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The Territories of Human Reason: Science and Theology in an Age of Multiple Rationalities

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6 From Observation to Theory: Deduction, Induction, and Abduction

  • Published: December 2018
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How do we move from observing the world to developing more complex and sophisticated ways of representing and understanding it? This chapter examines the intellectual journey from observing our world to representing it in theory, focussing on three distinct processes that are widely believed to be important in this process—deduction, induction, and abduction. Each of these rational strategies is used in theological or philosophical arguments relating to the existence of God. In each case, careful consideration is given to its application both in the natural sciences and in Christian theology. Particular attention is given to the American philosopher Charles S. Peirce’s use of abduction, and its potential significance for Christian theology.

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  • Semantics and Pragmatics of Language Usage
  • Analytic-Synthetic Distinction
  • Meaning of Words and Phrases
  • Philosophy of Science
  • Scientific Realism and Rationalism
  • Induction and the Hypothetico-Deductive Model
  • Theory-Ladenness and Underdetermination
  • Philosophy of Mind
  • Mind-Body Dualism and Emergentism
  • Materialism and Physicalism
  • Identity Theory and Personal Identity
  • Philosophy of Religion
  • Religious Pluralism and Exclusivism
  • The Problem of Evil and Suffering
  • Religious Experience and Faith
  • Metaphysical Theories
  • Idealism and Realism
  • Determinism, Fatalism, and Libertarianism
  • Phenomenalism and Nominalism
  • Epistemological Theories
  • Intuitionism, Skepticism, and Agnosticism
  • Rationalism and Empiricism
  • Foundationalism and Coherentism
  • Aesthetic Theories
  • Formalist Aesthetics, Emotional Aesthetics, Experiential Aesthetics
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  • Ethical Theories
  • Virtue Ethics, Utilitarianism, Deontology
  • Subjectivism, Egoism, Hedonism
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  • Metaphysical Terms
  • Cause, Necessity, Possibility, Impossibility
  • Identity, Persistence, Time, Space
  • Substance, Attribute, Essence, Accident
  • Logic and Argumentation Terms
  • Analogy, Syllogism, Deduction, Induction
  • Inference, Validity, Soundness, Refutation
  • Premise, Conclusion, Entailment, Contradiction
  • Epistemological Terms
  • Perception and Knowledge Claims
  • Infallibility, Verifiability, Coherence Theory of Truth
  • Justification, Beliefs and Truths
  • Ethical Terms
  • Modern Texts
  • A Vindication of the Rights of Woman by Mary Wollstonecraft
  • Thus Spoke Zarathustra by Friedrich Nietzsche
  • The Critique of Pure Reason by Immanuel Kant
  • Medieval Texts
  • The Guide for the Perplexed by Moses Maimonides
  • The Summa Theologiae by Thomas Aquinas
  • The Incoherence of the Incoherence by Averroes
  • Ancient Texts
  • The Art of Rhetoric by Cicero
  • The Republic by Plato
  • Comparing Analogy, Syllogism, Deduction and Induction
  • Philosophical Terms

Throughout the ages, philosophers have sought to understand how humans reason and come to logical conclusions. To do this, they have developed a number of tools to aid in their reasoning - Analogy, Syllogism, Deduction, and Induction. But what is the difference between these four tools? How can we use them to better understand our own reasoning processes? In this article, we will explore the differences between Analogy, Syllogism, Deduction, and Induction and discuss how they each help us gain insight into our own logic. Analogy, syllogism , deduction and induction are all types of reasoning used in logic and argumentation. Analogy is based on similarities between two objects or ideas, while syllogism uses two premises to draw a conclusion.

An example of analogy would be saying that a person is like a tree because both grow and change over time. An example of syllogism would be: All cats have fur; my pet is a cat; therefore, my pet has fur. Deduction is a type of logical reasoning in which a conclusion is drawn from a set of premises. An example of deduction would be: All mammals have fur; dogs are mammals; therefore, dogs have fur.

Induction is a type of logical reasoning in which a general rule is inferred from specific facts or observations. An example of induction would be: I have seen many cats with fur; therefore, all cats have fur. Analogy is a type of reasoning in which an argument is made from two previously established similarities. It is used to show that two objects or ideas are similar in some way, which can be used to draw conclusions about them.

Syllogism is a type of logical argument in which two premises are used to draw a conclusion. This type of reasoning allows for conclusions to be drawn from two given facts or premises. Deduction is a type of logical reasoning that uses a set of premises to draw a conclusion. This type of reasoning allows for conclusions to be drawn from existing knowledge or assumptions.

This type of reasoning allows for the formulation of general rules based on observed phenomena. Analogy, syllogism, deduction and induction are all important tools for logic and argumentation. Analogy can help explain relationships between two objects or ideas, while syllogism can be used to draw conclusions from two facts or premises. Deduction can be used to draw conclusions from existing knowledge or assumptions, while induction can be used to formulate general rules based on observed phenomena.

Deduction is the process of deriving a conclusion based on premises that are generally accepted as true, while induction is the process of deriving general principles from specific observations. An analogy typically relies on the similarity of two or more objects that are not necessarily related, but can be used to make a point about a third object. For example, one might use an analogy of a car and its driver to explain the relationship between a computer and its user. In this analogy, the car is the computer and the driver is the user – they are both necessary components of the system, but they cannot function without one another.

For example, if one were to observe an apple falling from a tree and then infer that all apples fall from trees, this would be an example of induction. When engaging in induction, the evidence provided must be sufficient to allow one to draw a reasonable conclusion. This means that if the evidence is limited or incomplete, it may be impossible to make a valid inference. As such, induction is considered less reliable than other forms of logic, as the results may be uncertain or inaccurate. Induction can be used in many areas of life, such as science and law.

The major premise is a general statement that applies to all members of a certain class, while the minor premise is a specific statement about a particular member of that class. The conclusion then follows logically from the two premises. For example, if the major premise is “All mammals are warm-blooded” and the minor premise is “Dogs are mammals,” then the conclusion is “Therefore, dogs are warm-blooded.”Syllogisms can be used to explain why something is true, or to draw inferences about a certain situation. They can also be used to prove that something is false, or to disprove an argument.

In deduction, the logical conclusion follows necessarily from the premises given. In other words, if the premises are true, then the conclusion must also be true. Deduction is often used in arguments to draw valid conclusions that are supported by reliable evidence. It is also a common technique used in legal and scientific arguments.

Deductive reasoning can be used to make logical connections between facts and to arrive at reasonable conclusions. For example, if someone were to make the statement “All apples are red” and then argue that “this apple is red”, they would be using deductive reasoning. The conclusion follows necessarily from the premise and is supported by reliable evidence (i.e., the fact that the apple is indeed red). Deduction is an important part of logic and argumentation as it allows for the drawing of valid conclusions based on reliable evidence.

It can help people make informed decisions based on facts and evidence rather than conjecture or speculation. Analogy, syllogism, deduction, and induction are all important forms of reasoning in logic and argumentation. Analogy is a type of inductive reasoning that draws parallels between two distinct objects or ideas. Syllogism is a deductive form of reasoning that reaches a conclusion based on two or more premises. Deduction is another type of logical reasoning that uses facts or premises to reach a conclusion.

Lastly, induction is a form of reasoning where the conclusion is reached by looking at the evidence. By understanding the differences between these four concepts, you can make stronger arguments and use logic to better understand the world around you.

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Analogy, Deduction and Learning

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Proceedings of the 38th Annual Hawaii International Conference on System Sciences

Related Papers

Hervé ZWIRN

Analogy plays an important role in science as well as in non-scientific domains such as taxonomy or learning. We make explicit the difference and complementarity between the concept of analogical statement, which merely states that two objects have a relevant similarity, and the concept of analogical inference, which relies on the former in order to draw a conclusion from some premises. For the first, we show that it is not possible to give an absolute definition of what it means for two objects to be analogous; a relative definition of analogy is introduced, only relevant from some point of view. For the second, we argue that it is necessary to introduce a background over-hypothesis relating two sets of properties; the belief strength of the conclusion is then directly related to the belief strength of the over-hypothesis. Moreover, we assert the syntactical identity between analogical inference and one case induction despite important pragmatic differences.

hypothesis generation by analogy induction deduction intuition

Flexible Query Answering Systems

Mary-Anne Williams

American Psychologist

Keith Holyoak

1. Analogy is a powerful cognitive mechanism that people use to make inferences and learn new abstractions. The history of work on analogy in modern cognitive science is sketched, focusing on contributions from cognitive psychology, artificial intelligence, and philosophy of science. This review sets the stage for the 3 articles that follow in this Science Watch section.(PsycINFO Database Record (c) 2012 APA, all rights reserved)

Cognitive Systems Research

This paper introduces the various forms of analogy in NARS, a general-purpose reasoning system. NARS is an AI system designed to be adaptive and to work with insufficient knowledge and resources. In the system, multiple types of inference, including analogy, deduction, induction, abduction, comparison, and revision, are unified both in syntax and in semantics. The system can also carry out

International Journal of Digital Content Technology and its Applications

Junsheng Zhang

Journal of Intelligent Information Systems

Fabio Leuzzi

Analogy is the cognitive process of matching the characterizing features of two different items. This may enable reuse of knowledge across domains , which can help to solve problems. Indeed, abstracting the 'role' of the features away from their specific embodiment in the single items is fundamental to recognize the possibility of an analogical mapping between them. The analogical reasoning process consists of five steps: retrieval, mapping, evaluation , abstraction and re-representation. This paper proposes two forms of an operator that includes all these elements, providing more power and flexibility than existing systems. In particular, the Roles Mapper leverages the presence of identical descriptors in the two domains, while the Roles Argumentation-based Mapper removes also this limitation. For generality and compliance with other reasoning operators in a multi-strategy inference setting, they exploit a simple formalism based on First-Order Logic and do not require any background knowledge or meta-knowledge. Applied to the most critical classical examples in the literature, they proved to be able to find insightful analogies.

Stuart J. Russell

Uncertainty in Pharmacology (Boston Studies in the Philosophy and History of Science 338)

Roland Poellinger

Analogical arguments are ubiquitous vehicles of knowledge transfer in science and medicine. This paper outlines a Bayesian evidence-amalgamation framework for the purpose of formally exploring different analogy-based inference patterns with respect to their justification in pharmacological risk assessment. By relating formal explications of similarity, analogy, and analog simulation, three sources of confirmatory support for a causal hypothesis are distinguished in reconstruction: relevant studies, established causal knowledge, and computational models.

  • Cognitive Science

Making analogies is an important way for people to explain and understand new concepts. Though making analogies is natural for human beings, it is not a trivial task for a dialogue agent. Making analogies requires the agent to establish a correspondence between concepts in two different domains. In this work, we explore a data-driven approach for making analogies automatically. Our proposed approach works with data represented as a flat graphical structure, which can either be designed manually or extracted from Internet data. For a given concept from the base domain, our analogy agent can automatically suggest a corresponding concept from the target domain, and a set of mappings between the relationships each concept has as supporting evidence. We demonstrate the working of this algorithm by both reproducing a classical example of analogy inference and making analogies in new domains generated from DBPedia data.

Studies in Computational Intelligence

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Mental Construction

Neurons to Abstraction, Similarity, and Associations leads to Creativity

Induction and Analogy

Induction is often handily described as reasoning from the specific to the general. We observe night is followed by day. By induction, we conclude when this night ends, day will follow.

How does Mental Construction explain induction’s operation?

Induction Operation

  • Abstraction. The Almost Gate automatically eliminates details above the threshold, yielding a common result. Almost Gate post explaining how it arises.
  • Categorization. Hebb’s Law explains that repeated experiences strengthen synaptic connections between firing neurons. Hebb’s Law explains both categorization into unnamed patterns and named patterns . Unnamed patterns are patterns you note but that do not have names (or names you know).
  • Abstraction and categorization occur at each stop of the concept elevator, the movement of patterns from senses and from memory towards the executive areas of the prefrontal lobes.
  • A behavioral choice is selected from a category or cluster. The choice becomes more specific as it approach expression, when it becomes a concrete behavioral expressions.

Induction operation relies on similarity of patterns which, across abstraction levels, supports association between patterns. A typical induction occurs when one compares the present situation with a past situation and, upon finding enough similarities, decides that the outcome of the current situation is likely to be the same as the outcome of the past situation.

Aristotle in De Poetica captures the essence of induction in his final clause lauding metaphor.

The greatest thing by far is to be a master of metaphor. It is the one thing that cannot be learned from others; and it is also a sign of genius, since a good metaphor implies an intuitive perception of the similarity in dissimilars.

The perception of the similarity in dissimilars. That is what the Almost Gate yields when a current input surmounts it, leading to same downstream action as did a previous input which also surmounted the Almost Gate. The two inputs where similar yet they are dissimilar (distinct). If an individual has a high Almost Gate, the two input must both be very similar to have topped the barrier, yet if another individual has a low Almost Gate, the two inputs need less similarity to toppled over the barrier.

How close the association must be? How many features in common must exist for a person to have confidence in the conclusion? The significance of fidelity transmission was broached in Neural Cascade . Completely relying on induction permits false conclusions. An induction conclusion is not guaranteed to be true, even when its starting facts are.

Figure 20.1 Induction and the Almost Gate

Figure 20.1 shows the general flow of induction in Mental Construction. Without effort, without conscious direction, our brain examines the current environment for patterns similar to those we came across in our past and to those in our learned knowledge. It’s automatic. This base level begins before the level of consciousness, prior to words. For simplicity of discussion, the winning single neuron and neural threshold will be used, although layers of neurons are involved in processing input.

  • Input. The originating source. Sensory data or processed data that is passed forward. At most, 0.1% of cortical neurons contact directly with sensory information.
  • Almost Gate. When the sum of the dendritic electric potentials meets or exceeds the neural threshold, the axon fires completely.
  • Abstraction. A set of different inputs have the capability to cause the neuron to fire, that detail is lost when the Almost Gate is bridged.
  • Category. The commonality of the abstraction exists as the organizing feature of the input into a category.
  • Category Members. Our learning and memory holds other members in each category. Given multiple levels of abstractions, all features are not necessarily identical in all members of the category.
  • Similarity. Remembered instances of the category run parallel through a copy of the same path as the input data feed, bringing over its unique overtones (features above the shared abstraction).
  • Replacement. Any remembered instance that has enough features in common can substitute for the original input.
  • Analogy. The substitution with its unique antecedents can offer new perspectives on the original situation.

At its core, a pattern is a non-verbal method of describing the world. Many patterns earn labels or names in our conscious mind, but they all start as an arrangement of inputs with no names. Patterns are produced in both cortical hemispheres, but the named patterns dominant on the hemisphere which generates speech. It’s easiest to think of a pattern at its origin, a portion of a sensory mode, like a visual snapshot, a sound that we hear but don’t name, or a taste that we crave but can’t describe. Patterns are not just snapshots, but personal encodings.

Patterns can also be sequences of actions that are meaningful to us. Every time that situation occurs, a minute later another thing happens. If one does this, then that follows. Many such sequences have names. Many don’t. The number of named sequences (relationships) you know affect the side of the brain that dominates in processing the information.

Patterns can capture more details than words. Consider a new mustache on your pal, as an example. His verbal name remains the same, but you still recognize him. His pattern is enlarged and more fluid than his name.

Figure 20.2 When all details are equally vivid, attention is diluted.

More detail is not always superior. Consider Figure 20.2, a painting by William Holman Hunt, with extreme detail throughout the image. The extraneous detail deflects from the attention that should be on the Christ figure.

Patterns and words vie to describe our internal world as they  travel along the corpus callosum . This pattern-word matching occurs periodically as they travel their concept elevator toward the frontal lobe.

Analogies have two significant characteristics that identify them.

  • They draw a comparison in order to show a similarity in some respect.

They imply an inference that if things agree in some respects, they probably agree in other ways.

The general form of an analogy has been known since ancient days. A is to B as C is to D. That’s often written A:B :: C:D.

Let’s start with a simple analog, using A is Soap, B is Wash. C is Broom, and D is Sweep

  • Soap is to Wash a Broom is to Sweep. We use soap to wash and we use a broom to sweep

Analogies are defined by similarities, not exact matches. Above, instead of the last term Sweep, a final term of Clean also fits. We use soap to clean our skin and we use a broom to clean a floor. An important characteristic of analogies is there exists more than one fourth element that can make sense. This becomes very important when we make inferences based on an analogy.

Analogy is the natural operation due to our neural brain Detecting associations between raw concepts is easy. It does not take effort when you know the features of the concepts. However, many analogies depend on knowledge to deliver the similarities required for an analogy to be recognized. Often the features in common are learned.

Figure 20.3 Simple Concrete Analogy

Consider the relationship in Figure 20.3. The question mark indicates an analogical conclusion that you might need to make. Perhaps on a test, but almost perhaps in understanding a comment from a friend. A Carpenter is to a Mason as Wood is to ?.

If you know the meaning of the words, it’s not hard to understand that D is stone. A carpenter works with wood. A mason works with stone.

Analogies, even with this uncluttered form can be quite difficult. Consider Land is to Water as Arable is to ? or Othello is to MacBeth as Jealousy is to ?  These analogies require background knowledge, which you may not have. This shows your knowledge controls which analogies occur to you . The more knowledge you have—whether gained by personal experience, observation of friends, discussions in classrooms or reports in media—the more analogies will occur to you.

Stock Market

Figure 20.4 Stock Market Analogy

Let’s consider an analogy that people based actions on, the stock market in 2008 (Figure 20.4). This is not a discussion of the wisdom of a particular choice, but a consideration of what the analogy was and why some people saw it and other people did not. A feature has been added to the analogy, an action can be performed before the result is seen. In 2008, a significant collapse of stock prices started. Some people were reminded of the crash started in 1929. Columns were written in business pages recommending that you get your money out of the market, because the Crash of 1929 led to a drop of 90% in stock prices.

The analogy is the Crash of ’29 is to the Crash of ’08 as the Loss of Money after ’29 will be to the Loss of Money after ’08, assuming you do the same thing in ’08 as was done in ’29. Therefore to get a different outcome, take a different action—remove your money out of the market.

Many people moved all their money out of the stock market in ’08 based on concern that the analogy would play out the same way as in the Great Depression.

Yet not everyone believed the stock market analogy between ’29 and ’08. Why? A few reasons.

  • The doubters had a higher Almost Gate . They naturally demand a greater number of common features before they see a similarity.
  • In this manner, the information entering into their Almost Gates is different.
  • Other doubters have distinct theories of stock market pricing which imply different stock market actions.

The essential point is the analogy is it depends on similarities in the abstract representation of the two crashes.The analogy is not the result of a logical deduction. It is an inductive inference.

General Analogy used in decision-making (Figure 20.5).

Figure 20.4 Decision-making analogy

Analogy and the Almost Gate

It is a known fact that, if it rains, the grass is wet. So, upon seeing that the grass is wet, a naive person may analogically conclude that it has rained. Of course, someone may have just watered the lawn. It may not have rained. It is possible to make mistakes with analogies. That mistakes are possible is not denied, but it is also true if we didn’t make analogical inferences we would decide hardly anything. Complete information is rarely available.

That brings to mind a contrary question. How can deductive logic arise given that our brain is entirely neural?

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Bowers, K.S., Regher G., Balthazard, C. & Parker, K. (1990). Intuition in the context of discovery. Cognitive Psychology , 22, 72-110.

Klein, Gary. The Power of Intuition. How To Use Your Gut Feelings To Make Better Decisions At Work . Doubleday Press. 2004. Kindle. eISBN: 978-0-307-42404-4

In general, each person has an idiosyncratic neural threshold. That is Almost Gates require different numbers of triggering inputs to fire.

A person with a high Almost Gate requires a close match (more similarities) between a new stimulus and a learned category to see a match. Their outlook is quite literal. Fewer categories are associated with the bar for matching so high. An extreme case would be a person who demands that the cover image of “ rose petals ” for a woman’s biking blog be explained. The metaphor makes no sense to him.

Contrary-wise, those with a low Almost Gate see associations between many, many things. That can be useful because they have more premises to draw conclusions upon; unfortunately, it also causes them often overlook differences that turn out to be significant.

Baddeley, Alan. Your Memory: A User’s Guide. Firefly Books, Buffalo, NY, 2004. Print. ISBN 1-55297-985-7

The Sapir-Whorf hypothesis is the theory that an individual’s thoughts and actions are determined by the language or languages that individual speaks.

The strong version of the hypothesis states that all human thoughts and actions are bound by the restraints of language, and is generally less accepted than the weak version.

The weak version says that language only somewhat shapes our thinking and behavior .

Instead of considering linguistic relativism as limiting the possibilities of thought, a more productive perspective is that language organizes experience in a manner which has yielded useful thoughts and behaviors over the language’s lifespan.

“Some believe their success is based on innate ability; these are said to have a “fixed” theory of intelligence (fixed mindset). Others, who believe their success is based on hard work, learning, training and doggedness are said to have a “growth” or an “incremental” theory of intelligence (growth mindset).

Dweck, Carol S. Mindset: The New Psychology of Success. Ballantine Books, Penguin Random House, New York, 2016. Print. 978-0-345-47232-8

A message box with a footnote

Spitzer, Manfred . The Mind Within the Net . Models of Learning, Thinking, and Acting . The MIT Press, 1999. Print. ISBN 0-262-69236-8

Information is believed to be transmitted not by a single firing of a neuron, but by the neuron’s spike train : either by overall rate of firing or by  precise timing of firing.

I have removed that complication in the discussion, because it does not alter the fundamental idea. Any set of input which exceeds the neuron’s threshold  is treated the same thereafter. The Almost Gate is operational.

Scholarpedia . http://www.scholarpedia.org/. Web site. Dec. 15, 2017.

Sternberg, Robert J. and Sternberg, Karin. Cognitive Psychology , 6th Edition. Wadsworth Cengage Learning, 2009. Print. ISBN 978-1-133-31391-5

From Internet Encyclopedia of Philosophy

The mathematical proof technique called “mathematical induction” is deductive and not inductive. Proofs that make use of mathematical induction typically take the following form:

Property P is true of the natural number 0. For all natural numbers  n , if P holds of  n then P also holds of  n + 1. Therefore, P is true of  all natural numbers.

When such a proof is given by a mathematician, and when all the premises are true, then the conclusion follows necessarily. Therefore, such an inductive argument is deductive. It is deductively sound, too.

From WikiPedia article . Bolding added.

Working memory is a cognitive system with a limited capacity that is responsible for temporarily holding information available for processing. Working memory is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-term memory, but some theorists consider the two forms of memory distinct , assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information

James, William. The Principles of Psychology. Encyclopedia Britannica, Inc and Henry Holt and Company, Inc.1952. Print. ISBN 0-85229-163-9

Memory is not a photograph of external reality stored in the brain, but a reconstruction based on observed event, personal emotional impact, and learned relationships.

Consider the Almost Gates that the current situational features go through. Our remembered situations also go through the same path. When there is sufficient matching of results (neural thresholds are surmounted), the situations fit in the same abstract category. Other features of the situations may or may not be comparable.

Carter, Rita. The Human Brain Book: An Illustrated Guide to its Structure, Function, and Disorders . DK. London,  New York, Melbourne, Munich, Delhi, 2009. Print with DVD. ISBN 978-0-7566-5441-2

Professor Maguire quoted in a Wellcome press release in Dec. 2011.

The current situation, remembered situations, and 3S imperatives – in their manifestations as emotions, personality traits, goals, desires, and fears – feed into neurons whose outputs lead ultimately to different actions.

The neuron whose Almost Gate is surmounted triggers its action chain. With so many neural inputs streaming from various sources, it’s unsurprising that typically our 3S imperatives are not completely satisfied by our response.

“… the cortex works as a rule-extraction machine and produces maps of input according to the principles of frequency and simularity.” Spitzer (p 138). Spitzer, Manfred . The Mind Within the Net . Models of Learning, Thinking, and Acting . The MIT Press, 1999. Print. ISBN 0-262-69236-8

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Bayes’ theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if cancer is related to age, then, using Bayes’ theorem, a person’s age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person’s age.

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[M]emory is not entirely faithful. When you perceive an object, groups of neurons in different parts of your brain process the information about its shape, colour, smell, sound, and so on. Your brain then draws connections among these different groups of neurons, and these relationships constitute your perception of the object. Subsequently, whenever you want to remember the object, you must reconstruct these relationships. The parallel processing that your cortex does for this purpose, however, can alter your memory of the object. McGill Memory and Learning

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[pdb_single record_id = 975 groups=works_cited]

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9.7: Inductive and Deductive Reasoning

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  • Differentiate between deductive and inductive reasoning

Deductive and Inductive Arguments: Two Ways of Understanding

We have two basic approaches for how we come to believe something is true.

The first way is that we are exposed to several different examples of a situation, and from those examples, we conclude a general truth. For instance, you visit your local grocery store daily to pick up necessary items. You notice that on Friday, two weeks ago, all the clerks in the store were wearing football jerseys. Again, last Friday, the clerks wore their football jerseys. Today, also a Friday, they’re wearing them again. From just these observations, you can conclude that on all Fridays, these supermarket employees will wear football jerseys to support their local team.

This type of pattern recognition, leading to a conclusion, is known as inductive reasoning .

Knowledge can also move the opposite direction. Say that you read in the news about a tradition in a local grocery store, where employees wore football jerseys on Fridays to support the home team. This time, you’re starting from the overall rule, and you would expect individual evidence to support this rule. Each time you visited the store on a Friday, you would expect the employees to wear jerseys.

Such a case, of starting with the overall statement and then identifying examples that support it, is known as deductive reasoning .

In the process of deduction, you begin with some statements, called “premises,” that are assumed to be true, you then determine what else would have to be true if the premises are true.

For example, you could begin by assuming that God exists, and is good, and then determine what would logically follow from such an assumption. With this premise, you would look for evidence supporting a belief in God.

With deduction, you can provide absolute proof of your conclusions, given that your premises are correct. The premises themselves, however, remain unproven and unprovable.

Examples of deductive logic:

  • All men are mortal. Joe is a man. Therefore Joe is mortal. If the first two statements are true, then the conclusion must be true.
  • Bachelors are unmarried men. Bill is unmarried. Therefore, Bill is a bachelor.
  • To get a Bachelor’s degree at a college, a student must have 120 credits. Sally has more than 130 credits. Therefore, Sally has a bachelor’s degree.

Two rectangles. Left: General Principle. Right: Special Case. An arrow pointing left to right above them is labeled "deductive reasoning." An arrow pointing right to left below them is labeled "inductive reasoning."

In the process of induction, you begin with some data, and then determine what general conclusion(s) can logically be derived from those data. In other words, you determine what theory or theories could explain the data.

For example, you note that the probability of becoming schizophrenic is greatly increased if at least one parent is schizophrenic, and from that you conclude that schizophrenia may be inherited. That is certainly a reasonable hypothesis given the data.

However, induction does not prove that the theory is correct. There are often alternative theories that are also supported by the data. For example, the behavior of the schizophrenic parent may cause the child to be schizophrenic, not the genes.

What is important in induction is that the theory does indeed offer a logical explanation of the data. To conclude that the parents have no effect on the schizophrenia of the children is not supportable given the data, and would not be a logical conclusion.

Examples of inductive logic:

  • This cat is black. That cat is black. A third cat is black. Therefore all cats are black.
  • This marble from the bag is black. That marble from the bag is black. A third marble from the bag is black. Therefore all the marbles in the bag black.
  • Most universities and colleges in Utah ban alcohol from campus. Therefore most universities and colleges in the U.S. ban alcohol from campus.

Deduction and induction by themselves are inadequate to make a compelling argument. While deduction gives absolute proof, it never makes contact with the real world, there is no place for observation or experimentation, and no way to test the validity of the premises. And, while induction is driven by observation, it never approaches actual proof of a theory. Therefore an effective paper will include both types of logic.

Argument terminology showing a flowchart that an argument can rely on either deductive or inductive reasoning, and then be considered either valid or invalid, and strong or weak.

This video reviews some of the distinctions between inductive and deductive reasoning.

You can view the transcript for “Inductive VS Deductive Reasoning by Shmoop” here (opens in new window) .

https://assessments.lumenlearning.co...essments/20280

https://assessments.lumenlearning.co...essments/20281

deductive reasoning : top-down reasoning; a method of reasoning in which a certain conclusion follows general premises.

inductive reasoning : bottom-up reasoning; a method of reasoning in which several premises provide evidence of a probable conclusion.

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  • Inductive VS Deductive Reasoning by Shmoop. Authored by : Shmoop. Located at : https://www.youtube.com/watch?v=VXW5mLE5Y2g&feature=youtu.be . License : Other . License Terms : Standard YouTube License
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Model-Based Reasoning in Science and Technology pp 107–119 Cite as

Abduction, Induction, and Analogy

On the Compound Character of Analogical Inferences

  • Gerhard Minnameier 5  

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10 Citations

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 314))

Analogical reasoning has been investigated by philosophers and psychologists who have produced different approaches like “schema induction” (Gick and Holyoak) or the “structure-mapping theory” (Gentner).What is commonplace, however, is that analogical reasoning involves processes of matching and mapping. Apart from the differences that exist between these approaches, one important problem appears to be the lack of inferential precision with respect to these processes of matching and mapping. And this is all the more problematic, because analogical reasoning is widely conceived of as “inductive” reasoning. However, inductive reasoning - in a narrow and technical sense - is not creative, whereas analogical reasoning counts as an important source of human creativity. It is C. S. Peirce’s merit to have pointed to this fact and that induction can merely extrapolate and generalize something already at hand, but not the kind of reasoning that leads to new concepts. Indeed, inventive reasoning is usually identified with abduction, and consequently abduction should play at least some role in analogy. Peirce has claimed that analogy is a compound form of reasoning that integrates abduction and induction, but the intriguing question is still, how these two inferences are to be reconstructed precisely. In the proposed paper I hold that analogical reasoning can indeed be analyzed in this way and that this helps us to reach a much more precise and differentiated understanding of the forms and processes of analogical reasoning. In particular I hold that (at least) two forms of analogical reasoning have to be distinguished, because they represent different inferential paths. The underlying inferential processed will be explicated in detail and illustrated by various examples.

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Minnameier, G. (2010). Abduction, Induction, and Analogy. In: Magnani, L., Carnielli, W., Pizzi, C. (eds) Model-Based Reasoning in Science and Technology. Studies in Computational Intelligence, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15223-8_5

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IMAGES

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  3. Inductive vs Deductive Reasoning (With Definitions & Examples)

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  4. Induction, Deduction, and Hypothesis

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  5. Inductive vs. Deductive Reasoning

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VIDEO

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  4. The hypothesis of sixth-generation fighter aircraft (HD Enhanced Edition)

  5. Syllogism I Induction Deduction I Statement Conclusion I Cause Effect

  6. Hypothesis And Deduction

COMMENTS

  1. The Scientific Endeavor: Chapter 3 Flashcards

    Statistical procedures are used to select an appropriate sample. Control group. 1. The ball drop experiment is a simple one in which only two variables are involved: the density of the fluid and the time of drop. 2. A way around this problem is to divide the study into test subjects and control subjects.

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    Scientific Endeavor. Hypothesis generation by anology, induction, deduction, intuition. Click the card to flip 👆. Analogy- similiar situations lead to similar results. Induction- arises from observation of a specific phenomena. Deduction- based off better -established scientific knowledge. Intuition- statement as to what "seems right". Click ...

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    If C. S. Peirce had only developed his triad of reasoning and arguments - abduction, induction, and deduction - and the consequences of this triad for his renewed conception of science and its methods, that would have been enough to guarantee his fame in the future. In fact, his abductive logic constitutes an extremely original contribution ...

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    However, deduction is used at least in the procedures of the hypothetico-deductive method (i.e., deduction step) introduced as a scientific method aiming at hypothesis generation. Deduction also plays a major role in the proof of mathematical propositions, including mathematical induction (refer to Box "Mathematical Induction").

  5. PDF Abduction, Induction, and Analogy

    Fig. 1 The dynamic interaction of the three inferences. explanatory or practical problem2. Deduction produces necessary quences of the suggested approaches or concepts and induction answers to the question whether a theory (explanatory) or a strategy nological) ought to be accepted or rejected.

  6. PDF Analogy and Deduction for Knowledge Discovery

    Analogy-based hypothesis generation is a promising technique for knowledge discovery. Howev er, some hypotheses generated are nonsensical. This paper describes a two -phased method to increase the quality of analogy reasoning. The first phase employs an established approach to generate hypotheses through similarity matching.

  7. Analogy and Deduction for Knowledge Discovery.

    Analogy-based hypothesis generation combined with ontology-based deduction is a promising technique for knowledge discovery and validation. We are using this combined approach to improve the ...

  8. Analogy, Deduction and Learning

    Analogy-based hypothesis generation combined with ontology-based deduction is a promising technique for knowledge discovery and validation. We are using this combined approach to improve the quality of analogy reasoning. This paper is a report of our work in progress in that direction. We will discuss the formal basis and method of the approach from a symbolic machine-learning point of view ...

  9. From Observation to Theory: Deduction, Induction, and Abduction

    The natural sciences represent a complex intellectual enterprise that essentially consists of two interdependent episodes: the first, developing a hypothesis, is essentially imaginative or creative; the second, in which such a hypothesis is interrogated, is fundamentally critical. To advance a hypothesis is a creative exercise.

  10. What is the role of induction and deduction in reasoning and scientific

    A long-standing and continuing controversy exists regarding the role of induction and deduction in reasoning and in scientific inquiry. Given the inherent difficulty in reconstructing reasoning patterns based on personal and historical accounts, evidence about the nature of human reasoning in scientific inquiry has been sought from a controlled experiment designed to identify the role played ...

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  13. 4 Kinds of reasoning ( Intuition , Analogy , Inductive ...

    Discussed here are the different kinds of reasoning namely : Intuition, Analogy, Inductive reasoning and Deductive reasoning.

  14. Comparing Analogy, Syllogism, Deduction and Induction

    Analogy can help explain relationships between two objects or ideas, while syllogism can be used to draw conclusions from two facts or premises. Deduction can be used to draw conclusions from existing knowledge or assumptions, while induction can be used to formulate general rules based on observed phenomena. Each type of reasoning has its own ...

  15. (PDF) Analogy, Deduction and Learning

    Furthermore, we have in the unmatched portion of the base. generalized the model for analogy-based hypothesis Therefore, deductive reasoning is deployed as a general generation by including inductive learning algorithms solution to this problem. In the next section we will other than the SME to find the analogy.

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    It is an inductive inference. General Analogy used in decision-making (Figure 20.5). ... Intuition in the context of discovery. Cognitive Psychology, 22, 72-110. CLOSE Klein, Gary. The Power of Intuition. How To Use Your Gut ... The Sapir-Whorf hypothesis is the theory that an individual's thoughts and actions are determined by the language ...

  17. Deduction, Induction, and Hypothesis 1

    Bocardo may be considered as an induction, so timid as to lose its amplificative character entirely. The analogy of hypothesis with induction is so strong that some logicians have confounded them. But, after all, there is an immense difference between the relation of Baroco and Bocardo to Barbara and that of Induction and Hypothesis to Deduction.

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    Then if induction is ultimately justified by appeals to intuition, one will find himself in a situation of 'It is your intuition against mine'. 5 Analogy Analogy is a kind of reasoning which infers, from the fact that two things are similar in certain respects and one of them has a certain property, that the other has that property.

  19. 1

    The pattern of analogical argument, Brewer says, includes three steps: 1. Abduction in a context of doubt. The reasoner is uncertain about the extension of some term - what it refers to - that has legal consequences in the case under consideration. More concretely, he is uncertain about how legally to classify some phenomenon - person ...

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  21. 9.7: Inductive and Deductive Reasoning

    While deduction gives absolute proof, it never makes contact with the real world, there is no place for observation or experimentation, and no way to test the validity of the premises. And, while induction is driven by observation, it never approaches actual proof of a theory. Therefore an effective paper will include both types of logic. Figure 2.

  22. Abduction, Induction, and Analogy

    Analogical reasoning has been investigated by philosophers and psychologists who have produced different approaches like "schema induction" (Gick and Holyoak) or the "structure-mapping theory" (Gentner).What is commonplace, however, is that analogical reasoning involves processes of matching and mapping. Apart from the differences that ...

  23. Geography 1401 Exam 2 Flashcards

    Study with Quizlet and memorize flashcards containing terms like Hypothesis generation by analogy, induction, deduction, intuition, Serendipity, Independent & dependent variables and more. Try Magic Notes and save time.