History of logic

Universal (metaphysics)

In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things.[1] For example, suppose there are two chairs in a room, each of which is green. These two chairs both share the quality of "chairness", as well as greenness or the quality of being green; in other words, they share a "universal". There are three major kinds of qualities or characteristics: types or kinds (e.g. mammal), properties (e.g. short, strong), and relations (e.g. father of, next to). These are all different types of universals.[2]

Paradigmatically, universals are abstract (e.g. humanity), whereas particulars are concrete (e.g. the personhood of Socrates). However, universals are not necessarily abstract and particulars are not necessarily concrete.[3] For example, one might hold that numbers are particular yet abstract objects. Likewise, some philosophers, such as D.M. Armstrong, consider universals to be concrete.

Most do not consider classes to be universals, although some prominent philosophers do, such as John Bigelow.



Let no one ignorant of geometry enter here.

— Inscribed over the entrance to Plato's Academy.
Plato's academy

None of the surviving works of the great fourth-century philosopher Plato (428–347 BC) include any formal logic,[34] but they include important contributions to the field of philosophical logic. Plato raises three questions:

  • What is it that can properly be called true or false?
  • What is the nature of the connection between the assumptions of a valid argument and its conclusion?
  • What is the nature of definition?

Why Aristotelian logic
does not work

The logic of Aristotle, and particularly his theory of the syllogism, has had an enormous influence in" Western thought"

Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.

Sun, 13 Dec 2009

World's shortest explanation of Gödel's theorem
A while back I started writing up an article titled "World's shortest explanation of Gödel's theorem". But I didn't finish it, and later I encountered Raymond Smullyan's version, which is much shorter anyway. So here, shamelessly stolen from Smullyan, is the World's shortest explanation of Gödel's theorem.

We have some sort of machine that prints out statements in some sort of language. It needn't be a statement-printing machine exactly; it could be some sort of technique for taking statements and deciding if they are true. But let's think of it as a machine that prints out statements.

In particular, some of the statements that the machine might (or might not) print look like these:

P*x (which means that the machine will print x)
NP*x (which means that the machine will never print x)
PR*x (which means that the machine will print xx)
NPR*x (which means that the machine will never print xx)

For example, NPR*FOO means that the machine will never print FOOFOO. NP*FOOFOO means the same thing. So far, so good.

Now, let's consider the statement NPR*NPR*. This statement asserts that the machine will never print NPR*NPR*.

Either the machine prints NPR*NPR*, or it never prints NPR*NPR*.

If the machine prints NPR*NPR*, it has printed a false statement. But if the machine never prints NPR*NPR*, then NPR*NPR* is a true statement that the machine never prints.

So either the machine sometimes prints false statements, or there are true statements that it never prints.

So any machine that prints only true statements must fail to print some true statements.

Or conversely, any machine that prints every possible true statement must print some false statements too.

The proof of Gödel's theorem shows that there are statements of pure arithmetic that essentially express NPR*NPR*; the trick is to find some way to express NPR*NPR* as a statement about arithmetic, and most of the technical details (and cleverness!) of Gödel's theorem are concerned with this trick. But once the trick is done, the argument can be applied to any machine or other method for producing statements about arithmetic.

The conclusion then translates directly: any machine or method that produces statements about arithmetic either sometimes produces false statements, or else there are true statements about arithmetic that it never produces. Because if it produces something like NPR*NPR* then it is wrong, but if it fails to produce NPR*NPR*, then that is a true statement that it has failed to produce.

So any machine or other method that produces only true statements about arithmetic must fail to produce some true statements.

Hope this helps!

(This explanation appears in Smullyan's book 5000 BC and Other Philosophical Fantasies, chapter 3, section 65, which is where I saw it. He discusses it at considerable length in Chapter 16 of The Lady or the Tiger?, "Machines that Talk About Themselves". It also appears in The Mystery of Scheherezade.)

I gratefully acknowledge Charles Colht for his generous donation to this blog.

A excerpt from;

There has been a spate of recent books and papers on why people make errors in their thinking, together with constant attempts to classify these errors under various headings. But many of the errors are much more basic than the classifications used, and all stem from fundamental errors in the approach to problems, rather than the specific, somewhat artifical, categories that these writings suggest.

As psychology is advancing, large numbers of categories are being invented and used with greater or lesser utility or sense. Many of the categories used in these recent meanderings appear counter-productive to me (though I shall list some of them). But they all appear to me to arise from similar basic errors in thought. A prime root of these errors is a seeking for closure.

In a Hurry!!!

,gotta get it done,no time to contemplate on what we are doing!...the very idea that is nearly American mainstream, sub-subconscious

I do know as fact :

                                   1. Nearly all traffic Accidents are caused by rushing,being hurried,poor logic

                                    2. Nearly all Aviation Accidents stem from one basic cause-rushing,being on time

                                         a.I personal have a background in Aviation..studying two years to be commercial pilot
                                         b. the number one on list at site below is,-  
                                                                                                          pilot error- WEATHER CONDITION | LOW CEILING

                                                                                                           pilot error -  LIGHT CONDITION | DARK NIGHT1173

                                                                                                   pilot error- AIRCRAFT CONTROL | NOT MAINTAINED1095

                                                                                                                                          pilot error-STALL | INADVERTENT1087

                                                                                                                              pilot error-AIRSPEED | NOT MAINTAINED1075

                                                                                                                                  pilot error-WEATHER CONDITION | FOG1016

     conculsion,except for :


All these accidents where avoidable with todays technologies

                 And even the wing separation,maybe not by pilot,yet whomever maintained the aircraft,,Yet for example the Pilot allowed the plane to stall,thus it drops into a nose down power on spin-(the never exeed limit on a 1985 Cessna 152 is 145 kcas)..cruise speed is 108,,not a lot play time before airframe failure can occur=37 mph

Here is writing I just read of Aristotle of Logos:

Logos is the appeal towards logical reason, thus the speaker wants to present an argument that appears to be sound to the audience. It encompasses the content and arguments of the speech. Like ethos and pathos the aim is to create an persuasive effect, thus the apparent is sufficient:

Thirdly, persuasion is effected through the speech itself when we have proved a truth or an apparent truth by means of the persuasive arguments suitable to the case in question.
 –Aristotle 1356a 2,3

For the argumentation the arguments, argument schemes, the different forms of proof and the reasoning are of special interest. There are two different forms of proofs: the natural and the artificial/technical proof. Natural proofs are those that are based on given data like documents, testimonies, etc. The artificial/technical proof are those that are created with combination of information (hints, examples, etc.) and the art of logic

What is Art of Logic? = Logical Grammar  ?,   On the Purity of the Art of Logic, a handbook of logic written in Latin by English philosopher Walter Burley (c.1275–1344/5).?,   TRANSLATION OF MAIMONIDES' TREATISE ON LOGIC
A Treatise on the art of logic,
by the head of the religion of Israel, Musa ibn 'Obaid Allah of Cordova, may God be gracious unto him! ?
                          the two Forms of proof,in my opinion are not defined clear enough to have any use

Universalism is a theological and philosophical concept that some ideas have universal application or applicability.[citation needed] A community that calls itself universalist may emphasize the universal principles of most religions and accept other religions in an inclusive manner, believing in a universal reconciliation between humanity and the divine

Type–token distinction

Although this flock is made of the same type of bird, each individual bird is a different token. (50 MB video of a flock of birds in Rome)

The type–token distinction is used in disciplines such as logic, linguistics, metalogic, typography, and computer programming to clarify what words mean.


The sentence "they drive the same car" is ambiguous. Do they drive the same type of car (the same model) or the same instance of a car type (a single vehicle)? Clarity requires us to distinguish words that represent abstract types from words that represent objects that embody or exemplify types. The type–token distinction separates types (representing abstract descriptive concepts) from tokens (representing objects that instantiate concepts).

For example: "bicycle" is a type that represents the concept of a bicycle; whereas "my bicycle" is a token that represents an object that instantiates that type. In the sentence "the bicycle is becoming more popular" the word "bicycle" is a type representing a concept; whereas in the sentence "the bicycle is in the garage" the word "bicycle" is a token representing a particular object.

Ascribed symbolic meaning to material objects