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Criminal Law/Argument by Analogy could be deductively valid?


QUESTION: Respected Jeffrey,
  Greetings! Hope things good at your end.I just came across this intricate subject as Argument by Analogy.With determined attitude i sorted of out every possible source to comprehend the concept of analogical argument being considered as deductively valid.Unfortunately i failed to understand the concept.
Can you explain me with example of how analogical arguments can be deductively valid elucidating with easy explanations??



ANSWER: Bilal,

Analogical reasoning is extremely common, both in philosophy as well as in more ordinary contexts. Usually, people employ analogies to help establish a relatively controversial claim. They do so by trying to establish a similar claim in a less controversial case, which they claim is analogous.  Now, it should be noted that analogical arguments ARE NOT deductively valid. The premises can be true without the conclusion being true. However, we ordinarily think that a good argument by analogy gives us strong reason to believe the conclusion.

So, the set-up for any argument by analogy is always the same. First, an analogy is drawn between the "controversial" case and the "uncontroversial" case. Second, a claim is made about the "uncontroversial" case.

"Valid" Arguments: An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.

"Sound" Arguments:  An argument is sound if and only if it is valid and the premises are true.

So, there are two ways for an argument to be bad:

   1. One (or more) of the premises could be false
   2. The premises could fail to support the conclusion(There could be some gap in the reasoning).

Please read the article "Analogy and Analogical Reasoning" infra.  It is very illuminating and should answer your question and further queries in detail.

Best Regards

Stanford Encyclopedia of Philosophy
Analogy and Analogical Reasoning
First published Tue Jun 25, 2013

An analogy is a comparison between two objects, or systems of objects, that highlights respects in which they are thought to be similar. Analogical reasoning is any type of thinking that relies upon an analogy. An analogical argument is an explicit representation of a form of analogical reasoning that cites accepted similarities between two systems to support the conclusion that some further similarity exists. In general (but not always), such arguments belong in the category of inductive reasoning, since their conclusions do not follow with certainty but are only supported with varying degrees of strength. Here, ‘inductive reasoning’ is used in a broad sense that includes all inferential processes that “expand knowledge in the face of uncertainty” (Holland et al. 1986: 1), including abductive inference.

Analogical reasoning is fundamental to human thought and, arguably, to some nonhuman animals as well. Historically, analogical reasoning has played an important, but sometimes mysterious, role in a wide range of problem-solving contexts. The explicit use of analogical arguments, since antiquity, has been a distinctive feature of scientific, philosophical and legal reasoning. This article focuses primarily on the nature, evaluation and justification of analogical arguments. Related topics include metaphor, models in science, and precedent and analogy in legal reasoning.

   1. Introduction: the many roles of analogy
   2. Analogical arguments
       2.1 Examples
       2.2 Characterization
       2.3 Plausibility
       2.4 Analogical inference rules?
   3. Criteria for evaluating analogical arguments
       3.1 Commonsense guidelines
       3.2 Aristotle's theory
       3.3 Material criteria: Hesse's theory
       3.4 Formal criteria: the structure-mapping theory
       3.5 Other theories
   4. Philosophical foundations for analogical reasoning
       4.1 Deductive justification
       4.2 Inductive justification
       4.3 A priori justification
       4.4 Pragmatic justification
   5. Analogy and confirmation
   Academic Tools
   Other Internet Resources
       Online Manuscript
   Related Entries

1. Introduction: the many roles of analogy

Analogies are widely recognized as playing an important heuristic role, as aids to discovery. They have been employed, in a wide variety of settings and with considerable success, to generate insight and to formulate possible solutions to problems. According to Joseph Priestley, a pioneer in chemistry and electricity,

   analogy is our best guide in all philosophical investigations; and all discoveries, which were not made by mere accident, have been made by the help of it. (1769/1966: 14)

Priestley may be over-stating the case, but there is no doubt that analogies have suggested fruitful lines of inquiry in many fields. Because of their heuristic value, analogies and analogical reasoning have been a focus of AI research.

Analogies have a related (and not entirely separable) justificatory role. This role is most obvious where an analogical argument is explicitly offered in support of some conclusion. The intended degree of support for the conclusion can vary considerably. At one extreme, these arguments can be demonstrative. For example (Example 1), hydrodynamic analogies exploit mathematical similarities between the equations governing ideal fluid flow and torsional problems. To predict stresses in a planned structure, one can construct a fluid model, i.e., a system of pipes through which water passes (Timoshenko and Goodier 1970). Here we have a special type of analogy, nomic isomorphism (Hempel 1965): the physical laws governing the two systems have identical mathematical form. Within the limits of idealization, the analogy allows us to make demonstrative inferences from a measured quantity in the fluid model to the analogous value in the torsional problem. In practice, there are numerous complications (Sterrett 2006).

At the other extreme, an analogical argument may provide very weak support for its conclusion, establishing no more than minimal plausibility. Consider (Example 2) Thomas Reid's (1785) argument for the existence of life on other planets (Stebbing 1933; Mill 1843/1930; Robinson 1930; Copi 1961). Reid notes a number of similarities between Earth and the other planets in our solar system: all orbit and are illuminated by the sun; several have moons; all revolve on an axis. In consequence, he concludes, it is “not unreasonable to think, that those planets may, like our earth, be the habitation of various orders of living creatures” (1785: 24).

Such modesty is not uncommon. Often the point of an analogical argument is just to persuade people to take an idea seriously. For instance (Example 3), Darwin takes himself to be using an analogy between artificial and natural selection to argue for the plausibility of the latter:

   Why may I not invent the hypothesis of Natural Selection (which from the analogy of domestic productions, and from what we know of the struggle of existence and of the variability of organic beings, is, in some very slight degree, in itself probable) and try whether this hypothesis of Natural Selection does not explain (as I think it does) a large number of facts…. (Letter to Henslow, May 1860 in Darwin 1903)

Here it appears, by Darwin's own admission, that his analogy is employed to show that the hypothesis is probable to some “slight degree” and thus merits further investigation.

Sometimes analogical reasoning is the only available form of justification for a hypothesis. The method of ethnographic analogy is used to interpret

   the nonobservable behaviour of the ancient inhabitants of an archaeological site (or ancient culture) based on the similarity of their artifacts to those used by living peoples. (Hunter and Whitten 1976: 147)

For example (Example 4), Shelley (1999, 2003) describes how ethnographic analogy was used to determine the probable significance of odd markings on the necks of Moche clay pots found in the Peruvian Andes. Contemporary potters in Peru use these marks (called sígnales) to indicate ownership; the marks enable them to reclaim their work when several potters share a kiln or storage facility. Analogical reasoning may be the only avenue of inference to the past in such cases, though this point is subject to dispute (Gould and Watson 1982; Wylie 1982, 1985).

As philosophers and historians such as Kuhn (1996) have repeatedly pointed out, there is not always a clear separation between the two roles that we have identified, discovery and justification. Indeed, the two functions are blended in what we might call the programmatic (or paradigmatic) role of analogy: over a period of time, an analogy can shape the development of a program of research. For example (Example 5), an ‘acoustical analogy’ was employed for many years by certain nineteenth-century physicists investigating spectral lines. Discrete spectra were thought to be

   completely analogous to the acoustical situation, with atoms (and/or molecules) serving as oscillators originating or absorbing the vibrations in the manner of resonant tuning forks. (Maier 1981: 51)

Guided by this analogy, physicists looked for groups of spectral lines that exhibited frequency patterns characteristic of a harmonic oscillator. This analogy served not only to underwrite the plausibility of conjectures, but also to guide and limit discovery by pointing scientists in certain directions.

In some cases, a programmatic analogy culminates in the theoretical unification of two different areas of inquiry. Descartes's (1637/1954) correlation between geometry and algebra, for example (Example 6), provided methods for systematically handling geometrical problems that had long been recognized as analogous. A very different relationship between analogy and discovery exists when a programmatic analogy breaks down, as was the ultimate fate of the acoustical analogy. That atomic spectra have an entirely different explanation became clear with the advent of quantum theory. In this case, novel discoveries emerged against background expectations shaped by the guiding analogy. There is a third possibility: an unproductive or misleading programmatic analogy may simply become entrenched and self-perpetuating as it leads us to “construct… data that conform to it” (Stepan 1996: 133). Arguably, the danger of this third possibility provides strong motivation for developing a critical account of analogical reasoning and analogical arguments.

Analogical reasoning goes well beyond the three roles already identified (heuristic, justificatory and programmatic). For example, analogies are often pedagogically useful. In general, analogical cognition, which embraces all cognitive processes involved in discovering, constructing and using analogies, is much broader than analogical reasoning (Hofstadter 2001). Understanding these processes is an important objective of current cognitive science research, and an objective that generates many excellent questions. How do humans identify analogies? Do nonhuman animals use analogies and analogical reasoning in ways similar to humans? How do analogies and metaphors influence concept formation?

This entry, however, concentrates specifically on analogical arguments. Specifically, it focuses on three central epistemological questions:

   What criteria should we use to evaluate analogical arguments?
   What philosophical justification can be provided for analogical inferences?
   How do analogical arguments fit into a broader inferential context (i.e., how do we combine them with other forms of inference)?

Following a preliminary discussion of the basic structure of analogical arguments, the entry reviews selected attempts to provide answers to these three questions. To find such answers would constitute an important first step towards understanding the nature of analogical reasoning. To isolate these questions, however, is to make the non-trivial assumption that there can be a theory of analogical arguments—an assumption which, as we shall see, is attacked in different ways by both philosophers and cognitive scientists.
2. Analogical arguments
2.1 Examples

Analogical arguments vary greatly in subject matter, strength and logical structure. In order to appreciate this variety, it is helpful to increase our stock of examples. First, a geometric example:

Example 7 (Rectangles and boxes). Suppose that you have established that of all rectangles with a fixed perimeter, the square has maximum area. By analogy, you conjecture that of all boxes with a fixed surface area, the cube has maximum volume.

Two examples from the history of science:

Example 8 (Morphine and meperidine). In 1934, the pharmacologist Schaumann was testing synthetic compounds for their anti-spasmodic effect. These drugs had a chemical structure similar to morphine. He observed that one of the compounds—meperidine, also known as Demerol—had a physical effect on mice that was previously observed only with morphine: it induced an S-shaped tail curvature. By analogy, he conjectured that the drug might also share morphine's narcotic effects. Testing on rats, rabbits, dogs and eventually humans showed that meperidine, like morphine, was an effective pain-killer (Lembeck 1989: 11; Reynolds and Randall 1975: 273).

Example 9 (Priestley on electrostatic force). In 1769, Priestley suggested that the absence of electrical influence inside a hollow charged spherical shell was evidence that charges attract and repel with an inverse square force. He supported his hypothesis by appealing to the analogous situation of zero gravitational force inside a hollow shell of uniform density.

Finally, an example from legal reasoning:

Example 10 (Duty of reasonable care). In a much-cited case (Donoghue v. Stevenson 1932 AC 562), the United Kingdom House of Lords found the manufacturer of a bottle of ginger beer liable for damages to a consumer who became ill as a result of a dead snail in the bottle. The court argued that the manufacturer had a duty to take “reasonable care” in creating a product that could foreseeably result in harm to the consumer in the absence of such care, and where the consumer had no possibility of intermediate examination. The principle articulated in this famous case was extended, by analogy, to allow recovery for harm against an engineering firm whose negligent repair work caused the collapse of a lift (Haseldine v. CA Daw & Son Ltd. 1941 2 KB 343). By contrast, the principle was not applicable to a case where a workman was injured by a defective crane, since the workman had opportunity to examine the crane and was even aware of the defects (Farr v. Butters Brothers & Co. 1932 2 KB 606).
2.2 Characterization

What, if anything, do all of these examples have in common? We begin with a simple, quasi-formal characterization (versions may be found in most elementary critical thinking texts, e.g., Copi and Cohen 2005). An analogical argument has the following form:

   S is similar to T in certain (known) respects.
   S has some further feature Q.
   Therefore, T also has the feature Q, or some feature Q* similar to Q.

(1) and (2) are premises. (3) is the conclusion of the argument. The argument form is inductive; the conclusion is not guaranteed to follow from the premises.

S and T are referred to as the source domain and target domain, respectively. A domain is a set of objects, properties, relations and functions, together with a set of accepted statements about those objects, properties, relations and functions. More formally, a domain consists of a set of objects and an interpreted set of statements about them. The statements need not belong to a first-order language, but to keep things simple, any formalizations employed here will be first-order. We use unstarred symbols (a, P, R, f) to refer to items in the source domain and starred symbols (a*, P*, R*, f*) to refer to corresponding items in the target domain. In Example 9, the source domain items pertain to gravitation; the target items pertain to electrostatic attraction.

Formally, an analogy between S and T is a one-to-one mapping between objects, properties, relations and functions in S and those in T. Not all of the items in S and T need to be placed in correspondence. Commonly, the analogy only identifies correspondences between a select set of items. In practice, we specify an analogy simply by indicating the most significant similarities (and sometimes differences).

We can improve on this preliminary characterization of the argument from analogy by introducing the tabular representation found in Hesse (1966). We place corresponding objects, properties, relations and propositions side-by-side in a table of two columns, one for each domain. For instance, Reid's argument (Example 2) can be represented as follows (using ⇒ for the analogical inference):

   ↑   Earth (S)      Mars (T)
   vertical   Known similarities:
   orbits the sun    ← horizontal →    orbits the sun
   has a moon   has moons
   revolves on axis   revolves on axis
   subject to gravity   subject to gravity
   Inferred similarity:
   ↓   supports life   ⇒   may support life

Hesse introduced useful terminology based on this tabular representation. The horizontal relations in an analogy are the relations of similarity (and difference) in the mapping between domains, while the vertical relations are those between the objects, relations and properties within each domain. The correspondence (similarity) between earth's having a moon and Mars' having moons is a horizontal relation; the causal relation between having a moon and supporting life is a vertical relation within the source domain (with the possibility of a distinct such relation existing in the target as well).

In an earlier discussion of analogy, Keynes (1921) introduced some terminology that is also helpful.

Positive analogy.
   Let P stand for a list of accepted propositions P1, …, Pn about the source domain S. Suppose that the corresponding propositions P*1, …, P*n, abbreviated as P*, are all accepted as holding for the target domain T, so that P and P* represent accepted (or known) similarities. Then we refer to P as the positive analogy.

Negative analogy.
   Let A stand for a list of propositions A1, …, Ar accepted as holding in S, and B* for a list B1*, …, Bs* of propositions holding in T. Suppose that the analogous propositions A* = A1*, …, Ar* fail to hold in T, and similarly the propositions B = B1, …, Bs fail to hold in S, so that A, ~A* and ~B, B* represent accepted (or known) differences. Then we refer to A and B as the negative analogy.

Neutral analogy.
   The neutral analogy consists of accepted propositions about S for which it is not known whether an analogue holds in T.

Finally we have:

Hypothetical analogy.
   The hypothetical analogy is simply the proposition Q in the neutral analogy that is the focus of our attention.

These concepts allow us to provide a characterization for an individual analogical argument that is somewhat richer than the original one.

   Augmented tabular representation
   P   P*    [positive analogy]
   A   ~A*   [negative analogy]
   ~B   B*
      Q*   (plausibly)

An analogical argument may thus be summarized:

   It is plausible that Q* holds in the target because of certain known (or accepted) similarities with the source domain, despite certain known (or accepted) differences.

In order for this characterization to be meaningful, we need to say something about the meaning of ‘plausibly.’ To ensure broad applicability over analogical arguments that vary greatly in strength, we interpret plausibility rather liberally as meaning ‘with some degree of support’. In general, judgments of plausibility are made after a claim has been formulated, but prior to rigorous testing or proof. The next sub-section provides further discussion.

Note that this characterization is incomplete in a number of ways. The manner in which we list similarities and differences, the nature of the correspondences between domains: these things are left unspecified. Nor does this characterization accommodate reasoning with multiple analogies (i.e., multiple source domains), which is ubiquitous in legal reasoning and common elsewhere. To characterize the argument form more fully, however, is not possible without either taking a step towards a substantive theory of analogical reasoning or restricting attention to certain classes of analogical arguments.
2.3 Plausibility

To say that a hypothesis is plausible is to convey that it has epistemic support: we have some reason to believe it, even prior to testing. An assertion of plausibility within the context of an inquiry typically has pragmatic connotations as well: to say that a hypothesis is plausible suggests that we have some reason to investigate it further. For example, a mathematician working on a proof regards a conjecture as plausible if it “has some chances of success” (Polya 1954 (v. 2): 148). On both points, there is ambiguity as to whether an assertion of plausibility is categorical or a matter of degree. These observations point to the existence of two distinct conceptions of plausibility, probabilistic and modal, either of which may reflect the intended conclusion of an analogical argument.

On the probabilistic conception, plausibility is naturally identified with rational credence (rational subjective degree of belief) and is typically represented as a probability. A classic expression may be found in Mill's analysis of the argument from analogy in A System of Logic:

   There can be no doubt that every resemblance [not known to be irrelevant] affords some degree of probability, beyond what would otherwise exist, in favour of the conclusion. (Mill 1843/1930: 333)

In the terminology introduced in §2.2, Mill's idea is that each element of the positive analogy boosts the probability of the conclusion. Contemporary ‘structure-mapping’ theories (§3.4) employ a restricted version: each structural similarity between two domains contributes to the overall measure of similarity, and hence to the strength of the analogical argument.

On the alternative modal conception, ‘it is plausible that p’ is not a matter of degree. The meaning, roughly speaking, is that there are sufficient initial grounds for taking p seriously, i.e., for further investigation (subject to feasibility and interest). Informally: p passes an initial screening procedure. There is no assertion of degree. Instead, ‘It is plausible that’ may be regarded as a modal epistemic operator that aims to capture a notion, prima facie plausibility, that is somewhat stronger than ordinary epistemic possibility. The intent is to single out p from an undifferentiated mass of ideas that remain bare epistemic possibilities. To illustrate: in 1769, Priestley's argument (Example 9), if successful, would establish the prima facie plausibility of an inverse square law for electrostatic attraction. The set of epistemic possibilities—hypotheses about electrostatic attraction compatible with knowledge of the day—was much larger. Individual analogical arguments in mathematics (such as Example 7) are almost invariably directed towards prima facie plausibility.

The modal conception figures importantly in some discussions of analogical reasoning. The physicist N. R. Campbell (1957) writes:

   But in order that a theory may be valuable it must … display an analogy. The propositions of the hypothesis must be analogous to some known laws…. (1957: 129)

Commenting on the role of analogy in Fourier's theory of heat conduction, Campbell writes:

   Some analogy is essential to it; for it is only this analogy which distinguishes the theory from the multitude of others… which might also be proposed to explain the same laws. (1957: 142)

The interesting notion here is that of a “valuable” theory. We may not agree with Campbell that the existence of analogy is “essential” for a novel theory to be “valuable.” But consider the weaker thesis that an acceptable analogy is sufficient to establish that a theory is “valuable”, or (to qualify still further) that an acceptable analogy provides defeasible grounds for taking the theory seriously. (Possible defeaters might include internal inconsistency, inconsistency with accepted theory, or the existence of a (clearly superior) rival analogical argument.) The point is that Campbell, following the lead of 19th century philosopher-scientists such as Herschel and Whewell, thinks that analogies can establish this sort of prima facie plausibility. Snyder (2006) provides a detailed discussion of the latter two thinkers and their earlier ideas about the role of analogies in science.

In general, analogical arguments may be directed at establishing either sort of plausibility for their conclusions; they can have a probabilistic use or a modal use. Examples 7 through 9 are best interpreted as supporting modal conclusions. In those arguments, an analogy is used to show that a conjecture is worth taking seriously. To insist on putting the conclusion in probabilistic terms distracts attention from the point of the argument. The conclusion might be modeled (by a Bayesian) as having a certain probability value because it is deemed prima facie plausible, but not vice versa. Example 2, perhaps, might be regarded as directed primarily towards a probabilistic conclusion.

There should be connections between the two conceptions. Indeed, we might think that the same analogical argument can establish both prima facie plausibility and a degree of probability for a hypothesis. But it is difficult to translate between modal epistemic concepts and probabilities (Cohen 1980; Douven and Williamson 2006; Huber 2009; Spohn 2009, 2012). We cannot simply take the probabilistic notion as the primitive one. It seems wise to keep the two conceptions of plausibility separate. Further discussion of this point is found in section 5.
2.4 Analogical inference rules?

Schema (4) is a template that represents all analogical arguments, good and bad. It is not an inference rule. Despite the confidence with which particular analogical arguments are advanced, nobody has ever formulated an acceptable rule, or set of rules, for valid analogical inferences. There is not even a plausible candidate. This situation is in marked contrast not only with deductive reasoning, but also with elementary forms of inductive reasoning, such as induction by enumeration. (Carnap and his followers (Carnap 1980, Niiniluoto 1988 and elsewhere) have formulated principles of “analogy by similarity” in inductive logic, but their project does not concern analogical reasoning as characterized here and will not be discussed further.)

Of course, it is difficult to show that no successful analogical inference rule will ever be proposed. But consider the following candidate, formulated using the concepts of schema (4) and taking us only a short step beyond that basic characterization.

   Suppose S and T are the source and target domains. Suppose P1, …, Pn (with n ≥ 1) represents the positive analogy, A1, …, Ar and ~B1, …, ~Bs represent the (possibly vacuous) negative analogy, and Q represents the hypothetical analogy. In the absence of reasons for thinking otherwise, infer that Q* holds in the target domain with degree of support p > 0, where p is an increasing function of n and a decreasing function of r and s.

Rule (5) is modeled on the straight rule for enumerative induction and inspired by Mill's view of analogical inference, as described in §2.3. We use the generic phrase ‘degree of support’ in place of probability, since other factors besides the analogical argument may influence our probability assignment for Q*.

It is pretty clear that (5) is a non-starter. The main problem is that the rule justifies too much. The only substantive requirement introduced by (5) is that there be a nonempty positive analogy. Plainly, there are analogical arguments that satisfy this condition but establish no prima facie plausibility and no measure of support for their conclusions.

Here is a simple illustration. Achinstein (1964: 328) observes that there is a formal analogy between swans and line segments if we take the relation ‘has the same color as’ to correspond to ‘is congruent with’. Both relations are reflexive, symmetric, and transitive. Yet it would be absurd to find positive support from this analogy for the idea that we are likely to find congruent lines clustered in groups of two or more, just because swans of the same color are commonly found in groups. The positive analogy is antecedently known to be irrelevant to the hypothetical analogy. In such a case, the analogical inference should be utterly rejected. Yet rule (5) would wrongly assign non-zero degree of support.

To generalize the difficulty: not every similarity increases the probability of the conclusion and not every difference decreases it. Some similarities and differences are known to be (or accepted as being) utterly irrelevant and should have no influence whatsoever on our probability judgments. To be viable, rule (5) would need to be supplemented with considerations of relevance, which depend upon the subject matter, historical context and logical details particular to each analogical argument. To search for a simple rule of analogical inference thus appears futile.

Norton (2010, and 2012—see Other Internet Resources) has argued that the project of formalizing inductive reasoning in terms of one or more simple formal schemata is doomed. His criticisms seem especially apt when applied to analogical reasoning. He writes:

   If analogical reasoning is required to conform only to a simple formal schema, the restriction is too permissive. Inferences are authorized that clearly should not pass muster… The natural response has been to develop more elaborate formal templates… The familiar difficulty is that these embellished schema never seem to be quite embellished enough; there always seems to be some part of the analysis that must be handled intuitively without guidance from strict formal rules. (2012: 1)

Norton takes the point one step further, in keeping with his “material theory” of inductive inference. He argues (in 2012) that there is no universal logical principle that “powers” analogical inference “by asserting that things that share some properties must share others.” Rather, each analogical inference is warranted by some local constellation of facts about the target system that he terms “the fact of analogy”. These local facts are to be determined and investigated on a case by case basis. Notice: the point about warrant must apply to the initial plausibility of the analogical argument as well as to the worked-out theory for the target. (One difficulty with this position will be explored in §4.1.)

To embrace a purely formal approach to analogy and to abjure formalization entirely are two extremes in a spectrum of strategies. There are intermediate positions. Most recent analyses (both philosophical and computational) have been directed towards elucidating general criteria and procedures, rather than formal rules, for reasoning by analogy. So long as these are not intended to provide a universal ‘logic’ of analogy, there is room for such criteria even if one accepts Norton's basic point. The next section discusses some of these criteria and procedures.
3. Criteria for evaluating analogical arguments
3.1 Commonsense guidelines

Logicians and philosophers of science have identified ‘textbook-style’ general guidelines for evaluating analogical arguments (Mill 1843/1930; Keynes 1921; Robinson 1930; Stebbing 1933; Copi and Cohen 2005; Moore and Parker 1998; Woods, Irvine, and Walton 2004). Here are some of the most important ones:

   The more similarities (between two domains), the stronger the analogy.
   The more differences, the weaker the analogy.
   The greater the extent of our ignorance about the two domains, the weaker the analogy.
   The weaker the conclusion, the more plausible the analogy.
   Analogies involving causal relations are more plausible than those not involving causal relations.
   Structural analogies are stronger than those based on superficial similarities.
   The relevance of the similarities and differences to the conclusion (i.e., to the hypothetical analogy) must be taken into account.
   Multiple analogies supporting the same conclusion make the argument stronger.

These principles can be helpful, but are frequently too vague to provide much insight. How do we count similarities and differences in applying (G1) and (G2)? Why are the structural and causal analogies mentioned in (G5) and (G6) especially important, and which structural and causal features merit attention? More generally, in connection with the all-important (G7): how do we determine which similarities and differences are relevant to the conclusion? Furthermore, what are we to say about similarities and differences that have been omitted from an analogical argument but might still be relevant?

An additional problem is that the criteria can pull in different directions. To illustrate, consider Reid's argument for life on other planets (Example 2). Stebbing (1933) finds Reid's argument “suggestive” and “not unplausible” because the conclusion is weak (G4), while Mill (1843/1930) appears to reject the argument on account of our vast ignorance of properties that might be relevant (G3).

There is a further problem that relates to the distinction just made (in §2.3) between two kinds of plausibility. Each of the above criteria apart from (G7) is expressed in terms of the strength of the argument, i.e., the degree of support for the conclusion. The criteria thus appear to presuppose the probabilistic interpretation of plausibility. The problem is that a great many analogical arguments aim to establish prima facie plausibility rather than any degree of probability. Most of the guidelines are not directly applicable to such arguments.
3.2 Aristotle's theory

Aristotle sets the stage for all later theories of analogical reasoning. In his theoretical reflections on analogy and in his most judicious examples, we find a sober account that lays the foundation both for the commonsense guidelines noted above and for more sophisticated analyses.

Although Aristotle employs the term analogy (analogia) and talks about analogical predication, he never talks about analogical reasoning or analogical arguments per se. He does, however, identify two argument forms, the argument from example (paradeigma) and the argument from likeness (homoiotes), both closely related to what would we now recognize as an analogical argument.

The argument from example (paradeigma) is described in the Rhetoric and the Prior Analytics:

   Enthymemes based upon example are those which proceed from one or more similar cases, arrive at a general proposition, and then argue deductively to a particular inference. (Rhetoric 1402b15)

   Let A be evil, B making war against neighbours, C Athenians against Thebans, D Thebans against Phocians. If then we wish to prove that to fight with the Thebans is an evil, we must assume that to fight against neighbours is an evil. Conviction of this is obtained from similar cases, e.g., that the war against the Phocians was an evil to the Thebans. Since then to fight against neighbours is an evil, and to fight against the Thebans is to fight against neighbours, it is clear that to fight against the Thebans is an evil. (Pr. An. 69a1)

Aristotle notes two differences between this argument form and induction (69a15ff.): it “does not draw its proof from all the particular cases” (i.e., it is not a “complete” induction), and it requires an additional (deductively valid) syllogism as the final step. The argument from example thus amounts to single-case induction followed by deductive inference. It has the following structure (using ⊃ for the conditional):

   [a tree diagram where S is source domain and T is target domain. First node is P(S)&Q(S) in the lower left corner. It is connected by a dashed arrow to (x)(P(x) superset Q(x)) in the top middle which in turn connects by a solid arrow to P(T) and on the next line P(T) superset Q(T) in the lower right. It in turn is connected by a solid arrow to Q(T) below it.]

In the terminology of §2.2, P is the positive analogy and Q is the hypothetical analogy. In Aristotle's example, S (the source) is war between Phocians and Thebans, T (the target) is war between Athenians and Thebans, P is war between neighbours, and Q is evil. The first inference (dashed arrow) is inductive; the second and third (solid arrows) are deductively valid.

The paradeigma has an interesting feature: it is amenable to an alternative analysis as a purely deductive argument form. Let us concentrate on Aristotle's assertion, “we must assume that to fight against neighbours is an evil,” represented as ∀x(P(x) ⊃ Q(x)). Instead of regarding this intermediate step as something reached by induction from a single case, we might instead regard it as a hidden presupposition. This transforms the paradeigma into a syllogistic argument with a missing or enthymematic premise, and our attention shifts to possible means for establishing that premise (with single-case induction as one such means). Construed in this way, Aristotle's paradeigma argument foreshadows deductive analyses of analogical reasoning (see §4.1).

The argument from likeness (homoiotes) seems to be closer than the paradeigma to our contemporary understanding of analogical arguments. This argument form receives considerable attention in Topics I, 17 and 18 and again in VIII, 1. The most important passage is the following.

   Try to secure admissions by means of likeness; for such admissions are plausible, and the universal involved is less patent; e.g. that as knowledge and ignorance of contraries is the same, so too perception of contraries is the same; or vice versa, that since the perception is the same, so is the knowledge also. This argument resembles induction, but is not the same thing; for in induction it is the universal whose admission is secured from the particulars, whereas in arguments from likeness, what is secured is not the universal under which all the like cases fall. (Topics 156b10–17)

This passage occurs in a work that offers advice for framing dialectical arguments when confronting a somewhat skeptical interlocutor. In such situations, it is best not to make one's argument depend upon securing agreement about any universal proposition. The argument from likeness is thus clearly distinct from the paradeigma, where the universal proposition plays an essential role as an intermediate step in the argument. The argument from likeness, though logically less straightforward than the paradeigma, is exactly the sort of analogical reasoning we want when we are unsure about underlying generalizations.

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QUESTION: Greetings Jeffrey!
Advanced Happy Christmas!!:)))
I read the entire passage and concluded that reasoning by analogy are not deductively valid.I just need to ask you couple of questions.

Q1. Deductive valid patterns as Modus Ponen,Modus Tollens,Hypothetical syllogism,Disjunctive syllogism,Categorical Syllogism ,Delimma and Reduce to Absurdity
Are they all considered fallacies or ways to construct an argument???

Q2. In Problem solving strategy IRAC,All arguments whether plaintiff or prosecutions's included in Application part of Irac?



ANSWER: Bilal,

Thank you.  Merry Christmas to you as well.  Modus Ponens, Modus Tollens, Hypothetical syllogism, Disjunctive syllogism, Categorical Syllogism, Dilemma, and Reduce to Absurdity are all ways to construct or form arguments.  Take Modus Ponens (MP) for example.  It is one of the accepted mechanisms for the construction of deductive proofs which allows one to eliminate a conditional statement from a logical proof or argument.  

Yes, the Issue-Rule-Application-Conclusion problem solving strategy provides a step-by-step framework to solving legal problems for both plaintiff and defendant.

Be well.


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Thank you so much for your response.Jeff i have one more issue to discuss with you.
Can you tell me how may i use tree diagram when answering essay questions?
Could you illustrate me with examples ? whats the thesis and topic sentences.
I am familiar about introduction,body and conclusion
But could you give me a worked example so i could enhance further understanding
I am student currently enrolled external programs of university of london
the book does not specifically highlights every feature so i need your help
Could you assist me jeff?


Although I cannot provide illustrations as this format will not support it I will point your attention to this article discussing thesis and topic sentences:

Thesis Statements and Topic Sentences

Thesis Statements

A thesis statement defines the scope and purpose of the paper. It needs to meet three criteria:

1. It must be arguable rather than a statement of fact. It should also say something original about the topic.

   Bad thesis: Lily Bart experiences the constraints of many social conventions in The House of Mirth. [Of course she does. What does she do with these social conventions, and how does she respond to them? What's your argument about this idea?]

   Better thesis: Lily Bart seeks to escape from the social conventions of her class in The House of Mirth, but her competing desires for a place in Selden's "republic of the spirit" and in the social world of New York cause her to gamble away her chances for a place in either world. [You could then mention the specific scenes that you will discuss.]

2. It must be limited enough so that the paper develops in some depth.

   Bad thesis: Lily Bart and Clare Kendry are alike in some ways, but different in many others. [What ways?]

   Better thesis: Lily Bart and Clare Kendry share a desire to "pass" in their respective social worlds, but their need to take risks and to reject those worlds leads to their destruction.

3. It must be unified so that the paper does not stray from the topic.

   Bad thesis: Lily Bart gambles with her future, and Lawrence Selden is only a spectator rather than a hero of The House of Mirth. [Note: This is really the beginning of two different thesis statements.]

   Better thesis: In The House of Mirth, Lawrence Selden is a spectator who prefers to watch and judge Lily than to help her. By failing to assist her on three separate occasions, he is revealed as less a hero of the novel than as the man responsible for Lily's downfall. [Note: Sometimes thesis statements are more than one sentence long.]

4. Statements such as "In this essay I will discuss " or "I will compare two stories in this paper" or "I was interested in Marji's relationship with God, so I thought I would talk about it in this essay" are not thesis statements and are unnecessary, since mentioning the stories in the introduction already tells the reader this.

Topic Sentences

Good topic sentences can improve an essay's readability and organization. They usually meet the following criteria:

1. First sentence. A topic sentence is usually the first sentence of the paragraph, not the last sentence of the previous paragraph.

2. Link to thesis. Topic sentences use keywords or phrases from the thesis to indicate which part of the thesis will be discussed.

3. Introduce the subject of the paragraph. They tell the reader what concept will be discussed and provide an introduction to the paragraph.

4. Link to the previous paragraph. They link the subject of the present paragraph to that of the previous paragraph.

5. Indicate the progression of the essay. Topic sentences may also signal to the reader where the essay has been and where it is headed through signposting words such as "first," "second," or "finally."

Good topic sentences typically DON'T begin with the following.

1. A quotation from a critic or from the piece of fiction you're discussing. The topic sentence should relate to your points and tell the reader what the subject of the paragraph will be. Beginning the paragraph with someone else's words doesn't allow you to provide this information for the reader.

2. A piece of information that tells the reader something more about the plot of the story. When you're writing about a piece of literature, it's easy to fall into the habit of telling the plot of the story and then adding a sentence of analysis, but such an approach leaves the reader wondering what the point of the paragraph is supposed to be; it also doesn't leave you sufficient room to analyze the story fully. These "narrative" topic sentences don't provide enough information about your analysis and the points you're making.

   Weak "narrative" topic sentence: Lily Bart next travels to Bellomont, where she meets Lawrence Selden again.

   Stronger "topic-based" topic sentence: A second example of Lily's gambling on her marriage chances occurs at Bellomont, where she ignores Percy Gryce in favor of Selden. [Note that this tells your reader that it's the second paragraph in a series of paragraph relating to the thesis, which in this case would be a thesis related to Lily's gambling on her marriage chances.]

3. A sentence that explains your response or reaction to the work, or that describes why you're talking about a particular part of it, rather than why the paragraph is important to your analysis.

   Weak "reaction" topic sentence: I felt that Lily should have known that Bertha Dorset was her enemy.

   Stronger "topic-based" topic sentence: Bertha Dorset is first established as Lily's antagonist in the train scene, when she interrupts Lily's conversation with Percy Gryce and reveals that Lily smokes.


I would direct you to download this PDF file on essay writing:

It should cover everything you want to know.  

I do hope this helps you.  God bless!  

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Jeffrey Hauck


I would welcome the opportunity to answer questions relating to or related to the field of criminal law.


Criminologist. Professor of Criminal Justice. Licensed Private Detective with expansive clientele base encompassing hundreds of cases. Donates resources and time to the Children's Rescue Network in Orlando, FL.

Associate of Science; Bachelor of Arts; Master of Science, Doctor of Jurisprudence Degree.

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