The Abduction of the Atom: An Exercise in Hypothesizing" 

JOSEPH A. NOVAK University a/Waterloo 

Keywords: abduction, hypothesis formation, atomic theory, informal logic, scientific 
revolution, conjecture, affirming the consequent, C.S. Peirce. 
Abstract: The paper attempts to schematize, in the form of abductive inferences, the mlljor 
changes in the developing picture of the atom during the modem period of scientific 
investigation. The aim of this presentation is to enable students in logic or the philosophy of 
science to see how a sustained application of abduction might be seen as operative in the 
development of changing conceptions of the atom, a development which may well be seen as a 
scientific revolution. The sustained example also illustrates, in pedagogic fashion, the role of 
images in abduction, the theory-observation distinction, and the analytic-synthetic distinction. 

Part I 

Many current textbooks in informal logic and the philosophy of science devote 
some pages at least to a discussion of the hypothetical method. I This is in marked 
contrast to, and a genuine advance over, earlier textbooks which generally divided 
logical reasoning into deductive and inductive, thereby excluding, or only giving 
marginal consideration to, the method of hypothesis. 2 However, many of the 
examples used to show the workings of "hypothesis-making" have a very limited 
scope and fail to illustrate the complex interplay of moves in the formulation of a 
major theory. The purpose of this paper is to examine the role of hypothetical 
reasoning in the case of a series of developments which led to the popular picture 
of the atom in twentieth century. The advantages of this particular case of 
hypothetical or abductive reasoning are several. First, the discovery took place 
over a period of decades-various proposals were formulated by different 
thinkers in different research areas. This allows one to view the various proposals 
not simply as logically possible alternatives in the quest of an explanation but 
more importantly as genuinely distinct contributions which provide historical 
illustrations of the nuances in the development of an explanation. Second, the 
process of discovery can be seen as closely tied to an imaginative dimension in 
the uncovering of a viable explanation of some data. This aspect of the discussion 
has become more pertinent in the eyes of some current philosophers of science 
and those working in cognitive science.3 Third, the concept of the atom is so 
familiar and universal and allows such easy entertainment of logical possibilities, 
that no special historical explanations need be made to get the example off the 
ground. This example, then, allows for the additional exemplification of the 
purely logical links within a theory, i.e., the consequences that follow from, or are 
in conflict with, a theory. 

Informal Logic Vol. 17, No.2 (Spring 1995): 223.234 © Informal Logic 1995 



The Abduction a/the Atom: An Exercise in Hypothesizing 213 

Part II: Asimov's Summary 

Although some logic texts do employ examples of hypothetical reasoning that 
bear on significant developments in the history of science, many employ 
examples that are brief or disengaged from their contexts. In his work, 
Understanding Physics: The Electron, Proton, and Neutron, Isaac Asimov 
describes in a very few pages4 how our twentieth century conception of the atom 
came to be. His account is lucid and, although it is somewhat oversimplified- as 
all popularizations are--it does accurately describe the basic moves involved in 
the transition from an earlier conception of the atom to the contemporary one. His 
book, then, serves as a good source for an example that can be analyzed by 
students to understand better what is occurring in the hypothetical reasoning and 
other forms of reasoning employed in theory development. Since the paperback 
text is in print, students have ready access not only to something which provides a 
rich example, but also to something which will require them to formulate the 
moves which have occurred in the discovery process. The teacher of logic or 
philosophy of science can request introductory students read the text and then, as 
an exercise, "formalize" the steps that took place the process. What follows in 
Part IV is a proposal to capture at least the chief steps of this process and serve as 
a model for the exercise. 

Part III: Peirce and the Origin of Abduction 

As noted above, several logic texts have already used examples of so-called 
hypothetical reasoning. This type of reasoning departs from the narrower model 
of scientific reasoning which was seen as exhausted by either inductive or 
deductive reasoning or some combination of the two. This narrower model had 
dominated text-books for a long time. Although there seem to be numerous 
adherents of this type of reasoning in current circles, one of the great nineteenth 
century proponents of the reasoning, C.S. Peirce, stood practically alone as the 
proponent of this structure for hypothetical reasoning. In his collected works, he 
is found to have said, "abduction must cover all the operations by which theories 
and conceptions are engendered" (5.590).5 He derives the name abduction from 
what he conjectures was the original Greek in Aristotle. 6 Abduction is the 
process whereby an explanatory hypothesis is formed by suggesting what may be 
the case; it itself cannot be rationally grounded.7 While it is itself not rationally 
grounded, the use of this form of reasoning need not be considered irrational. 
Although Peirce presents the three types of inference in terms of syllogisms,s he 
presumably saw this form of reasoning as being capable of assuming other than a 
syllogistic shape. The present paper will examine the atomic development under 
consideration by formulating various stages in that development by means of the 
propositional calculus. 



214 Joseph A. Novak 

Part IV: The Analysis of the Development of Atomic Theory 

Stage I 

The first stage is that of Dalton's atom. This is the inherited theory (the foil, if 
you will) against which the development will take place. Dalton's atom was 
indivisible and as such it seems that no particles could be emitted from it when 
exposed to a light source, precisely because it had no parts to emit. (See Model I 
in the Appendix.) Yet, the theoretical postulation of indivisibility was confronted 
with the factual evidence of emissions, for when a negatively charged zinc plate 
was exposed to ultraviolet light, there would be an emission of electrons in a 
spark. How is this conflict of theory and fact to be explained? There seem to be 
three options: reject the theory, reject the evidence, or provide an additional 
theoretical dimension to explain the phenomena. It was this third route that was 
adopted and that will be considered in the following logical analysis. The letters 
used will represent the various propositions involved in explaining the initial 
situation and the subsequent theoretical development: 9 

H: the atom is indivisible 
C: electrons exist in the interstices of the atoms 
J: electrons are emitted from a material affected by appropriate 

wavelengths of light 
E: electrons are equally emitted by different wavelengths 

The initial problem can be represented as: 

H~-J 

That is, the theory of the atom's indivisibility should exclude any emissions. This 
is the conflict position which is rectified by the third option of providing an 
additional theoretical component, namely, that there are interstices between the 
atoms in which electrons exist and from which, presumably, they could be emitted 
(C). 10 This can be represented as C ~ J. The hypothetical aspect of reasoning 
which now introduces itself is the (technically invalid) affirmation of the 
consequent which can be symbolized as: 

1). C ~ J 
2). J 
3). C 

Thus, if the compatibility of C with H allows us to assume that C is a consequent 
of H, then we can say that H -* C. Having supposed that C ~ J, it seems 
possible to say that C -* E as well. The fact of the matter is, however, that 
electrons are not equally emitted by different wavelengths of light.1I This causes 
problems for our initial hypothesis (H), as is clear from the following argument: 

1). H ~ C assumption 
2). C ~ E assumption 
3). -E factual datum 
4). -C Modus Tollens 1,2 
5). -H Modus Tollens 1,4 



The Abduction of the Atom: An Exercise in Hypothesizing 215 

Thus it becomes clear that Dalton's atom cannot explain the emission of 
electrons even on the supposition that they exist in the interstices between atoms. 
Hence, one must suppose that the indivisible ballbearing model of the atom 
(Modell) needs revision. 

Stage II 

The second stage is that of Thomson's atom. Given the assumption that 
negatively charged particles (electrons) existed somehow in association with the 
atom, and given that they did not exist in the interstices of atoms, the need for a 
new model arises. Thomson provided this by suggesting the atom was a sphere in 
which a sufficient number of electrons were embedded to neutralize it. (See 
Model II in the Appendix.) Thomson's proposal was prompted by some 
additional considerations. He had to explain first, why the overall charge of the 
atoms was neutral and second, why only negatively charged particles were 
emitted. 12 Clearly, at first blush, the image of a sphere with embedded electrons 
(similar to a muffin containing chocolate chips) seemed to be one that contained 
the answers. 

The theory allowed the emission of electrons to be easily explained, whether 
they were emitted as the result of light (earlier designated as J) or heat. n The 
theory has the additional explanatory power of rendering the following two facts 
intelligible: first, the fact that only negative particles are emitted and not positive 
ones; second, the fact of ionization, namely, the existence of both (a) positive ions 
and (b) negative ions. Since the positive component of the atom was too great to 
be emitted, only electrons would be emitted under the appropriate stimulus. 
Since the subtraction or addition of electrons would allow for a change in the 
charge of the atom, the process of ionization could be explained. 

Consider the following designation for the elements in the theory process: 
I: The atom has a positively charged solid center (It) and has 
embedded electrons (h). 
P: Positive particles are not emitted. 
K: Ionization occurs for an atom. 
L: There is a loss or gain of electrons. 

Thomson's reasoning process, accomplished by means of affirming the 
consequent, could be represented as the following: 

1). 1 ~ P assumption 
2). P factual datum 
3). I Affirming the Consequent 1,2 

However, it is not this sole instance of affirming the consequent that seems to be 
operative in Thomson's theorizing. He also seems to have the following at work 

1). I ~ L assumption 
2). L ~ K assumption 
3). I ~ K Syllogism 1,2 
4). K factual datum 

5). I Affirming the Consequent 3,4 



216 Joseph A. Novak 

It is not always easy to determine which aspects of a theory were used as initial 
data to be explained (exp/ananda) and which were derived as subsequent 
consequences predictable by the theory (consequentia) as, for instance, ionization 
which might seem predictable on a certain model. This only a careful historical 
study would reveal in each case. 

Thomson's picture of the atom as the "raisins in a pound cake" style of 
atom l4 can then be called Model II. However, this model, as did Model I, ran into 
a difficulty and the difficulty resulted in the rejection of the theory. Lenard was 
confronted by the fact that a stream of particles, rays of a negative charge 
(cathode rays) could pass through small thicknesses of matter without much 
scattering. This fact was difficult to reconcile with the "pound cake" model on 
which there would have to be significant scattering, i.e., the rays would have to 
wind their ways between the relatively large particles in which electrons were 
embedded. 15 Thus, if 

R: Cathode rays undergo considerable scattering after passing 
through matter. 

Lenard supposes, given Model II, that: 
I ~ R. 

Since, however, the scattering predictable on the basis of Thomson's theory does 
not occur, the theory falters: 

Stage III 

1). I ~ R 
2). -R 
3). -I 

assumption 
factual datum 
Modus Tollens 1,2 

Lenard then searches for a new explanatory hypothesis which wiII account for the 
lack of scattering. He proposes a picture of the atom in which there is little solid 
mass, mainly empty space, and in which particles of opposed charge are paired 
off to yield an overall neutral charge for the atom. (See Model III in the 
Appendix.) This would allow for the non-scattered emissions of negative 
charge. 16 Once again, one is presented with a theory that seems to integrate into a 
coherent explanatory whole disparate facts needing explanation, a theory that 
seems to account for not a single exp/anandum but for multiple exp/ananda. His 
theory could be expressed as: 

U: The atom is composed of mainly empty space (U I ) and 
constituted of pairs of equal particles of opposing charge (Uz). 

Since the failure of rays to scatter is compatible with this hypothesis, one can go 
on to affirm that U ~ -R. Hence, the abductive form of Lenard's reasoning can 
be schematized as the previous cases: 

I). U ~ -R assumption 
2). -R factual datum 
3). U Affirming the Consequent 1,2 



The Abduction of the Atom: An Exercise in Hypothesizing 217 

Lenard's understanding of the atom's makeup can be envisioned as paired 
battery tenninals and will be designated as Model III. However, there is a 
problem with this model as well. Given the equal balancing of the positive and 
negative particles within the atom, it seems logical that the positive particles 
should be emitted as charged rays as well (anode rays). However, none such were 
detectable. Let the release be represented propositionally as, 

T: Anode rays are released. 

Since this is compatible with the theory U, one would then conjecture further, as 
in the cases above, that U ~ T. Of course, there is no need to argue that this 
conditional cannot itself be derived from some other propositions; quite obviously 
other intuitions are at work to show that T will be implied by U (e.g., positive 
particles are not somehow held in place by forces other than those which hold 
negative ones, positive particles are capable of movement, etc.). Now it becomes 
clear that the rejection of the theory will follow the same pattern as noted above 
in the modus tollens type of argument: 

1). U ~ T assumption 
2). -T factual observation 
3). -U Modus Tollens 1,2 

Stage IV 

The fourth stage is that of Rutherford's atom. In looking at Lenard's theory, 
Rutherford realized that it did account for some of the phenomena, i.e., the atom 
seemed to be largely empty. He realized that this aspect of the theory was correct, 
for he had perfonned an experiment with alpha particles that seemed to 
substantiate it. He bombarded some metal with these particles and they passed 
through it-something which would not have been possible on a model of a 
largely solid atom.'7 Thus, in rejecting U it is important to remember that U is a 
compound proposition; the negation of merely one of its components is sufficient 
to warrant the rejection of the whole. It seems that it is Uz that is the 
objectionable component. Generally, of course, it is possible that both are at 
fault, but here, on account of the experiment, not only does U, not have to be 
rejected, but it also seems further confirmed. For it is clear from the propositional 
calculus that by DeMorgan's law, if 

U=U"Uz 
then 

-U -U, V -Uz 

As far as the truth value of U2, Rutherford did seem to have an additional reason 
why it was false. As he looked at the fogging on the plate caused by the 
bombardment, he noticed that it was not as sharp as it would have been if the 
alpha particles encountered no resistance. Moreover, the resistance seemed to be 
great enough to cause a considerable deflection of some of the particles. It 
appeared, then, that there was a sufficiently large component of the atom that was 
giving rise to this deflection.'s Thus, if the atom were composed of binary pairs of 



218 JosephA. Novak 

particles (V2) as on the Lenard model, there would be no structure to cause the 
fogging. Thus, if 

F: Alpha bombardment causes diffuse fogging on the photographic 
plate. 

then the following reasoning can take place: 
1). U2 -+ -F assumption 
2). F factual observation 
3). -V2 Modus Tollens 1,2 

However, this does not leave Rutherford with a new theory as yet. He must 
develop a positive alternative to the previous ones. His theory will incorporate 
elements of both the Thomson and Lenard models. From Thomson he will adopt 
the notion that the atom has a positively charged center (11) and from Lenard he 
will accept the notion that the atom is largely empty space (VI)' although these 
will be accepted with some modification. The picture of the atom that he draws 
is that of the nuclear atom: a solid mass surrounded by an electron cloud. Atoms 
would then be "fluffY balls of foam with a lead pellet at the center of each."19 
This is Model IV of the atom. (See Model IV in the Appendix.) His own 
conception can perhaps be expressed in 

s: The atom is a system with a dense nucleus and surrounding 
electron(s). 

Although it is the case that the bombardment experiment can be seen as providing 
the "evidence" for the theory, i.e., 

1). S -+ F assumption 
2). F factual datum 
3). S Affirming the Consequent 1,2 

it is possible to view this hypothesis as being a comprehensive one which 
includes not only elements (albeit sometimes transformed) of the older theories 
but also some of the data which they tried to explain. That is, not only is it the 
case that 

S -+ II' VI 
but it is also true that 

S -+ (J . p. -R· -T). 

All members of this conjunct could then be seen as together constituting evidence 
for an affirming of the antecedent S. In this way, the comprehensive explanatory 
power of the Rutherford atom becomes apparent. 

Part V: Conclusion 

As mentioned at the start of this piece, the pedagogic advantages of considering 
this particular development in the history of science are several and benefit both 
students in logic and students in the philosophy of science. First of all, since the 
transition from the Dalton atom to the Rutherford atom is not a "quantum leap" 
(no pun intended), the student is presented with a picture of the development of 
science that is more detailed than many of the examples provided in logic texts 



The Abduction o/the Atom: An Exercise in Hypothesizing 219 

(the phlogiston example, the Semmelweis example, etc.}.20 This can be used to 
show that the "revolutions" of science are often not as dramatic as portrayed by 
some authors. This may well have ramifications, of course, regarding the 
adoption of a realist vs. an instrumentalist view of scientific knowledge-at least 
one can use the historical illustration to argue the pros or cons of each position. 
Second, the distinction between experimental observations and theoretical 
speculations can be used to illustrate the differences which some philosophers 
have argued exist between theoretical statements and observation statements. Of 
course, one need not maintain that the distinction is hard and fast; today not many 
would hold for such a clear division of the two. Indeed, the example can be 
discussed to illustrate the theoretical aspects of observation statements. Third, the 
use of images in connection with theorizing becomes obvious in this presentation. 
Each model contains an image that not only was fuelled by experimental results 
but which also helped interpret the results and even gave rise to the prediction of 
other characteristics. Although the use of images in reasoning might be viewed 
as having little importance by some philosophers, especially those bent on 
developing eliminative materialist models of mind, other philosophers are now 
currently revaluing the role of images and the imagination in reasoning. Fourth, 
the developmental process can contribute, at least indirectly, to an understanding 
of the distinction between analytic and synthetic types of proposition (another 
distinction not without its opponents). This is linked to the previous point, for the 
successive images proposed arise from an analysis of the mere possibilities 
available, given the evidence. For instance, the question about the release of 
positive particles in Lenard's model, does not arise out of any empirical data but 
rather arises out of a logical possibility given the nature of the binary model itself. 
Similarly, the conjecture that electrons exist in the interstices of the atoms rather 
than within them results from a juxtaposing of logical options (something is 
"inside" or "outside"). The independence of analytic propositions from 
experience might be better illustrated in this way. 

In summation, one can say that the development in atomic theory has 
perhaps been overlooked as an instance of a scientific revolution largely because 
it is, as many a recent political upheaval on the planet has been, "a quiet 
revolution". It remains nonetheless--or, perhaps, even on account of this 
characteristic--a multifaceted exemplification of aspects of reasoning that is 
pedagogically useful for both students in logic and students in philosophy of 
science. 



220 Joseph A. Novak 

Model I 
Dalton's Atom 

ModelllI 
Lenard's Atom 

Appendix· Illustrations 

Model n 
Thomson's Atom 

Model IV 
Rutherford's Atom 



The Abduction o/the Atom: An Exercise in Hypothesizing 221 

• My thanks to P. Tenti and F. McCourt, J. van Evra, and R. Holmes of the University of 
Waterloo for their helpful criticisms. I would also like to thank L. Powers for his work as 
commentator on this paper. 

1 M. Salmon, Introduction to Logic and Critical Thinking (New York: Harcourt Brace 
Jovanovich, 1989); P. Churchill, Becoming Logical (New York: St. Martin's Press, 1986), c. 
11, pp. 370-408. Often textbooks employ the same examples; of some of those common to 
the logic texts, R. Giere in his work Understanding Scientific Reasoning (New York: Holt, 
Rinehart, and Winston, 1979) c. 6, pp. 84-115 seems to be the source. 

2 This method is also sometimes designated the "hypothetico-deductive method." One need 
only look at the following who omit or marginalize it: R. Purtill, Logic: Argument, 
Refutation, and Proof (New York: Harper & Row, 1979); R. B. Angell, in his Reasoning and 
Logic (New York: Appleton Century Crofts, 1964) holds to the inductive-deductive division 
in his text, but he does give some consideration to cases of hypothetical reasoning; 1. Copi 
and C. Cohen in their Introduction to Logic (New York, 1990), 8th ed. follow a middle 
ground-while holding to the basic deduction-induction distinction by giving them separate 
treatment in Part Two and Part Three respectively of the book, they do include the treatment 
of hypothesis under Part Three. 

3 Consider for instance A. Goldman who notes this feature in his book Philosophical 
Applications of Cognitive Science (Oxford: Westview Press, 1993), pp. 51-55. 

4 "Chapter Four: Electrons within Atoms", (New York: Signet Books, 1969). 

5 References are to the Collected Papers of Charles Sanders Peirce (Cambridge: Belknap Press 
of Harvard University Press, 1960). 

6 Section 5.144 "its replacement by a wrong word by his [Aristotle's] first editor, the stupid 
{Apellicon}, has completely altered the sense of the chapter on Abduction." He continues 
that Aristotle was trying to formulate "that mode of inference which I call by the otherwise 
quite useless name of Abduction--a word which is only employed in logic to translate the 
[apagoge] of that chapter." 

7 Section 5.172: "It is the only logical operation which introduces any new idea. . .. No reason 
whatever can be given for it ... and it needs no reason, since it merely offers suggestions." 

8 See sections 2.619-.644; 2.508-.511. 

9 Powers has proposed a more elaborate formulation for the following by utilizing a prior 
hypothesis H I which states that there are no smaller particles involved than the atoms. 
However, given that the atoms are the ultimate indivisibles on the physical level, the 
additional hypothesis seems to me unnecessary. 

10 I should note here that the assumptions are twofold: the existence of the electrons in the 
interstices, as well as their ability to be emitted. These could also be invoked to explain to 
students the complexity of the reasoning that actually does take place and the frequent 
enthymematic structure of our reasoning. 

II Asimov, p. 55: "Philipp Lenard had observed that the energy with which the electrons were 
ejected depended on the frequency of light, and that light of less than a certain frequency (the 
threshold value) did not eject electrons. . .. It seems only sensible to consider something 
always present near the atom, always bound to the atom with a characteristic force, to be part 
of the atom." 

12 Asimov writes, "The atoms were electrically neutral; if negatively-charged electrons existed 
about or within the atom, there had to be a positive charge somewhere to neutralize the 
negative charge of the electrons. If so where was it? Why didn't light ever bring about the 
ejection of very light positively-charged particles? Why were there only cathode rays, never 
analogous anode rays?" (p. 56). 



222 Joseph A. Novak 

13 Asimov, p. 57: "Light quanta would jar loose one or more of these electrons, but could 
scarcely budge the large atom-sphere of positive charge. Again, the heat in a vacuum tube 
filament would indeed 'boil off' electrons, for as atoms vibrated more strongly with rising 
temperature ... the electrons would be jarred loose while the atom itself would be essentially 
unaffected." 

14 This is Asimov's image, p. 57. 

IS Asimov, p.57: "To be sure, the electrons making up the cathode rays were very small and 
might be pictured as worming their ways between the atoms. If so, they would most likely 
emerge badly scattered." 

16 Asimov, p. 5: " ... cathode rays passed through small thicknesses of matter still travelling in 
an essentially parallel beam, as though they had passed through atoms without much 
interference. " 

17 "The stream of alpha particles passed right through the gold leaf as though it were not there 
and fogged the photographic plate behind it. . .. [The gold leaf had] a thickness of 20,000 
atoms .... [This] was strongly in favor of Lenard's notion ofan empty atom .... " p. 58. 

IS"In fact, Rutherford was able to show that some were deflected more than slightly! About one 
alpha particle out of every 8000 was deflected through a right angle or even more .... For an 
alpha particle to be set back on its heels, it must at the very least meet something nearly as 
massive as itself---something, in short ofatom-sized mass." 

19 Asimov, p. 58. 

20 These are found in the texts noted in footnote 1. 

JOSEPH A. NOVAK 
DEPARTMENT OF PHILOSOPHY 

UNIVERSITY OF WATERLOO 
WATERLOO, ONTARIO N2L 3G J 

o