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## Symmetry in Properties of Quantifiers

by: Cydney Tinsley

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# Symmetry in Properties of Quantifiers PHIL 2441-004

Marketplace > University of Colorado Denver > Philosophy > PHIL 2441-004 > Symmetry in Properties of Quantifiers
Cydney Tinsley
CU Denver
GPA 3.2

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These notes cover what quantifiers have symmetrical relations, examples, and a brief definition of non-standard quantifiers.
COURSE
Logic, Language and Scientific Reasoning
PROF.
Alexander Hughes
TYPE
Class Notes
PAGES
2
WORDS
CONCEPTS
philosophy, Quantifiers, logic, scientific, reasoning
KARMA
25 ?

## Popular in Philosophy

This 2 page Class Notes was uploaded by Cydney Tinsley on Tuesday August 30, 2016. The Class Notes belongs to PHIL 2441-004 at University of Colorado Denver taught by Alexander Hughes in Fall 2016. Since its upload, it has received 5 views. For similar materials see Logic, Language and Scientific Reasoning in Philosophy at University of Colorado Denver.

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Date Created: 08/30/16
Cydney Tinsley Logic, Language and Scientific Reasoning 8/29/16 Day 3: Using Validity to Explore Symmetry Properties of Quantifiers Symmetry Properties of Quantifiers 1. Any two things are symmetrical if for any two things (xy) if x is y than y is x. a. Ex: Shelby is Dan’s sibling. Dan is Shelby’s sibling. 2. Quantifiers: All, Some, No a. All has non-symmetrical relations. i. __1__ are __2__ = __2__ are __1__ ii. Dogs are mammals = Mammals are dogs b. Some has symmetrical relations. i. __1__ are __2__ = __2__ are __1__ ii. Some dogs are mammals = Some mammals are dogs. c. No has symmetrical relations. i. __1__ are __2__ = __2__ are __1__ ii. No dogs are monkeys = No monkeys are dogs. 3. Increasing/Decreasing Categories a. Ex: All __1__ are __2__ Category 1 Category 2 b. To go up in a category, make a broader statement; dogs to animals. c. To go down in a category, make a more specific statement; dogs to Labradors. i. All: Up in Category 1 1. All dogs are mammals. All dogs are canines. All canines are mammals. 2. This inference is valid! ii. All: Up in Category 2 1. All dogs are animals. 2. All dogs are mammals. 3. All animals are mammals. 4. This inference is not valid; all animals are not mammals. d. For ‘All’ i. If you increase category one or decrease category two, your inference will not be valid. If you decrease category one or increase category two, your inference will be valid. e. For ‘Some’ i. If you increase category one or two, your inference will be valid. If you decrease either category, your inference will not. f. For ‘No’ i. If you decrease category one or two, your inference will be valid. If you increase either category, your inference will not. g. Non-Standard Quantifiers i. Non-Standard Quantifiers are any quantifier that is not ‘All’, ‘Some’ or ‘No’. These can include, but are not limited to: 1. Exactly 2 Cydney Tinsley Logic, Language and Scientific Reasoning 8/29/16 Day 3: Using Validity to Explore Symmetry Properties of Quantifiers 2. Most 3. Many 4. Few

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