Category: Logic

List of common fallacies

In daily conversations, we come across many logical fallacies. Discussions and debates often lead nowhere, because the underlying logic is already wrong. Looking for better explanations or more evidence is a good approach, and another one is attacking the problems in your opponents position. The following list briefly describes some of the most common fallacies: You don’t need to take drugs to hallucinate; improper language can fill your world with phantoms and spooks of many kinds.  – Robert A. Wilson Common fallacies: ad hominem: Latin for “to the person.” An arguer who uses the ad hominem attack aims at the person instead of the...

A. M. Turing: Computing Machinery and Intelligence. 1950

Source: Mind 49: 433-460. 1. The Imitation Game I propose to consider the question, “Can machines think?” This should begin with definitions of the meaning of the terms “machine” and “think.” The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words “machine” and “think” are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, “Can machines think?” is to be sought in a...

Kurt Gödel

Here is the biographical sketch of Kurt Gödel’s life from the Stanford Encyclopedia of Philosophy: Biographical Sketch Kurt Gödel was born on April 28, 1906 in what was then the Austro-Hungarian city of Brünn, and what is now Brno in the Czech Republic. Gödel’s father Rudolf August was a businessman, and his mother Marianne was a well-educated and cultured woman to whom Gödel remained close throughout his life, as witnessed by the long and wide-ranging correspondence between them. The family was well off, and Gödel’s childhood was an uneventful one, with one important exception; namely, from about the age of four...

Incompleteness Theorem

The Incompleteness Theorem is Gödel’s main contribution to 20th century thought. Gödel showed that within a logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved or disproved. Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions. It appears to destroy the hope of mathematical certitude through the use of the obvious methods. It also deconstructs an ideal of science, that we...

A History of Set Theory

A set is a collection of things. A set can consist of numbers or letters (such as 1, 2, 3, 4 or a, b, c, d) or of objects (such as chairs or books). Set theory is the field of mathematics that deals with the properties of sets that are independent of the things that make up the set. For example, a mathematician might be interested in knowing about sets S and T without being interested at all about the concrete elements of the sets. The following article addresses the history of set theory, but it also serves as an...

Kalām Cosmological Argument

From: W. L. Craig: “Professor Mackie and the Kalām Cosmological Argument,” in: Religious Studies, No. 20 (1985), p. 367. “The kalām cosmological argument, as opposed to the Thomistic and Leibnizian, is one of the better-respected arguments for the existence of God. Because its validity is not controversial, because it aligns with the most prominent scientific theories of the universe, and because it agrees with general philosophical insight concerning properties of infinities, it is one of the more interesting pieces of religious philosophy. It can be stated as follows: (1) Whatever begins to exist has a cause of existence. (2) The...

Kurt Gödel’s philosophical viewpoint, and his proof of the existence of God.

Explanation of the terms  in the image above. This is Godel’s formalized proof of the existence of God. P(psi) P is “positive” G(x) x have the property God ess. essential E existing • (bullet) Necessary (Kurt Gödel (1995). “Ontological Proof”. Collected Works: Unpublished Essays & Lectures, Volume III. pp. 403–404. Oxford University Press. Gödel left in his papers a  fourteen-point outline of his philosophical beliefs, that are dated around 1960. They show his deep belief in the rational structure of the world. Here are his 14 points: The world is rational. Human reason can, in principle, be developed more highly (through certain...

The Unexpected Hanging Paradox

From the Wikipedia: “A judge tells a condemned prisoner that he will be hanged at noon on one day in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that if the hanging were on Friday then it would not be a surprise, since he would know...

Laws of Form

[easyazon_link identifier=”3890945805″ locale=”US” tag=”mainacademicsite-20″]George Spencer-Brown: Laws of Form[/easyazon_link], Chapter 12 Notes. “It seems hard to find an acceptable answer to the question of how or why the world conceives a desire, and discovers an ability, to see itself, and appears to suffer the process. That it does so is sometimes called the original mystery. Perhaps in view of the form in which we presently take ourselves to exist, the mystery arises from our insistence on framing a question when there is, in reality, nothing to question.” : “The form we take to exist arises from framing nothing.” Here are some...