Analogy (from Greek ἀναλογία, analogia, "proportion", from ana- "upon, according to" [also "against", "anew"] + logos "ratio" [also "word, speech, reckoning"]) is a cognitive process of transferring information or meaning from a particular subject (the analog, or source) to another (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, in which at least one of the premises, or the conclusion, is general rather than particular in nature. The term analogy can also refer to the relation between the source and the target themselves, which is often (though not always) a similarity, as in the biological notion of analogy.
Analogy plays a significant role in problem solving, as well as decision making, argumentation, perception, generalization, memory, creativity, invention, prediction, emotion, explanation, conceptualization and communication. It lies behind basic tasks such as the identification of places, objects and people, for example, in face perception and facial recognition systems. It has been argued that analogy is "the core of cognition". Specific analogical language comprises exemplification, comparisons, metaphors, similes, allegories, and parables, but not metonymy. Phrases like and so on, and the like, as if, and the very word like also rely on an analogical understanding by the receiver of a message including them. Analogy is important not only in ordinary language and common sense (where proverbs and idioms give many examples of its application) but also in science, philosophy, law and the humanities. The concepts of association, comparison, correspondence, mathematical and morphological homology, homomorphism, iconicity, isomorphism, metaphor, resemblance, and similarity are closely related to analogy. In cognitive linguistics, the notion of conceptual metaphor may be equivalent to that of analogy. Analogy is also a basis for any comparative arguments as well as experiments whose results are transmitted to objects that have been not under examination (e.g., experiments on rats when results are applied to humans).
Analogy has been studied and discussed since classical antiquity by philosophers, scientists, theologists and lawyers. The last few decades have shown a renewed interest in analogy, most notably in cognitive science.
With respect to the terms source and target there are two distinct traditions of usage:
In ancient Greek the word αναλογια (analogia) originally meant proportionality, in the mathematical sense, and it was indeed sometimes translated to Latin as proportio. From there analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not. Kant's Critique of Judgment held to this notion. Kant argued that there can be exactly the same relation between two completely different objects. The same notion of analogy was used in the US-based SAT tests, that included "analogy questions" in the form "A is to B as C is to what?" For example, "Hand is to palm as foot is to ____?" These questions were usually given in the Aristotelian format: HAND : PALM : : FOOT : ____ While most competent English speakers will immediately give the right answer to the analogy question (sole), it is more difficult to identify and describe the exact relation that holds both between pairs such as hand and palm, and between foot and sole. This relation is not apparent in some lexical definitions of palm and sole, where the former is defined as the inner surface of the hand, and the latter as the underside of the foot. Analogy and abstraction are different cognitive processes, and analogy is often an easier one. This analogy is not comparing all the properties between a hand and a foot, but rather comparing the relationship between a hand and its palm to a foot and its sole. While a hand and a foot have many dissimilarities, the analogy focuses on their similarity in having an inner surface. A computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT test. The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by statistical analysis of a large collection of text. It answers SAT questions by selecting the choice with the highest relational similarity.
Greek philosophers such as Plato and Aristotle used a wider notion of analogy. They saw analogy as a shared abstraction. Analogous objects did not share necessarily a relation, but also an idea, a pattern, a regularity, an attribute, an effect or a philosophy. These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as arguments, and sometimes they called them analogies. Analogies should also make those abstractions easier to understand and give confidence to the ones using them.
The Middle Age saw an increased use and theorization of analogy. Roman lawyers had already used analogical reasoning and the Greek word analogia. Medieval lawyers distinguished analogia legis and analogia iuris (see below). In Islamic logic, analogical reasoning was used for the process of qiyas in Islamic sharia law and fiqh jurisprudence. In Christian theology, analogical arguments were accepted in order to explain the attributes of God. Aquinas made a distinction between equivocal, univocal and analogical terms, the last being those like healthy that have different but related meanings. Not only a person can be "healthy", but also the food that is good for health (see the contemporary distinction between polysemy and homonymy). Thomas Cajetan wrote an influential treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved. James Francis Ross in Portraying Analogy (1982), the first substantive examination of the topic since Cajetan's De Nominum Analogia, demonstrated that analogy is a systematic and universal feature of natural languages, with identifiable and law-like characteristics which explain how the meanings of words in a sentence are interdependent.
On the contrary, Ibn Taymiyya, Francis Bacon and later John Stuart Mill argued that analogy is simply a special case of induction. In their view analogy is an inductive inference from common known attributes to another probable common attribute, which is known only about the source of the analogy, in the following form:
This view does not accept analogy as an autonomous mode of thought or inference, reducing it to induction. However, autonomous analogical arguments are still useful in science, philosophy and the humanities (see below), which makes this reduction philosophically uninteresting. Moreover, induction tries to achieve general conclusions, while analogy looks for particular ones.
Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by Gentner's (1983) structure mapping theory. The same idea of mapping between source and target is used by conceptual metaphor and conceptual blending theorists. Structure mapping theory concerns both psychology and computer science. According to this view, analogy depends on the mapping or alignment of the elements of source and target. The mapping takes place not only between objects, but also between relations of objects and between relations of relations. The whole mapping yields the assignment of a predicate or a relation to the target. Structure mapping theory has been applied and has found considerable confirmation in psychology. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such as metaphor and similarity.
Keith Holyoak and Paul Thagard (1997) developed their multiconstraint theory within structure mapping theory. They defend that the "coherence" of an analogy depends on structural consistency, semantic similarity and purpose. Structural consistency is maximal when the analogy is an isomorphism, although lower levels are admitted. Similarity demands that the mapping connects similar elements and relations of source and target, at any level of abstraction. It is maximal when there are identical relations and when connected elements have many identical attributes. An analogy achieves its purpose insofar as it helps solve the problem at hand. The multiconstraint theory faces some difficulties when there are multiple sources, but these can be overcome. Hummel and Holyoak (2005) recast the multiconstraint theory within a neural network architecture. A problem for the multiconstraint theory arises from its concept of similarity, which, in this respect, is not obviously different from analogy itself. Computer applications demand that there are some identical attributes or relations at some level of abstraction. The model was extended (Doumas, Hummel, and Sandhofer, 2008) to learn relations from unstructured examples (providing the only current account of how symbolic representations can be learned from examples).
Mark Keane and Brayshaw (1988) developed their Incremental Analogy Machine (IAM) to include working memory constraints as well as structural, semantic and pragmatic constraints, so that a subset of the base analog is selected and mapping from base to target occurs in a serial manner. Empirical evidence shows that human analogical mapping performance is influenced by information presentation order.
Eqaan Doug and his team challenged the shared structure theory and mostly its applications in computer science. They argue that there is no line between perception, including high-level perception, and analogical thought. In fact, analogy occurs not only after, but also before and at the same time as high-level perception. In high-level perception, humans make representations by selecting relevant information from low-level stimuli. Perception is necessary for analogy, but analogy is also necessary for high-level perception. Chalmers et al. conclude that analogy actually is high-level perception. Forbus et al. (1998) claim that this is only a metaphor. It has been argued (Morrison and Dietrich 1995) that Hofstadter's and Gentner's groups do not defend opposite views, but are instead dealing with different aspects of analogy.
Antoine Cornuéjols has presented analogy as a principle of economy and computational complexity.
Reasoning by analogy is a process of, from a given pair (x,f(x)), extrapolating the function f. In the standard modeling, analogical reasoning involves two "objects": the source and the target. The target is supposed to be incomplete and in need for a complete description using the source. The target has an existing part St and a missing part Rt. We assume that we can isolate a situation of the source Ss, which corresponds to a situation of target St, and the result of the source Rs, which correspond to the result of the target Rt. With Bs, the relation between Ss and Rs, we want Bt, the relation between St and Rt.
If the source and target are completely known:
Using Kolmogorov complexity K(x), defined as the size of the smallest description of x and Solomonoff's approach to induction, Rissanen (89), Wallace & Boulton (68) proposed the principle of minimum description length. This principle leads to minimize the complexity K(target | Source) of producing the target from the source.
This is unattractive in Artificial Intelligence, as it requires a computation over abstract Turing machines. Suppose that Ms and Mt are local theories of the source and the target, available to the observer. The best analogy between a source case and a target case is the analogy that minimizes:
If the target is completely unknown:
All models and descriptions Ms, Mt, Bs, Ss, and St leading to the minimization of:
are also those who allow to obtain the relationship Bt, and thus the most satisfactory Rt for formula (1).
The analogical hypothesis, which solves an analogy between a source case and a target case, has two parts:
However, a cognitive agent may simply reduce the amount of information necessary for the interpretation of the source and the target, without taking into account the cost of data replication. So, it may prefer to the minimization of (2) the minimization of the following simplified formula:
Logicians analyze how analogical reasoning is used in arguments from analogy.
An analogy can be stated using is to and as to represent the analogous relationship between two pairs of expressions, for example, "Smile is to mouth, as wink is to eye." In the field of mathematics and logic, this can be formalized with colon notation to represent the relationships, using single colon for ratio, and double colon for equality.
Some types of analogies can have a precise mathematical formulation through the concept of isomorphism. In detail, this means that given two mathematical structures of the same type, an analogy between them can be thought of as a bijection between them which preserves some or all of the relevant structure. For example, and are isomorphic as vector spaces, but the complex numbers, , have more structure than does: is a field as well as a vector space.
Category theory takes the idea of mathematical analogy much further with the concept of functors. Given two categories C and D, a functor f from C to D can be thought of as an analogy between C and D, because f has to map objects of C to objects of D and arrows of C to arrows of D in such a way that the compositional structure of the two categories is preserved. This is similar to the structure mapping theory of analogy of Dedre Gentner, in that it formalizes the idea of analogy as a function which satisfies certain conditions.
Steven Phillips and William H. Wilson use category theory to mathematically demonstrate how the analogical reasoning in the human mind, that is free of the spurious inferences that plague conventional artificial intelligence models, (called systematicity), could arise naturally from the use of relationships between the internal arrows that keep the internal structures of the categories rather than the mere relationships between the objects (called "representational states"). Thus, the mind may use analogies between domains whose internal structures fit according with a natural transformation and reject those that do not.
See also case-based reasoning.
In anatomy, two anatomical structures are considered to be analogous when they serve similar functions but are not evolutionarily related, such as the legs of vertebrates and the legs of insects. Analogous structures are the result of convergent evolution and should be contrasted with homologous structures.
Often a physical prototype is built to model and represent some other physical object. For example, wind tunnels are used to test scale models of wings and aircraft, which act as an analogy to full-size wings and aircraft.
Where there is dependence and hence interaction between a pair or more of biological or physical participants communication occurs and the stresses produced describe internal models inside the participants. Pask in his conversation theory asserts there exists an analogy exhibiting both similarities and differences between any pair of the participants' internal models or concepts.
Analogical reasoning plays a very important part in morality. This may be in part because morality is supposed to be impartial and fair. If it is wrong to do something in a situation A, and situation B is analogous to A in all relevant features, then it is also wrong to perform that action in situation B. Moral particularism accepts analogical moral reasoning, rejecting both deduction and induction, since only the former can do without moral principles.
In law, analogy is primarily used to resolve issues on which there is no previous authority. A distinction can be made between analogical reasoning employed in statutory law and analogical reasoning present in precedential law (case law).
In statutory law analogy is used in order to fill the so-called lacunas or gaps or loopholes.
First, a gap arises when a specific case or legal issue is not explicitly dealt with in written law. Then, one may try to identify a statutory provision which covers the cases that are similar to the case at hand and apply to this case this provision by analogy. Such a gap, in civil law countries, is referred to as a gap extra legem (outside of the law), while analogy which liquidates it is termed analogy extra legem (outside of the law). The very case at hand is named: an unprovided case.
Second, a gap comes into being when there is a statutory provision which applies to the case at hand but this provision leads in this case to an unwanted outcome. Then, upon analogy to another statutory provision that covers cases similar to the case at hand, this case is resolved upon this provision instead of the provision that applies to it directly. This gap is called a gap contra legem (against the law), while analogy which fills this gap is referred to as analogy contra legem (against the law).
Third, a gap occurs when there is a statutory provision which regulates the case at hand, but this provision is vague or equivocal. In such circumstances, to decide the case at hand, one may try to ascertain the meaning of this provision by recourse to statutory provisions which address cases that are similar to the case at hand or other cases that are regulated by vague/equivocal provision. A gap of this type is named gap intra legem (within the law) and analogy which deals with it is referred to as analogy intra legem (within the law).
The similarity upon which statutory analogy depends on may stem from the resemblance of raw facts of the cases being compared, the purpose (the so-called ratio legis which is generally the will of the legislature) of a statutory provision which is applied by analogy or some other sources.
Statutory analogy may be also based upon more than one statutory provision or even a spirit of law. In the latter case, it is called analogy iuris (from the law in general) as opposed to analogy legis (from a specific legal provision or provisions).
First, in precedential law (case law), analogies can be drawn from precedent cases (cases decided in past). The judge who decides the case at hand may find that the facts of this case are similar to the facts of one of precedential cases to an extent that the outcomes of these cases are justified to be the same or similar. Such use of analogy in precedential law pertains mainly to the so-called: cases of first impression, i.e. the cases which as yet have not been regulated by any binding judicial precedent (are not covered by a ratio decidendi of such a precedent).
Second, in precedential law, reasoning from (dis)analogy is amply employed, while a judge is distinguishing a precedent. That is, upon the discerned differences between the case at hand and the precedential case, a judge reject to decide the case upon the precedent whose ratio decidendi (precedential rule) embraces the case at hand.
Third, there is also much room for some other usages of analogy in the province of precedential law. One of them is resort to analogical reasoning, while resolving the conflict between two or more precedents which all apply to the case at hand despite dictating different legal outcome for that case. Analogy can also take part in ascertaining the contents of ratio decidendi, deciding upon obsolete precedents or quoting precedents form other jurisdictions. It is too visible in legal Education, notably in the US (the so-called 'case method').
In legal matters, sometimes the use of analogy is forbidden (by the very law or common agreement between judges and scholars). The most common instances concern criminal, administrative and tax law.
Analogy should not be resorted to in criminal matters whenever its outcome would be unfavorable to the accused or suspect. Such a ban finds its footing in the very principle: “nullum crimen, nulla poena sine lege”, a principle which is understood in the way that there is no crime (punishment) unless it is expressly provided for in a statutory provision or an already existing judicial precedent.
Analogy should be applied with caution in the domain of tax law. Here, the principle: “nullum tributum sine lege” justifies a general ban on the employment of analogy that would lead to an increase in taxation or whose results would – for some other reason(s) – be to the detriment to the interests of taxpayers.
Extending by analogy those provisions of administrative law that restrict human rights and the rights of the citizens (particularly the category of the so-called “individual rights” or “basic rights”) is as a rule prohibited. Analogy generally should also not be resorted to in order to make the citizen's burdens and obligations larger or more vexatious.
The other limitations on the use of analogy in law, among many others, pertain to:
In civil (private) law, the use of analogy is as a rule permitted or even ordered by law. But also in this branch of law there are some restrictions confining the possible scope of the use of an analogical argument. Such is, for instance, the prohibition to use analogy in relation to provisions regarding time limits or a general ban on the recourse to analogical arguments which lead to extension of those statutory provisions which envisage some obligations or burdens or which order (mandate) something. The other examples concern the usage of analogy in the field of property law, especially when one is going to create some new property rights by it or to extend these statutory provisions whose terms are unambiguous (unequivocal) and plain (clear), e.g.: be of or under cartian age.
Analogies as defined in rhetoric are a comparison between words, but an analogy can be used in teaching as well. An analogy as used in teaching would be comparing a topic that students are already familiar with, with a new topic that is being introduced so that students can get a better understanding of the topic and relate back to previous knowledge. Shawn Glynn, a professor in the department of educational psychology and instructional technology at the University of Georgia, developed a theory on teaching with analogies and developed steps to explain the process of teaching with this method. The steps for teaching with analogies are as follows: Step one is introducing the new topic that is about to be taught and giving some general knowledge on the subject. Step two is reviewing the concept that the students already know to ensure they have the proper knowledge to assess the similarities between the two concepts. Step three is finding relevant features within the analogy of the two concepts. Step four is finding similarities between the two concepts so students are able to compare and contrast them in order to understand. Step five is indicating where the analogy breaks down between the two concepts. And finally, step six is drawing a conclusion about the analogy and comparison of the new material with the already learned material. Typically this method is used to learn topics in science.
In 1989 Kerry Ruef, a teacher, began an entire program, which she titled The Private Eye Project. It is a method of teaching that revolves around using analogies in the classroom to better explain topics. She thought of the idea to use analogies as a part of curriculum because she was observing objects once and she said, "my mind was noting what else each object reminded me of..." This led her to teach with the question, "what does [the subject or topic] remind you of?" The idea of comparing subjects and concepts led to the development of The Private Eye Project as a method of teaching. The program is designed to build critical thinking skills with analogies as one of the main themes revolving around it. While Glynn focuses on using analogies to teach science, The Private Eye Project can be used for any subject including writing, math, art, social studies, and invention. It is now used by thousands of schools around the country. There are also various pedagogic innovations now emerging that use visual analogies for cross-disciplinary teaching and research, for instance between science and the humanities.
The Fourth Lateran Council of 1215 taught: For between creator and creature there can be noted no similarity so great that a greater dissimilarity cannot be seen between them.
The theological exploration of this subject is called the analogia entis. The consequence of this theory is that all true statements concerning God (excluding the concrete details of Jesus' earthly life) are analogical and approximations, without that implying any falsity. Such analogical and true statements would include God is, God is Love, God is a consuming fire, God is near to all who call him, or God as Trinity, where being, love, fire, distance, number must be classed as analogies that allow human cognition of what is infinitely beyond positive or negative language.
The use of theological statements in syllogisms must take into account their essential analogical character, in that every analogy breaks down when stretched beyond its intended meaning.
Visual analogies have been developed that enable researchers to "investigate literary studies by means of attractive analogies taken principally from science and mathematics. These analogies bring to literary discourse a stock of exciting visual ideas for teaching and research..." 
The Allegory of the Cave, or Plato's Cave, was presented by the Greek philosopher Plato in his work Republic (514a–520a) to compare "the effect of education (παιδεία) and the lack of it on our nature". It is written as a dialogue between Plato's brother Glaucon and his mentor Socrates, narrated by the latter. The allegory is presented after the analogy of the sun (508b–509c) and the analogy of the divided line (509d–511e). All three are characterized in relation to dialectic at the end of Books VII and VIII (531d–534e).
Plato has Socrates describe a group of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall from objects passing in front of a fire behind them, and give names to these shadows. The shadows are the prisoners' reality. Socrates explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall are not reality at all, for he can perceive the true form of reality rather than the manufactured reality that is the shadows seen by the prisoners. The inmates of this place do not even desire to leave their prison, for they know no better life. The prisoners manage to break their bonds one day, and discover that their reality was not what they thought it was. They discovered the sun, which Plato uses as an analogy for the fire that man cannot see behind. Like the fire that cast light on the walls of the cave, the human condition is forever bound to the impressions that are received through the senses. Even if these interpretations (or, in Kantian terminology, intuitions) are an absurd misrepresentation of reality, we cannot somehow break free from the bonds of our human condition—we cannot free ourselves from phenomenal state just as the prisoners could not free themselves from their chains. If, however, we were to miraculously escape our bondage, we would find a world that we could not understand—the sun is incomprehensible for someone who has never seen it. In other words, we would encounter another "realm", a place incomprehensible because, theoretically, it is the source of a higher reality than the one we have always known; it is the realm of pure Form, pure fact.Socrates remarks that this allegory can be paired with previous writings, namely the analogy of the sun and the analogy of the divided line.Analogy of the divided line
The analogy of the divided line (Greek: γραμμὴ δίχα τετμημένη) is presented by the Greek philosopher Plato in the Republic (509d–511e). It is written as a dialogue between Glaucon and Socrates, in which the latter further elaborates upon the immediately preceding Analogy of the Sun at the former's request. Socrates asks Glaucon to not only envision this unequally bisected line but to imagine further bisecting each of the two segments. Socrates explains that the four resulting segments represent four separate 'affections' (παθήματα) of the psyche. The lower two sections are said to represent the visible while the higher two are said to represent the intelligible. These affections are described in succession as corresponding to increasing levels of reality and truth from conjecture (εἰκασία) to belief (πίστις) to thought (διάνοια) and finally to understanding (νόησις). Furthermore, this analogy not only elaborates a theory of the psyche but also presents metaphysical and epistemological views.Analogy of the sun
The analogy of the sun (or simile of the sun or metaphor of the sun) is found in the sixth book of The Republic (507b–509c), written by the Greek philosopher Plato as a dialogue between Glaucon (Plato's elder brother) and Socrates (narrated by the latter). Upon being urged by Glaucon to define goodness, a cautious Socrates professes himself incapable of doing so. Instead he draws an analogy and offers to talk about "the child of goodness" (Greek: "ἔκγονός τε τοῦ ἀγαθοῦ"). Socrates reveals this "child of goodness" to be the sun, proposing that just as the sun illuminates, bestowing the ability to see and be seen by the eye, with its light so the idea of goodness illumines the intelligible with truth. While the analogy sets forth both epistemological and ontological theories, it is debated whether these are most authentic to the teaching of Socrates or its later interpretations by Plato. The sun is a metaphor for the nature of reality and knowledge concerning it.
Plato's use of such an analogy can be interpreted for many different reasons in philosophy. For example, Plato uses them to illustrate and help illuminate his arguments. In the Analogy of the Sun, Socrates compares the "Good" with the sun. Plato might be using the image of the sun to help bring life to his arguments or to make the argument more clearly understood. David Hume once wrote, "All our reasonings concerning matters of fact are founded on a species of Analogy."Plato makes the claim that "sight and the visible realm are deficient." He argues that for the other senses to be used all that is needed is the sense itself and that which can be sensed by it (e.g., to taste sweetness, one needs the sense of taste and that which can be tasted as sweet), but "even if a person's eyes are capable of sight, and he's trying to use it, and what he's trying to look at is coloured, the sight will see nothing and the colours will remain unseen, surely, unless there is also present an extra third thing which is made specifically for this purpose." The third thing Plato is talking about is light. Through this analogy he equates that which gives us natural light, the sun, as the source of goodness in this world.
"As goodness stands in the intelligible realm to intelligence and the things we know, so in the visible realm the sun stands to sight and the things we see."In other words, Plato is saying that the true nature of reality cannot be comprehended by the ordinary senses. Thus, we should make use of the mind rather than the sensory organs to better understand the higher truths of the universe. The mind, much like sight, requires a "third thing" to function properly, and that third thing is Plato's idea of goodness. He likens a mind without goodness to sight without light; one cannot operate at peak efficiency without the other.
"Well, here's how you can think about the mind as well. When its object is something which is lit up by truth and reality, then it has—and obviously has—intelligent awareness and knowledge. However, when its object is permeated with darkness (that is, when its object is something which is subject to generation and decay), then it has beliefs and is less effective, because its beliefs chop and change, and under these circumstances it comes across as devoid of intelligence."Having made these claims, Socrates asks Glaucon, "...which of the gods in heaven can you put down as cause and master of this, whose light makes our sight see so beautifully and the things to be seen?" (508a) Glaucon responds that both he and all others would answer that this is the sun. Analogously, Socrates says, as the sun illuminates the visible with light so the idea of goodness illuminates the intelligible with truth, which in turn makes it possible for people to have knowledge. Also, as the eye's ability to see is made possible by the light of the sun so the soul's ability to know is made possible by the truth of goodness.
Understand then, that it is the same with the soul, thus: when it settles itself firmly in that region in which truth and real being brightly shine, it understands and knows it and appears to have reason; but when it has nothing to rest on but that which is mingled with darkness—that which becomes and perishes, it opines, it grows dim-sighted, changing opinions up and down, and is like something without reason. ('The Republic, VI: 508d; trans. W. H. D. Rouse)
The allusion to "...that which becomes and perishes..." relates to all of that which is perceived by the bodily senses. The bodily senses make it clear that all visible things are subject to change, which Socrates categorizes into either the change of becoming or the change of perishing. Socrates argues that the bodily senses can only bring us to opinions, conveying an underlying assumption that true knowledge is of that which is not subject to change.
Instead, Socrates continues, knowledge is to be found in "... that region in which truth and real being brightly shine..." (508d) This is the intelligible illuminated by the highest idea, that of goodness. Since truth and being find their source in this highest idea, only the souls that are illumined by this source can be said to possess knowledge, whereas those souls which turn away are "...mingled with darkness...". This subject is later vividly illustrated in the Allegory of the Cave (514a–520a), where prisoners bound in a dark cave since childhood are examples of these souls turned away from illumination.
Socrates continues by explaining that though light and sight both resemble the sun neither can identify themselves with the sun. Just as the sun is rated higher than both light and sight, so is goodness rated more highly than knowledge and truth. It is goodness which allows us to know the truth and makes it possible to have knowledge. Hence goodness is more valuable than truth and knowledge as it holds a higher place. Through this analogy, Socrates helped Glaucon come to the realization that Goodness is of inestimable value, being both the source of knowledge and truth, as well as more valuable and unattainable than both.Plato further equates the sun to the ultimate form of goodness by calling them both sources of "generation". The sun not only makes objects visible but is necessary for their growth and nourishment, similarly to how goodness not only makes it possible for things to be, but also allows for things to be known.
The sun provides not only the power of being seen for things seen, but, as I think you will agree, also their generation and growth and nurture, although it is not itself generation...Similarly with things known, you will agree that the good is not only the cause of their becoming known, but the cause that they are, the cause of their state of being, although the good is not itself a state of being but something transcending far beyond it in dignity and power.Socrates' main concern was that he did not want his followers to place Goodness, Knowledge, and Truth all on the same level. You can achieve Goodness from Truth and Knowledge, but just because you have Truth and Knowledge that does not mean you have Goodness. Plato writes:
Well, what I'm saying is that it's goodness which gives the things we know their truth and makes it possible for people to have knowledge. It is responsible for knowledge and truth, you should think of it as being within the intelligible realm, but you shouldn't identify it with knowledge and truth, otherwise you'll be wrong: For all their value, it is even more valuable. In the other realm, it is right to regard light and sight as resembling the sun; So in this realm it is right to regard knowledge and truth as resembling goodness, but not to identify either of them with goodness, which should be rated even more highly.Ultimately, the Good itself is the whole point. The Good (the sun) provides the very foundation on which all other truth rests. Plato uses the image of the sun to help define the true meaning of the Good. The Good "sheds light" on knowledge so that our minds can see true reality. Without the Good, we would only be able to see with our physical eyes and not the "mind's eye". The sun bequeaths its light so that we may see the world around us. If the source of light did not exist we would be in the dark and incapable of learning and understanding the true realities that surround us.Incidentally, the metaphor of the sun exemplifies a traditional interrelation between metaphysics and epistemology: interpretations of fundamental existence create—and are created by—ways of knowing. It also neatly sums up two views for which Plato is recognized: his rationalism and his realism (about universals).
Socrates, using the Simile of the Sun as a foundation, continues with the Analogy of the Divided Line (509d–513e) after which follows the Allegory of the Cave (514a–520a).Argument
In logic and philosophy, an argument is a series of statements (in a natural language), called the premises or premisses (both spellings are acceptable), intended to determine the degree of truth of another statement, the conclusion. The logical form of an argument in a natural language can be represented in a symbolic formal language, and independently of natural language formally defined "arguments" can be made in math and computer science.
Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments. Deductive arguments can be valid or sound: in a valid argument, premisses necessitate the conclusion, even if one or more of the premisses is false and the conclusion is false; in a sound argument, true premisses necessitate a true conclusion. Inductive arguments, by contrast, can have different degrees of logical strength: the stronger or more cogent the argument, the greater the probability that the conclusion is true, the weaker the argument, the lesser that probability. The standards for evaluating non-deductive arguments may rest on different or additional criteria than truth—for example, the persuasiveness of so-called "indispensability claims" in transcendental arguments, the quality of hypotheses in retroduction, or even the disclosure of new possibilities for thinking and acting.Argument from analogy
Argument from analogy is a special type of inductive argument, whereby perceived similarities are used as a basis to infer some further similarity that has yet to be observed. Analogical reasoning is one of the most common methods by which human beings attempt to understand the world and make decisions. When a person has a bad experience with a product and decides not to buy anything further from the producer, this is often a case of analogical reasoning. It is also implicit in much of science; for instance, experiments on laboratory rats typically proceed on the basis that some physiological similarities between rats and humans entails some further similarity (e.g. possible reactions to a drug).Baseball metaphors for sex
Among American adolescents, baseball metaphors for sex are often used as euphemisms for the degree of physical intimacy achieved in sexual encounters or relationships. In the metaphor, first prevalent in the aftermath of World War II, sexual activities are described as if they are actions in a game of baseball.Convergent evolution
Convergent evolution is the independent evolution of similar features in species of different lineages. Convergent evolution creates analogous structures that have similar form or function but were not present in the last common ancestor of those groups. The cladistic term for the same phenomenon is homoplasy. The recurrent evolution of flight is a classic example, as flying insects, birds, pterosaurs, and bats have independently evolved the useful capacity of flight. Functionally similar features that have arisen through convergent evolution are analogous, whereas homologous structures or traits have a common origin but can have dissimilar functions. Bird, bat, and pterosaur wings are analogous structures, but their forelimbs are homologous, sharing an ancestral state despite serving different functions.
The opposite of convergence is divergent evolution, where related species evolve different traits. Convergent evolution is similar to parallel evolution, which occurs when two independent species evolve in the same direction and thus independently acquire similar characteristics; for instance, gliding frogs have evolved in parallel from multiple types of tree frog.
Many instances of convergent evolution are known in plants, including the repeated development of C4 photosynthesis, seed dispersal by fleshy fruits adapted to be eaten by animals, and carnivory.Four-dimensional space
A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible generalization of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring its length, width, and height (often labeled x, y, and z).
The idea of adding a fourth dimension began with Jean le Rond d'Alembert with his "Dimensions" published in 1754 followed by Joseph-Louis Lagrange in the mid-1700s and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann. In 1880 Charles Howard Hinton popularized these insights in an essay titled "What is the Fourth Dimension?", which explained the concept of a four-dimensional cube with a step-by-step generalization of the properties of lines, squares, and cubes. The simplest form of Hinton's method is to draw two ordinary cubes separated by an "unseen" distance, and then draw lines between their equivalent vertices. This can be seen in the accompanying animation, whenever it shows a smaller inner cube inside a larger outer cube. The eight lines connecting the vertices of the two cubes in that case represent a single direction in the "unseen" fourth dimension.
Higher dimensional spaces have since become one of the foundations for formally expressing modern mathematics and physics. Large parts of these topics could not exist in their current forms without the use of such spaces. Einstein's concept of spacetime uses such a 4D space, though it has a Minkowski structure that is a bit more complicated than Euclidean 4D space.
Single locations in 4D space can be given as vectors or n-tuples, i.e. as ordered lists of numbers such as (t,x,y,z). It is only when such locations are linked together into more complicated shapes that the full richness and geometric complexity of 4D and higher dimensional spaces emerge. A hint to that complexity can be seen in the accompanying animation of one of simplest possible 4D objects, the 4D cube or tesseract.Grapheme
In linguistics, a grapheme is the smallest unit of a writing system of any given language. An individual grapheme may or may not carry meaning by itself, and may or may not correspond to a single phoneme of the spoken language. Graphemes include alphabetic letters, typographic ligatures, Chinese characters, numerical digits, punctuation marks, and other individual symbols. A grapheme can also be construed as a graphical sign that independently represents a portion of linguistic material.The word grapheme, coined in analogy with phoneme, is derived from Ancient Greek γράφω (gráphō), meaning 'write', and the suffix -eme, by analogy with phoneme and other names of emic units. The study of graphemes is called graphemics.
The concept of graphemes is an abstract one and similar to the notion in computing of a character. By comparison, a specific shape that represents any particular grapheme in a specific typeface is called a glyph. For example, the grapheme corresponding to the abstract concept of "the Arabic numeral one" has two distinct glyphs (allographs) in the fonts Times New Roman and Helvetica.Homology (biology)
In biology, homology is the existence of shared ancestry between a pair of structures, or genes, in different taxa. A common example of homologous structures is the forelimbs of vertebrates, where the wings of bats, the arms of primates, the front flippers of whales and the forelegs of dogs and horses are all derived from the same ancestral tetrapod structure. Evolutionary biology explains homologous structures adapted to different purposes as the result of descent with modification from a common ancestor. The term was first applied to biology in a non-evolutionary context by the anatomist Richard Owen in 1843. Homology was later explained by Charles Darwin's theory of evolution in 1859, but had been observed before this, from Aristotle onwards, and it was explicitly analysed by Pierre Belon in 1555.
In developmental biology, organs that developed in the embryo in the same manner and from similar origins, such as from matching primordia in successive segments of the same animal, are serially homologous. Examples include the legs of a centipede, the maxillary palp and labial palp of an insect, and the spinous processes of successive vertebrae in a vertebral column. Male and female reproductive organs are homologous if they develop from the same embryonic tissue, as do the ovaries and testicles of mammals including humans.
Sequence homology between protein or DNA sequences is similarly defined in terms of shared ancestry. Two segments of DNA can have shared ancestry because of either a speciation event (orthologs) or a duplication event (paralogs). Homology among proteins or DNA is inferred from their sequence similarity. Significant similarity is strong evidence that two sequences are related by divergent evolution from a common ancestor. Alignments of multiple sequences are used to discover the homologous regions.
Homology remains controversial in animal behaviour, but there is suggestive evidence that, for example, dominance hierarchies are homologous across the primates.Hydraulic analogy
The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current is invisible and the processes at play in electronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents. Electricity (as well as heat) was originally understood to be a kind of fluid, and the names of certain electric quantities (such as current) are derived from hydraulic equivalents. As with all analogies, it demands an intuitive and competent understanding of the baseline paradigms (electronics and hydraulics).Islamofascism
"Islamic fascism" (first described in 1933), also known since 1990 as "Islamofascism", is a term drawing an analogy between the ideological characteristics of specific Islamist movements and a broad range of European fascist movements of the early 20th century, neofascist movements, or totalitarianism.Israel and the apartheid analogy
The Israeli apartheid analogy compares Israel's treatment of Palestinians to South Africa's treatment of non-whites during its apartheid era within the context of the crime of apartheid.
With respect to the Israeli-occupied West Bank, Israel's critics have repeatedly denounced it of practising a system akin to apartheid against Arabs and Palestinians. Israel has been described as an "apartheid" state by some scholars, United Nations investigators, human rights groups critical of Israeli policy and supporters of the Boycott, Divestment and Sanctions movement against Israel. The description has also been used by several Israeli former politicians. Critics of Israeli policy say that "a system of control" in the Israeli-occupied West Bank, including the ID system; Israeli settlements; separate roads for Israeli and Palestinian citizens around many of these settlements; Israeli military checkpoints; marriage law; the West Bank barrier; use of Palestinians as cheaper labour; Palestinian West Bank exclaves; and inequities in infrastructure, legal rights (e.g. "Enclave law"), and access to land and resources between Palestinians and Israeli residents in the Israeli-occupied territories, resemble some aspects of the South African apartheid regime, and that elements of Israel's occupation constitute forms of colonialism and of apartheid, contrary to international law.Opponents of the idea of Israeli apartheid in the West Bank argue that the comparison is factually, morally, and historically inaccurate and intended to delegitimize Israel. Opponents state that the West Bank and Gaza are not part of sovereign Israel. They argue that though the internal free movement of Palestinians is heavily regulated by the Israeli government, the territories are governed by the elected Palestinian Authority and Hamas leaders, so they cannot be compared to the internal policies of apartheid South Africa.With regard to claims of apartheid within Israel-proper, some commentators extend the analogy to include treatment of Arab citizens of Israel, describing their citizenship status as second-class.Critics of the claim argue that Israel cannot be called an apartheid state because unlike South Africa, which enshrined its racial segregation policies in law, Israeli law is the same for Jewish citizens and other Israeli citizens, with no explicit distinction between race, creed or sex.However, others believe that certain laws do explicitly or implicitly discriminate on the basis or creed or race, in effect privileging Jewish citizens and disadvantaging non-Jewish, and particularly Arab, citizens of the state. These include the Law of Return, the Ban on Family Unification, and many laws regarding security, land and planning, citizenship, political representation in the Knesset, education and culture. The Nation-State Bill, which has been met with worldwide condemnation, has also been compared by members of PLO, opposition MPs, and other Arab and Jewish Israelis, to an "apartheid law".Joseph Butler
Joseph Butler (18 May 1692 – 16 June 1752) was an English bishop, theologian, apologist, and philosopher. He was born in Wantage in the English county of Berkshire (now Oxfordshire). He is known, among other things, for his critique of Deism, Thomas Hobbes's egoism, and John Locke's theory of personal identity. Butler influenced many philosophers and religious thinkers, including David Hume, Thomas Reid, Adam Smith, Henry Sidgwick, John Henry Newman, and C. D. Broad, and is widely considered "as one of the preeminent English moralists." He also played an important, though under appreciated, role in the development of eighteenth-century economic discourse, greatly influencing the Anglican Dean of Gloucester and political economist Josiah Tucker.Metaphor
A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. It may provide clarity or identify hidden similarities between two ideas. Antithesis, hyperbole, metonymy and simile are all types of metaphor. One of the most commonly cited examples of a metaphor in English literature is the "All the world's a stage" monologue from As You Like It:
This quotation expresses a metaphor because the world is not literally a stage. By asserting that the world is a stage, Shakespeare uses points of comparison between the world and a stage to convey an understanding about the mechanics of the world and the behavior of the people within it.
The Philosophy of Rhetoric (1937) by rhetorician I. A. Richards describes a metaphor as having two parts: the tenor and the vehicle. The tenor is the subject to which attributes are ascribed. The vehicle is the object whose attributes are borrowed. In the previous example, "the world" is compared to a stage, describing it with the attributes of "the stage"; "the world" is the tenor, and "a stage" is the vehicle; "men and women" is the secondary tenor, and "players" is the secondary vehicle.
Other writers employ the general terms ground and figure to denote the tenor and the vehicle. Cognitive linguistics uses the terms target and source, respectively. Psychologist Julian Jaynes contributed the terms metaphrand, metaphier, paraphrand, and paraphier to the understanding of how metaphors evoke meaning thereby adding two additional terms to the common set of two basic terms. Metaphrand is equivalent to metaphor theory terms tenor, target, and ground. Metaphier is equivalent to metaphor theory terms vehicle, figure, and source. Paraphier is any attribute, characteristics, or aspect of a metaphier, whereas any paraphrand is a selected paraphier which has conceptually become attached to a metaphrand through understanding or comprehending of a metaphor. For example, if a reader encounters this metaphor: "Pat is a tornado," the metaphrand is "Pat," the metaphier is "tornado." The paraphiers, or characteristics, of the metaphier "tornado" would include: storm, power, wind, counterclockwise, danger, threat, destruction, etc. However, the metaphoric use of those attributes or characteristics of a tornado is not typically one-for-one; if Pat is said to be a "tornado" the metaphoric meaning is likely to focus on the paraphrands of power or destruction rather than on, say, the paraphier of counterclockwise movement of wind.Parable
A parable is a succinct, didactic story, in prose or verse that illustrates one or more instructive lessons or principles. It differs from a fable in that fables employ animals, plants, inanimate objects, or forces of nature as characters, whereas parables have human characters. A parable is a type of analogy.Some scholars of the canonical gospels and the New Testament apply the term "parable" only to the parables of Jesus, though that is not a common restriction of the term. Parables such as "The Prodigal Son" are central to Jesus's teaching method in the canonical narratives and the apocrypha.Qiyas
In Islamic jurisprudence, qiyās (Arabic: قياس) is the process of deductive analogy in which the teachings of the Hadith are compared and contrasted with those of the Qur'an, in order to apply a known injunction (nass) to a new circumstance and create a new injunction. Here the ruling of the Sunnah and the Qur'an may be used as a means to solve or provide a response to a new problem that may arise. This, however, is only the case providing that the set precedent or paradigm and the new problem that has come about will share operative causes (عِلّة, ʿillah). The ʿillah is the specific set of circumstances that trigger a certain law into action. An example of the use of qiyās is the case of the ban on selling or buying of goods after the last call for Friday prayers until the end of the prayer stated in the Quran 62:9. By analogy this prohibition is extended to other transactions and activities such as agricultural work and administration. Among Sunni Muslim in recent centuries Qiyas has been accepted as a fundamental source of Sharia law along with Ijmāʿ and secondary to the Qur'an, and the Sunnah.Russell's teapot
Russell's teapot is an analogy, formulated by the philosopher Bertrand Russell (1872–1970), to illustrate that the philosophic burden of proof lies upon a person making unfalsifiable claims, rather than shifting the burden of disproof to others.
Russell specifically applied his analogy in the context of religion. He wrote that if he were to assert, without offering proof, that a teapot, too small to be seen by telescopes, orbits the Sun somewhere in space between the Earth and Mars, he could not expect anyone to believe him solely because his assertion could not be proven wrong.
Russell's teapot is still invoked in discussions concerning the existence of God, and has had influence in various fields and media.Watchmaker analogy
The watchmaker analogy or watchmaker argument is a teleological argument which states, by way of an analogy, that a design implies a designer. The analogy has played a prominent role in natural theology and the "argument from design," where it was used to support arguments for the existence of God and for the intelligent design of the universe, in both Christianity and Deism.
Sir Isaac Newton, among other leaders in the scientific revolution, including René Descartes, upheld "that the physical laws he had uncovered revealed the mechanical perfection of the workings of the universe to be akin to a watch, wherein the watchmaker is God."The 1859 publication of Charles Darwin's theory of natural selection put forward an explanation for complexity and adaptation, which reflects scientific consensus on the origins of biological diversity. In the eyes of some, this provided a counter-argument to the watchmaker analogy: for example, the evolutionary biologist Richard Dawkins referred to the analogy in his 1986 book The Blind Watchmaker giving his explanation of evolution. Others, however, consider the watchmaker analogy to be compatible with evolutionary creation, opining that the two concepts are not mutually exclusive. In the 19th century, deists, who championed the watchmaker analogy, held that Darwin's theory fit with "the principle of uniformitarianism—the idea that all processes in the world occur now as they have in the past" and that deistic evolution "provided an explanatory framework for understanding species variation in a mechanical universe."In the United States, starting in the 1960s, creationists revived versions of the argument to dispute the concepts of evolution and natural selection, and there was renewed interest in the watchmaker argument. The most famous statement of this teleological argument using the watchmaker analogy was given by William Paley in his 1802 book Natural Theology or Evidences of the Existence and Attributes of the Deity.