_m) \longrightarrow M(X_i | \theta_k, \nu_\ell) \]

Fit the model to the data to make inferences on the theory:

\[ \{X_i\}_j \longrightarrow M(X_{ij} | \theta_k, \nu_\ell) \longrightarrow \hat{\theta}_k \pm \sigma_{\hat{\theta}_k} , \hat{\nu}_\ell \pm \sigma_{\hat{\nu}_\ell} \longrightarrow T(\hat{\theta}_k \pm \sigma_{\hat{\theta}_k}, \psi_m) \]


The very word model implies idealization of the real system and, except just possibly in the more esoteric parts of modern physics … it hardly makes sense to talk of a model being true.138


Morgan and Morrison (1999) rally around the idea that models are instruments that mediate between theories and the world. Models are “autonomous agents” in that they are independent from both theories and their target systems, and it is this independence that allows them to mediate between the two. Theories do not provide us with algorithms for the construction of a model; they are not “vending machines” into which one can insert a problem and a model pops out (Cartwright 1999). The construction of a model often requires detailed knowledge about materials, approximation schemes, and the setup, and these are not provided by the corresponding theory. Furthermore, the inner workings of a model are often driven by a number of different theories working cooperatively. In contemporary climate modeling, for instance, elements of different theories—among them fluid dynamics, thermodynamics, electromagnetism—are put to work cooperatively. What delivers the results is not the stringent application of one theory, but the voices of different theories when put to use in chorus with each other in one model.139

Digression: Some physicists have semantic differences


The demarcation problem


Science is the belief in the ignorance of experts. When someone says “science teaches such and such,” he is using the word incorrectly. Science doesn’t teach it; experience teaches it. If they say to you science has shown such and such, you might ask, “How does science show it—how did the scientists find out—how, what, where?” Not science has shown, but this experiment, this effect, has shown. And you have as much right as anyone else, upon hearing about the experiments (but we must listen to all the evidence), to judge whether a reasonable conclusion has been arrived at.151


My thoughts

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Annotated bibliography

Hume, D. (1748). An Enquiry Concerning Human Understanding.

  • Hume (2007)

1. Of the different Species of Philosophy

2. Of the Origin of Ideas

3. Of the Association of Ideas

4. Sceptical Doubts concerning the Operations of the Understanding

5. Sceptical Solution of these Doubts

6. Of Probability

7. Of the Idea of necessary Connexion

8. Of Liberty and Necessity

9. Of the Reason of Animals

10. Of Miracles

11. Of a particular Providence and of a future State

12. Of the academical or sceptical Philosophy

My thoughts

  • TODO.

Pigliucci, M. (2010). Nonsense on Stilts: How to Tell Science From Bunk.

  • Pigliucci (2010)

My thoughts

  • TODO.

French, S. (2007). Science: Key Concepts in Philosophy.

  • S. French (2007)

1. Introduction

Do not become archivists of facts. Try to penetrate to the secret of their occurrence, persistently search for the laws which govern them.

– Ivan Pavlov

The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.

– W.L. Bragg


  • summarize
  • Feynman
  • Giere
  • Darwin
  • Einstein

2. Discovery

  • Eureka moments
    • Archimedes
    • Kary Mullis - Nobel Prize 1993 for Polymerase Chain Reaction (PCR)
    • “Eureka moments” fit well with the “romantic view” of discovery - Kant
    • “In other words, discovery is ultimately irrational and unanalysable.”
  • Hypothetico-deductive account of discovery
    • Hypotheses arrived at via creative Eureka moments.
    • (Make a number of relevant observations.)
    • Verification via deductive account of observations.
  • Inductive account of discovery
    • (Hypotheses arrived at via creative Eureka moments.)
    • Make a number of relevant observations.
    • Inductively support hypotheses.

3. Heuristics

4. Justification

5. Observation

6. Experiment

7. Realism

8. Anti-realism

9. Independence

10. Gender Bias

My thoughts

  • TODO.

  • TODO.






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  1. Prado (2006).↩︎

  2. Rovelli (2007).↩︎

  3. Whitehead (1978), p. 39.↩︎

  4. Weinberg (2015), p. 76.↩︎

  5. B. Russell (2003), p. 66–67.↩︎

  6. Weinberg (2015), p. 7.↩︎

  7. Weinberg (2015), p. 11.↩︎

  8. Weinberg (2015), p. 13.↩︎

  9. Davis (2015).↩︎

  10. Keoke & Porterfield (2002).↩︎

  11. Sabra (1978), p. 121–2.↩︎

  12. Heraclitus, Fragment 55.↩︎

  13. Descartes (2008).↩︎

  14. Hume (2009).↩︎

  15. Hume (2007).↩︎

  16. Hume (2007), §XII, pp. 109–110.↩︎

  17. Newton (2016).↩︎

  18. Kant (1996).↩︎

  19. Plato, Republic V 477–8, Cooper & Hutchinson (1997), p. 1103–4.↩︎

  20. Plato, Theaetetus 186–7, Cooper & Hutchinson (1997), p. 205–7.↩︎

  21. Plato, Meno 80d, Cooper & Hutchinson (1997), p. 879.↩︎

  22. Plato, Theaetetus 201b–d, Cooper & Hutchinson (1997), p. 222–3.↩︎

  23. Descartes (1996), vol. 10, p. 362.↩︎

  24. Chisholm (1966).↩︎

  25. Nozick (1981).↩︎

  26. Ichikawa & Jenkins (2017).↩︎

  27. Feynman (1998), p. 26–27.↩︎

  28. B. Russell (2009).↩︎

  29. Gettier (1963).↩︎

  30. Clark (1963).↩︎

  31. Martínez-Ordaz (2021).↩︎

  32. Aristotle (2007), book 1, chapter 2.↩︎

  33. Aristotle (1993), book 1, chapter 2.↩︎

  34. Dicker (1991).↩︎

  35. Hume (2007), §XII, p. 120.↩︎

  36. Kant (1996), p. B15–16.↩︎

  37. Kant (1996), p. A6–7, B10–11.↩︎

  38. Kant (1996), p. Bviii–ix.↩︎

  39. Kant (1996), p. B19.↩︎

  40. Moore (1903), p. 6–7.↩︎

  41. Hahn, Neurath, & Carnap (1973), §2.↩︎

  42. Hendricks (2006).↩︎

  43. Hansson & Hendricks (2018).↩︎

  44. Pettigrew & Weisberg (2019).↩︎

  45. Carnap (1937), p. 182.↩︎

  46. Carnap (1937), p. 184.↩︎

  47. Carnap (1950a).↩︎

  48. Awodey & Carus (2007).↩︎

  49. Kripke (1980).↩︎

  50. Papineau (2012).↩︎

  51. Einstein (1922), p. TODO.↩︎

  52. Norton (2017).↩︎

  53. Quine (1951).↩︎

  54. Quine & Carnap (1990).↩︎

  55. G. Russell (2008).↩︎

  56. Juhl & Loomis (2009).↩︎

  57. Weatherson (2017).↩︎

  58. de Swart (2018).↩︎

  59. de Swart (2018), p. 141–2.↩︎

  60. G. Russell (2008), p. xi.↩︎

  61. Sextus Empiricus (1933), p. 283.↩︎

  62. Leibniz (1996), p. TODO.↩︎

  63. First footnote in the essay “On Probability” in Hume (2007), p. 56.↩︎

  64. Hume (2007), p. TODO.↩︎

  65. Weintraub (1995).↩︎

  66. Dewey (1938), p. 419.↩︎

  67. Salmon (1953).↩︎

  68. Gould (1965).↩︎

  69. Newton (2016), p. TODO.↩︎

  70. Aronson (2007), p. 128.↩︎

  71. Mill (1843).↩︎

  72. Earman (2000), p. 25.↩︎

  73. Vickers (2014) (emphasis added).↩︎

  74. Peirce (1883), p. 176–7.↩︎

  75. Carnap (1945).↩︎

  76. Carnap (1950b).↩︎

  77. Carnap (1952).↩︎

  78. Carnap (1966).↩︎

  79. Carnap (1973).↩︎

  80. C. F. French (2015).↩︎

  81. Reichenbach (1938) and Reichenbach (1940). TODO: Break up and go through these references.↩︎

  82. Reichenbach (1968), p. 93-4.↩︎

  83. Aumann (1976).↩︎

  84. Geanakoplos & Polemarchakis (1982).↩︎

  85. Aaronson (2005).↩︎

  86. K. Popper & Miller (1983).↩︎

  87. Eells (1988).↩︎

  88. Sankey (2008), p. 79.↩︎

  89. Douven (2011).↩︎

  90. Bhaskar (2008).↩︎


  92. Ibid.↩︎

  93. Schurz (2019), p. 3.↩︎

  94. Doyle (1890), ch. 6.↩︎

  95. TODO: Find Reichenbach references; could use previous ones.↩︎

  96. Weisberg (2019), Appendix D.↩︎

  97. Salmon (1963), Salmon (1966), Salmon (1967), Salmon (1991). TODO: Break up and go through these references.↩︎

  98. Good (1988).↩︎

  99. TODO: Go through the Howson articles.↩︎

  100. Hacking (2001).↩︎

  101. Huber (2007).↩︎

  102. Rao (1997).↩︎

  103. Earnshaw (2017).↩︎

  104. Schurz (2019).↩︎

  105. Feynman (1998), p. 15–16.↩︎

  106. Feynman (1998), p. 17.↩︎

  107. Sagan (1997), p. 197.↩︎

  108. S. French (2007), p. TODO.↩︎

  109. Nola & Sankey (2007), p. TODO.↩︎

  110. Hempel & Oppenheim (1948).↩︎

  111. S. French (2007), p. TODO.↩︎

  112. K. R. Popper (2002).↩︎

  113. Nola & Sankey (2007), p. TODO.↩︎

  114. Kuhn (1962).↩︎

  115. Ladyman, Ross, Spurrett, & Collier (2007).↩︎

  116. Mayo & Spanos (2011).↩︎

  117. Heesen (2017).↩︎

  118. Bright & Heesen (2023).↩︎

  119. Kant (1996), p. B vii.↩︎

  120. Spivak (2013).↩︎

  121. Spivak (2013), p. 5.↩︎

  122. Feyerabend (1974).↩︎

  123. McComas (1996).↩︎

  124. McComas (2002).↩︎

  125. McComas (2008).↩︎

  126. Allain (2013).↩︎

  127. Blachowicz (2009).↩︎

  128. Blachowicz (2016).↩︎

  129. Nola & Sankey (2007), p. 6.↩︎

  130. Nola & Sankey (2007), p. 5.↩︎

  131. Nola (1999).↩︎

  132. Nola & Sankey (2007), p. TODO.↩︎

  133. Hintikka (1999).↩︎

  134. Schurz (2019), p. X.↩︎

  135. Marks (2009).↩︎

  136. S. French (2007), p. 81.↩︎

  137. Holm (2011), p. xvi.↩︎

  138. Cox (2006), p. 84.↩︎

  139. Frigg & Hartmann (2020).↩︎

  140. Suppes (1961).↩︎

  141. Suppes (1967).↩︎

  142. Bunge (1974), p. 101.↩︎

  143. Box (1976).↩︎

  144. Morgan & Morrison (1999).↩︎

  145. Frigg & Nguyen (2017).↩︎

  146. Feynman (1999), p. 189.↩︎

  147. Bunge (1991).↩︎

  148. Bunge (2011).↩︎

  149. Pigliucci & Boudry (2013).↩︎

  150. Blancke & Boudry (2022).↩︎

  151. Feynman (1999), p. 187.↩︎