Difference between revisions of "Deductive Rules"
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| − | + | Deductive reasoning is reaching a conclusion by combining known truths to create a new truth. Unlike inductive reasoning, deductive reasoning is certain, provided that the normal rules of logic are used to conclude such truths. In order to use deductive reasoning there must be a starting point, normally called the axioms or postulates of the theory. For example, an axiom in geometry asserts that given two points, there is only one line that contains both points. Observe that while this is an axiom, it can be used to deduce that two different lines that are not parallel will intersect at only one point. | |
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| + | Not only axioms can be used to deduce new truths. Other knowledge deduced from the axioms using the rules of logic can be used to validate new truths. For example, we can conclude that if three points A, B and C are not in the same line, the lines determined by two of them can only meet at A, B and C (since we already know that two lines can only intersect at one point, all that is necessary to prove is that the lines determined by two of the three points are different, and that is immediate since the given points do not belong to any one line). | ||
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| + | ==Simple example== | ||
| + | An example of an argument using deductive reasoning: | ||
| + | # All men are mortal. (First premise) | ||
| + | # Socrates is a man. (Second premise) | ||
| + | # Therefore, Socrates is mortal. (Conclusion) | ||
| + | |||
| + | 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." | ||
==Resources== | ==Resources== | ||
* [https://en.wikipedia.org/wiki/Deductive_reasoning#:~:text=Deductive%20reasoning%20goes%20in%20the,conclusion%20reached%20is%20necessarily%20true. Deductive Reasoning], Wikipedia | * [https://en.wikipedia.org/wiki/Deductive_reasoning#:~:text=Deductive%20reasoning%20goes%20in%20the,conclusion%20reached%20is%20necessarily%20true. Deductive Reasoning], Wikipedia | ||
| + | * [https://en.wikibooks.org/wiki/Geometry/Chapter_1 Chapter 1], Wikibooks: Geometry | ||
* [https://cs.brynmawr.edu/Courses/cs231/spring2015/PC.pdf Deductive Reasoning and Logical Connectives], Bryn Mawr College | * [https://cs.brynmawr.edu/Courses/cs231/spring2015/PC.pdf Deductive Reasoning and Logical Connectives], Bryn Mawr College | ||
* [https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-deductive-and-inductive-reasoning/v/deductive-reasoning-1 Inductive and Deductive Reasoning], Khan Academy | * [https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-deductive-and-inductive-reasoning/v/deductive-reasoning-1 Inductive and Deductive Reasoning], Khan Academy | ||
* [https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-deductive-and-inductive-reasoning/v/deductive-reasoning-3 Using Deductive Reasoning], Khan Academy | * [https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-deductive-and-inductive-reasoning/v/deductive-reasoning-3 Using Deductive Reasoning], Khan Academy | ||
Revision as of 14:49, 14 October 2021
Deductive reasoning is reaching a conclusion by combining known truths to create a new truth. Unlike inductive reasoning, deductive reasoning is certain, provided that the normal rules of logic are used to conclude such truths. In order to use deductive reasoning there must be a starting point, normally called the axioms or postulates of the theory. For example, an axiom in geometry asserts that given two points, there is only one line that contains both points. Observe that while this is an axiom, it can be used to deduce that two different lines that are not parallel will intersect at only one point.
Not only axioms can be used to deduce new truths. Other knowledge deduced from the axioms using the rules of logic can be used to validate new truths. For example, we can conclude that if three points A, B and C are not in the same line, the lines determined by two of them can only meet at A, B and C (since we already know that two lines can only intersect at one point, all that is necessary to prove is that the lines determined by two of the three points are different, and that is immediate since the given points do not belong to any one line).
Simple example
An example of an argument using deductive reasoning:
- All men are mortal. (First premise)
- Socrates is a man. (Second premise)
- Therefore, Socrates is mortal. (Conclusion)
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."
Resources
- Deductive Reasoning, Wikipedia
- Chapter 1, Wikibooks: Geometry
- Deductive Reasoning and Logical Connectives, Bryn Mawr College
- Inductive and Deductive Reasoning, Khan Academy
- Using Deductive Reasoning, Khan Academy
