Tips to Pass an Analogies Test
A very different relationship between analogy and discovery exists when . need not belong to a first-order language, but to keep things simple. At its most basic, an analogy is a comparison of two things to show their similarities. Dusty Springfield knows, finding a small needle in a pile of hay takes a long time, This analogy highlights the relationship between the whole ( a tree and a. Analogy Relationships. Analogy Relationships Students also need to build their vocabulary base to have a better understanding words introduced in.
An analogy question asks students to select the answer that best mirrors the relationship between the two words in the question. As a simple example, the question might start with: Here is a complete analogy example question: Hot is to cold as: Fat is to obese Parent is to mother Tepid is to warming The reader should see that inside is to outside is the only pair of opposites and select it as the correct response.
Analogies are revealing test questions causing the reader to hypothesize the relationship between the example words and then finding the best match for that analogy. Common types of analogies used on standardized tests with examples: Opposites or antonyms Synonyms or words with identical or similar meetings Near synonyms with variations by degree: Some students think to look outside the meaning of words. As far as I know, none of the standardized tests will base analogies on alliteration.
Desk is to door as wall is to wind book is to read dwarf is to decade. A student, unfamiliar with these types of questions, might reason like this: 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 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 2perhaps, 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 ; Douven and Williamson ; Huber ; Spohn 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. 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. 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.
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. 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: Some similarities and differences are known to be or accepted as being utterly irrelevant and should have no influence whatsoever on our probability judgments.
Architectural Vocabularies: exploring the analogous relationship between light and water
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.
Nortonand —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. 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.
These local facts are to be determined and investigated on a case by case basis.
Analogy - Wikipedia
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. The next section discusses some of these criteria and procedures.
Here are some of the most important ones: G1 The more similarities between two domainsthe stronger the analogy. G2 The more differences, the weaker the analogy. G3 The greater the extent of our ignorance about the two domains, the weaker the analogy. G4 The weaker the conclusion, the more plausible the analogy. G5 Analogies involving causal relations are more plausible than those not involving causal relations.
G6 Structural analogies are stronger than those based on superficial similarities. G7 The relevance of the similarities and differences to the conclusion i. G8 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: 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.
Each of the above criteria apart from G7 is expressed in terms of the strength of the argument, i. 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. 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 predicationhe 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 homoiotesboth 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.
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. 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. The argument from example thus amounts to single-case induction followed by deductive inference.
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: 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.
The argument from likeness homoiotes seems to be closer than the paradeigma to our contemporary understanding of analogical arguments.
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. 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 b10—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. In Topics I 17, Aristotle states that any shared attribute contributes some degree of likeness: We should also look at things which belong to the same genus, to see if any identical attribute belongs to them all, e.
Topics a13 It is natural to ask when the degree of likeness between two things is sufficiently great to warrant inferring a further likeness. In other words, when does the argument from likeness succeed? Aristotle does not answer explicitly, but a clue is provided by the way he justifies particular arguments from likeness.
As Lloyd has observed, Aristotle typically justifies such arguments by articulating a causal principle which governs the two phenomena being compared.
For example, Aristotle explains the saltiness of the sea, by analogy with the saltiness of sweat, as a kind of residual earthy stuff exuded in natural processes such as heating.
The common principle is this: Mete a17 From this method of justification, we might conjecture that Aristotle believes that the important similarities are those that enter into such general causal principles. Summarizing, Aristotle's theory provides us with four important and influential criteria for the evaluation of analogical arguments: The strength of an analogy depends upon the number of similarities.
Similarity reduces to identical properties and relations. Good analogies derive from underlying common causes or general laws. A good analogical argument need not pre-suppose acquaintance with the underlying universal generalization. These four principles form the core of a common-sense model for evaluating analogical arguments which is not to say that they are correct; indeed, the first three will shortly be called into question.
The first, as we have seen, appears regularly in textbook discussions of analogy. Versions of the third are found in most sophisticated theories. The final point, which distinguishes the argument from likeness and the argument from example, is endorsed in many discussions of analogy e. A slight generalization of Aristotle's first principle helps to prepare the way for discussion of later developments.
As that principle suggests, Aristotle, in common with just about everyone else who has written about analogical reasoning, organizes his analysis of the argument form around overall similarity. In the terminology of section 2. Hume makes the same point, though stated negatively, in his Dialogues Concerning Natural Religion: Wherever you depart, in the least, from the similarity of the cases, you diminish proportionably the evidence; and may at last bring it to a very weak analogy, which is confessedly liable to error and uncertainty.
Disagreement relates to the appropriate way of measuring overall similarity. Some theories assign greatest weight to material analogy, which refers to shared, and typically observable, features. Others give prominence to formal analogy, emphasizing high-level structural correspondence. The next two sub-sections discuss representative accounts that illustrate these two approaches.
Hesse offers a sharpened version of Aristotle's theory, specifically focused on analogical arguments in the sciences. She formulates three requirements that an analogical argument must satisfy in order to be acceptable: Requirement of material analogy.
The horizontal relations must include similarities between observable properties. The essential properties and causal relations of the source domain must not have been shown to be part of the negative analogy.
Material analogy is contrasted with formal analogy. A second example is the analogy between the flow of electric current in a wire and fluid in a pipe. This has the same mathematical form as Poiseuille's law for ideal fluids: Both of these systems can be represented by a common equation. These are horizontal relationships of similarity between properties of objects in the source and the target.
Similarities between echoes sound and reflection lightfor instance, were recognized long before we had any detailed theories about these phenomena. There are good reasons not to accept Hesse's requirement of material analogy, construed in this narrow way.
First, it is apparent that formal analogies are the starting point in many important inferences. That is certainly the case in mathematics, a field in which material analogy, in Hesse's sense, plays no role at all. Analogical arguments based on formal analogy have also been extremely influential in physics Steiner With reference to this broader meaning, Hesse proposes two additional material criteria.
Causal condition Hesse requires that the hypothetical analogy, the feature transferred to the target domain, be causally related to the positive analogy. She states the requirement as follows: The vertical relations in the model [source] are causal relations in some acceptable scientific sense, where there are no compelling a priori reasons for denying that causal relations of the same kind may hold between terms of the explanandum [target].
It derives support from the observation that many analogies do appear to involve a transfer of causal knowledge. The causal condition is on the right track, but is arguably too restrictive. For example, it rules out analogical arguments in mathematics.
Even if we limit attention to the empirical sciences, persuasive analogical arguments may be founded upon strong statistical correlation in the absence of any known causal connection.
Electrical fluid agrees with lightning in these particulars: Colour of the light. Being conducted by metals. Crack or noise in exploding. Subsisting in water or ice. Rending bodies it passes through.
Analogous | Definition of Analogous by Merriam-Webster
Let the experiment be made. Benjamin Franklin's Experiments, Franklin's hypothesis was based on a long list of properties common to the target lightning and source electrical fluid in the laboratory. Analogical arguments may be plausible even where there are no known causal relations. Once it was discovered that heat was not conserved, however, the analogy became unacceptable according to Hesse because conservation was so central to the theory of fluid flow.
This requirement, though once again on the right track, seems too restrictive. It can lead to the rejection of a good analogical argument. Consider the analogy between a two-dimensional rectangle and a three-dimensional box Example 7.
This does not mean that we should reject every analogy between rectangles and boxes out of hand. The problem derives from the fact that Hesse's condition is applied to the analogy relation independently of the use to which that relation is put.
Tips to Pass an Analogies Test
What counts as essential should vary with the analogical argument. The causal condition and the no-essential-difference condition incorporate local factors, as urged by Norton, into the assessment of analogical arguments.
These conditions, singly or taken together, imply that an analogical argument can fail to generate any support for its conclusion, even when there is a non-empty positive analogy. They propose formal criteria for evaluating analogies, based on overall structural or syntactical similarity. Let us refer to theories oriented around such criteria as structuralist.
A number of leading computational models of analogy are structuralist.
They are implemented in computer programs that begin with or sometimes build representations of the source and target domains, and then construct possible analogy mappings. First, the goodness of an analogical argument is based on the goodness of the associated analogy mapping. Second, the goodness of the analogy mapping is given by a metric that indicates how closely it approximates isomorphism. The most influential structuralist theory has been Gentner's structure-mapping theory, implemented in a program called the structure-mapping engine SME.
In its original form Gentnerthe theory assesses analogies on purely structural grounds. Analogies are about relations, rather than simple features.
No matter what kind of knowledge causal models, plans, stories, etc. She further distinguishes among different orders of relations and functions, defined inductively. Consider the sentence, Gravitational attraction between the sun and a planet, and the fact that the mass of the sun is much greater than that of the planet, causes the planet to orbit the sun.
Gentner represents this in the following form: An analogy mapping M is a one-to-one function from the items in the source domain to those in the target, such that if R holds of objects a1, …, an in the source domain, then M R holds of objects R a1…, R an in the target. The order of M R must be the same as the order of R. M may be a partial mapping; not every item in the source domain needs to have a target image. The best mapping M is determined by systematicity: Properties and functions are unimportant, unless they are part of a relational network.
Gentner's Systematicity Principle states: A predicate that belongs to a mappable system of mutually interconnecting relationships is more likely to be imported into the target than is an isolated predicate.
And a systematic analogy one that places high-order relations and their components in correspondence is better than a less systematic analogy.
Hence, an analogical inference has a degree of plausibility that increases monotonically with the degree of systematicity of the associated analogy mapping. Gentner's fundamental criterion for evaluating candidate analogies and analogical inferences thus depends solely upon the syntax of the given representations and not at all upon their content.
The contrast with Hesse's approach is striking. Still, some of the fundamental difficulties with the structure-mapping approach are easiest to appreciate if we focus on the early version.