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The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
Proof by intimidation (or argumentum verbosum) is a jocular phrase used mainly in mathematics to refer to a specific form of hand-waving whereby one attempts to advance an argument by giving an argument loaded with jargon and obscure results or by marking it as obvious or trivial. [1]
The titles of some books are self-explanatory. Good books on critical thinking commonly contain sections on fallacies, and some may be listed below. DiCarlo, Christopher (2011). How to Become a Really Good Pain in the Ass: A Critical Thinker's Guide to Asking the Right Questions. Prometheus Books. ISBN 9781616143978. Engel, S. Morris (1994).
Lateral thinking is a manner of solving problems using an indirect and creative approach via reasoning that is not immediately obvious. Synonymous to thinking outside the box, it involves ideas that may not be obtainable using only traditional step-by-step logic. [1] The cutting of the Gordian Knot is a classical example.
Circular reasoning (Latin: circulus in probando, "circle in proving"; [1] also known as circular logic) is a logical fallacy in which the reasoner begins with what they are trying to end with. [2] Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or ...
It is divided into formal and informal logic, which study formal and informal logical reasoning. [8] [9] [10] Traditionally, logical reasoning was primarily associated with deductive reasoning studied by formal logic. [11] But in a wider sense, it also includes forms of non-deductive reasoning, such as inductive, abductive, and analogical ...
In this process of reasoning, general assertions are made based on past specific pieces of evidence. This kind of reasoning allows the conclusion to be false even if the original statement is true. [28] For example, if one observes a college athlete, one makes predictions and assumptions about other college athletes based on that one observation.