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| Deductive reasoning moves from theory to observations or findings. So, in the above example, the theory is that "all men are mortal" and the observation is that "Socrates is a man". So, the conclusion can be made that "Socrates is mortal". | Deductive reasoning moves from theory to observations or findings. So, in the above example, the theory is that "all men are mortal" and the observation is that "Socrates is a man". So, the conclusion can be made that "Socrates is mortal". | ||
| ==Etymology & Development== | |||
| “The intellectual roots of critical thinking and reasoning are as ancient as their etymology, and they can be first located in the teaching practice and vision of Socrates 2,500 years ago who discovered by a method of probing questioning that people could not rationally justify their confident claims to knowledge."<ref>{{cite web|title=A Brief History of the Idea of Critical Thinking|url=http://www.criticalthinking.org/pages/a-brief-history-of-the-idea-of-critical-thinking/408|publisher=The Critical Thinking Community|accessdate=28 April 2012}}</ref> He saw that the supposedly eloquent speeches made by powerful and influential people were often confusing and largely self-contradicting. He was able to show the world the significance of raising queries and asking questions that led one to think carefully and analyze the problem at hand before believing anything to be true. Other renowned scholars and philosopher in the form of Plato, Aristotle, and many more, all followed his teachings and his ways. Socrates followed the method of inductive reasoning, in which one gathers particular premises, and then forms a general conclusion. The use of deductive reasoning was initiated mainly during the time of Aristotle, who used both methods to solve problems and come up with theories. The Greeks laid the foundation of critical thinking and reasoning, which would then be followed by the rest of the world in the ages to come. In the middle Ages, Thomas Aquinas, a priest and a well-known philosopher, lent his ears to anyone who his criticized his theories or ideas, and systematically answered his criticisms to ensure that his replies and reactions were relevant and based on reason. A bevy of scholars in Europe in the Renaissance era became highly critical about a wide variety of topics including religion, art, human behavior, law, and freedom, and gave a considerable amount of thought to them.<ref>{{cite web|title=A Brief History of the Idea of Critical Thinking|url=http://www.criticalthinking.org/pages/a-brief-history-of-the-idea-of-critical-thinking/408|publisher=The Critical Thinking Community|accessdate=28 April 2012}}</ref> The use of deductive reasoning was taken to the next level by Rene Descartes, a French philosopher and mathematician. He went on so far so as to question his very own existence, but then suggested that he was very much real and not a figment of someone’s imagination. He thought that human existence depended heavily on mankind’s capability to think. He theorized that the truth could be revealed by applying reason, and not through the means of experimentation.<ref>{{cite web|title=Sir Isaac Newton and Rene Descartes|url=http://www.historydoctor.net/Advanced%20Placement%20European%20History/Notes/Scientific%20Revolution_(3)_sir_isaac_newton_and_rene_descar.htm|publisher=History Doctor|accessdate=01 May 2012}}</ref> | |||
| In the 20th Century, we have a much better grasp of the concept of critical thinking, and its influence on the world. Psychologists have studied reasoning for a century. Although not until Jean Piaget, a reputed psychologist and philosopher known for his theory of cognitive development, did anyone purport to explain how people were able to make deductions. His theory of cognitive development consisted of four stages, and each stage was assigned to a particular age group. The first stage of his theory lasts from birth to the age of two, and was labeled by him as the sensorimotor period. In this stage, the cognitive system of a child is narrowed down to his motor skills. When they are seven months old, they have developed in themselves other refined and more complicated skills by gaining more experience and understanding of their environment. One of these more advanced skills is the child’s ability understanding of the fact that an object is still in the realm of existence, even if it is not visible to him, or situated right next to him at that time. By the age of two the child has slipped into the second stage. He named this stage the pre-operational period, and described it as one in which the child begins to grasp and use language, and takes the aid of visual images. A child in this stage follows his instincts to make decisions, as he hasn’t developed any reasoning skills yet. The phase reaches its end at the child’s age of seven, after which commences the third or the concrete operational stage, which usually starts at seven and continues until the child turns eleven or twelve. At this point the child is fully capable of understanding another person’s view point, and can look at certain situations through different sides and angles. He has enabled himself to arrive at particular conclusions through the use of reason, but he still lacks the potential to see the theoretical and intangible side of things and develop a wide range of outcomes. Factual information can be easily processed by the child, but he is not competent enough to handle the abstract nature of problems. The last phase is known as the formal operational stage, and one mostly arrives at that stage at the age of twelve, and continues to improve and enhance and improve the abilities and talents he acquires throughout his entire life. In it, one has the full capacity to use the means of reasoning for thinking about the logical as well as the theoretical aspects of various circumstances. Piaget mentioned the fourth and final stage in the process of one’s evolution as the ultimate stage of cognitive growth.<ref>{{cite web|last=Presnell|first=Faith|title=Jean Piaget|url=http://www.muskingum.edu/~psych/psycweb/history.htm|publisher=History of Psychology Archives|accessdate=04 May 2012}}</ref> | |||
| ==Law of Detachment== | ==Law of Detachment== | ||
Revision as of 03:33, 6 May 2012
Deductive reasoning, also called deductive logic, is the process of reasoning from one or more general statements regarding what is known to reach a logically certain conclusion. Deductive reasoning involves using given true premises to reach a conclusion that is also true. Deductive reasoning contrasts with inductive reasoning in that a specific conclusion is arrived at from a general principle. If the rules and logic of deduction are followed, this procedure ensures an accurate conclusion.
An example of a deductive argument:
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
The first premise states that all objects classified as "men" have the attribute "mortal". The second premise states that "Socrates" is classified as a "man" – a member of the set "men". The conclusion then states that "Socrates" must be "mortal" because he inherits this attribute from his classification as a "man".
Deductive reasoning moves from theory to observations or findings. So, in the above example, the theory is that "all men are mortal" and the observation is that "Socrates is a man". So, the conclusion can be made that "Socrates is mortal".
Law of Detachment
The law of detachment is the first form of deductive reasoning. A single conditional statement is made, and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and the hypothesis. The most basic form is listed below:
- P→Q (conditional statement)
- P (hypothesis stated)
- Q (conclusion deduced)
In deductive reasoning, we can conclude Q from P by using the law of detachment. However, if the conclusion (Q) is given instead of the hypothesis (P) then there is no valid conclusion.
The following is an example of an argument using the law of detachment in the form of an if-then statement:
- If an angle A>90°, then A is an obtuse angle.
- A=120°
- A is an obtuse angle.
Since the measurement of angle A is greater than 90°, we can deduce that A is an obtuse angle.
Law of Syllogism
The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form, with the true premise P:
- P→Q
- Q→R
- Therefore, P→R.
The following is an example:
- If Larry is sick, then he will be absent from school.
- If Larry is absent, then he will miss his classwork.
- If Larry is sick, then he will miss his classwork.
We deduced the final statement by combining the hypothesis of the first statement with the conclusion of the second statement. We also conclude that this could be a false statement.
Deductive Logic: Validity and Soundness
Deductive arguments are evaluated in terms of their validity and soundness. It is possible to have a deductive argument that is logically valid but is not sound.
An argument is valid if it is impossible for its premises to be true while its conclusion is false. In other words, the conclusion must be true if the premises, whatever they may be, are true. An argument can be valid even though the premises are false.
An argument is sound if it is valid and the premises are true.
The following is an example of an argument that is valid, but not sound:
- Everyone who eats steak is a quarterback.
- John eats steak.
- Therefore, John is a quarterback.
The example's first premise is false – there are people who eat steak and are not quarterbacks – but the conclusion must be true, so long as the premises are true (i.e. it is impossible for the premises to be true and the conclusion false). Therefore the argument is valid, but not sound.
In this example, the first statement uses categorical reasoning, saying that all steak-eaters are definitely quarterbacks. This theory of deductive reasoning – also known as term logic – was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.
Deductive reasoning can be contrasted with inductive reasoning, in regards to validity and soundness. In cases of inductive reasoning, even though the premises are true and the argument is "valid", it is possible for the conclusion to be false (determined to be false with a counterexample or other means).
Hume's Skepticism
See also: Problem of inductionPhilosopher David Hume presented grounds to doubt deduction by questioning induction. Hume's problem of induction starts by suggesting that the use of even the simplest forms of induction simply cannot be justified by inductive reasoning itself. Moreover, induction cannot be justified by deduction either. Therefore, induction cannot be justified rationally. Consequently, if induction is not yet justified, then deduction seems to be left to rationally justify itself – an objectionable conclusion to Hume.
Hume did not provide a strictly rational solution per se. He simply explained that we do induce, and that it is useful that we do so, but not necessarily justified. Certainly we must appeal to first principles of some kind, including laws of thought.
Reasoning and Education
Deductive reasoning is generally thought of as a skill that develops without any formal teaching or training. As a result of this belief, deductive skills are not taught in secondary schools, where students are expected to use reasoning more often and at a higher level. For example, students have an abrupt introduction to mathematical proofs – which heavily relies on deductive reasoning – in high school. Researchers identify this lack of proofs understanding as a possible explanation for the difficulties that many students face in mathematics. Since students don't seem to be indirectly learning deduction skills, direct instruction in earlier grades (and for extended periods of time) would likely increase students mathematical proficiency.
In addition, an increase in deduction skills will benefit those students who plan on continuing into higher education. Deductive reasoning is a central component to many scholarly disciplines and is often fundamental to success in many professional activities.
One efficient and guaranteed to succeed method that is being used to apply Piaget’s theory is utilizing the power of vision, and understanding the role it plays in reasoning. Educational software is being built to interact with the students visually, and take them on a step by step explanation to the answer of the problem, so that the students can deduce how they can get from one step to the next. Through the use of such resources, like a three dimensional drawing and analyzing software, a student can create something so intricate and so revolutionary with just a few permutations and combinations of the tools provided in it. The field of computer programming is another great example that illustrates the use of deductive reasoning. It is often so hard to learn because humans usually use inductive reasoning but computers always use deductive reasoning. They follow a set of rules and always abide by them. Thus, by observing the evolution of deductive reasoning through historical events, the fact that this gift will continue to play a major role in our future is hardly a difficult deduction. One area which exemplifies this method as an excellent tool is forensic science, in which it aids profilers and investigators in solving crimes. To reap its benefits as time goes on, in a project managed by Intel, students will delve into the world of criminal investigation. “They will engage in deductive reasoning activities and practice math and science forensics labs. Then, using the scientific inquiry process, they will collect clues, test and analyze evidence, and draw conclusions to solve the crime.”
See also
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References
- Sternberg, R. J. (2009). Cognitive Psychology. Belmont, CA: Wadsworth. p. 578. ISBN 978-0-495-50629-4.
- Guide to Logic
- Stylianides, G. J. (2008). "A. J.". Mathematical Thinking and Learning. 10 (2): 103–133. doi:10.1080/10986060701854425.
{{cite journal}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - Stylianides, G. J. (2008). "Proof in school mathematics: Insights from psychological research into students' ability for deductive reasoning". Mathematical Thinking and Learning. 10 (2): 103–133. doi:10.1080/10986060701854425.
{{cite journal}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - Leighton, J. P. (2006). "Teaching and assessing deductive reasoning skills". Journal of Experimental Education. 74 (2): 109–136. doi:10.3200/JEXE.74.2.107-136.
{{cite journal}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help) - Stylianides, G. J. (2008). "Proof in school mathematics: Insights from psychological research into students' ability for deductive reasoning". Mathematical Thinking and Learning. 10 (2): 103–133. doi:10.1080/10986060701854425.
{{cite journal}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - Leighton, J. P. (2006). "Teaching and assessing deductive reasoning skills". Journal of Experimental Education. 74 (2): 109–136. doi:10.3200/JEXE.74.2.107-136.
{{cite journal}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help) - "Designing Effective Projects : Project-Based Units to Engage Students". Intel. Retrieved 04 May 2012.
{{cite web}}: Check date values in:|accessdate=(help)
Further reading
- Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
- Philip Johnson-Laird, Ruth M. J. Byrne, Deduction, Psychology Press 1991, ISBN 978-0-86377-149-1jiii
- Zarefsky, David, Argumentation: The Study of Effective Reasoning Parts I and II, The Teaching Company 2002
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