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A distinction without a difference is a type of logical fallacy where an author or speaker attempts to describe a distinction between two things where no discernible difference exists. [1] It is particularly used when a word or phrase has connotations associated with it that one party to an argument prefers to avoid.
To formally state, and then prove, the completeness theorem, it is necessary to also define a deductive system. A deductive system is called complete if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense. Thus ...
A logical spreadsheet is a spreadsheet in which formulas take the form of logical constraints rather than function definitions.. In traditional spreadsheet systems, such as Excel, cells are partitioned into "directly specified" cells and "computed" cells and the formulas used to specify the values of computed cells are "functional", i.e. for every combination of values of the directly ...
Formal arguments that are invalid are often associated with at least one fallacy which should be verifiable. A standard view is that whether an argument is valid is a matter of the argument's logical form. Many techniques are employed by logicians to represent an argument's logical form.
Naturalistic fallacy fallacy is a type of argument from fallacy. Straw man fallacy – refuting an argument different from the one actually under discussion, while not recognizing or acknowledging the distinction. [110] Texas sharpshooter fallacy – improperly asserting a cause to explain a cluster of data. [111]
For instance, a false premise on its own does not justify rejecting an argument's conclusion; to assume otherwise is a logical fallacy called denying the antecedent. One way to prove that a proposition is false is to formulate a sound argument with a conclusion that negates that proposition.
In logic and deductive reasoning, an argument is sound if it is both valid in form and has no false premises. [1] Soundness has a related meaning in mathematical logic, wherein a formal system of logic is sound if and only if every well-formed formula that can be proven in the system is logically valid with respect to the logical semantics of the system.
Affirming a disjunct is a fallacy. The formal fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a deductive argument takes the following logical form: [1] A or B A Therefore, not B. Or in logical operators: