Thursday 28 June 2012

PHILOSOPHY-LESSON ONE.

'PHILO-SOPHERS', are, 'LOVERS', of, 'WISDOM'.
Is, there, a difference, between, 'knowledge', and 'Wisdom?'.....

KNOWLEDGE, IS, KNOWING, THAT, A TOMATO, IS, A FRUIT.
WISDOM, IS ,HAVING, THE KNOWLEDGE,THAT, A TOMATO, SHOULD NOT,
BE INCLUDED,IN, A FRUIT SALAD.

Euclid (play /ˈjuːklɪd/ ewk-lidAncient GreekΕὐκλείδης Eukleidēs), fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.[1][2][3] In the Elements, Euclid deduced the principles of what is now called Euclidean geometryfrom a small set of axioms. Euclid also wrote works on perspectiveconic sectionsspherical geometrynumber theory and rigor.
"Euclid" is the anglicized version of the Greek name Εὐκλείδης, meaning "Good Glory"
[READ, AND FOLLOW LINKS, source, wikipedia]

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook ongeometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions(theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians,[1] Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.[2] The Elements begins with plane geometry, still taught in secondary schoolas the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, couched in geometrical language.[3]
For over two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that Euclidean space is a good approximation to the properties of physical space only where the gravitational field is weak

FIRST QUESTION; 'WHAT IS A 'DIMENSION?'

Thursday 21 June 2012

Thoreau


I did not wish to take a cabin passage, but rather to go before the mast and on the deck of the world, for there I could best see the moonlight amid the mountains. I do not wish to go below now.



David Henry Thoreau.

Ice Cream







SUMMERTIME! AND THE LIVING, IS EASY.....

Friday 15 June 2012

A Thousand Years,A Town Called, Malice


I may be numberless, I may be innocent
I may know many things, I may be ignorant
Or I could ride with kings and conquer many lands
Or win this world at cards and let it slip my hands
I could be cannon food, destroyed a thousand times
Reborn as fortune’s child to judge another’s crimes
Or wear this pilgrim’s cloak, or be a common thief
I’ve kept this single faith, I have but one belief

I still love you
I still want you
A thousand times the mysteries unfold themselves
Like galaxies in my head
On and on the mysteries unwind themselves
Eternities still unsaid
’til you love me
[A Thousand Years, by, 'Sting']



Tuesday 12 June 2012

Symbolic Logic-Truth functions[part 1]

[wikipedia]


In mathematical logic, a truth function is a function from a set of truth values to truth values. Classically the domain and range of a truth function are {truth, falsehood}, but they may have any number of truth values, including an infinity of these.
A sentence is truth-functional if the truth-value of the sentence is a function of the truth-value of its sub-sentences. A class of sentences is truth-functional if each of its members is. For example, the sentence "Apples are fruits and carrots are vegetables" is truth-functional since it is true just in case each of its sub-sentences "apples are fruits" and "carrots are vegetables" is true, and it is false otherwise. Not all sentences of a natural language, such as English, are truth-functional.
Sentences of the form "x believes that..." are typical examples of sentences that are not truth-functional. Let us say that Mary mistakenly believes that Al Gore was President of the USA on April 20, 2000, but she does not believe that the moon is made of green cheese. Then the sentence
"Mary believes that Al Gore was President of the USA on April 20, 2000"
is true while
"Mary believes that the moon is made of green cheese"
is false. In both cases, each component sentence (i.e. "Al Gore was president of the USA on April 20, 2000" and "the moon is made of green cheese") is false, but each compound sentence formed by prefixing the phrase "Mary believes that" differs in truth-value. That is, the truth-value of a sentence of the form "Mary believes that..." is not determined solely by the truth-value of its component sentence, and hence the (unary) connective (or simply operator since it is unary) is non-truth-functional.
In classical logic a truth function is a compound proposition whose truth or falsity is unequivocally determined by the truth or falsity of its components for all cases, the class of its formulas (including sentences) is truth-functional since every sentential connective (e.g. &, →, etc.) used in the construction of formulas is truth-functional. Their values for various truth-values as argument are usually given by truth tablesTruth-functional propositional calculus is a formal system whose formulas may be interpreted as either true or false.

Boolian Function[part 1]
Contradiction/False
NotationEquivalent
formulas
Truth tableVenn diagram
\bot
"bottom"
P \wedge ¬P
Opq
Q
01
P0   0  0 
1   0  0 
Venn0000.svg

Tautology/True
NotationEquivalent
formulas
Truth tableVenn diagram
\top
"top"
P \vee ¬P
Vpq
Q
01
P0   1  1 
1   1  1 
Venn1111.svg

Proposition P
NotationEquivalent
formulas
Truth tableVenn diagram
Pp
Ipq
Q
01
P0   0  0 
1   1  1 
Venn0101.svg

Negation of P
NotationEquivalent
formulas
Truth tableVenn diagram
¬P
~P
Np
Fpq
Q
01
P0   1  1 
1   0  0 
Venn1010.svg

Proposition Q
NotationEquivalent
formulas
Truth tableVenn diagram
Qq
Hpq
Q
01
P0   0  1 
1   0  1 
Venn0011.svg

Negation of Q
NotationEquivalent
formulas
Truth tableVenn diagram
¬Q
~Q
Nq
Gpq
Q
01
P0   1  0 
1   1  0 
Venn1100.svg

Conjunction
NotationEquivalent
formulas
Truth tableVenn diagram
P \wedge Q
P & Q
P · Q
P AND Q
P \not\rightarrow¬Q
¬P \not\leftarrow Q
¬P \downarrow ¬Q
Kpq
Q
01
P0   0  0 
1   0  1 
Venn0001.svg

Alternative denial
NotationEquivalent
formulas
Truth tableVenn diagram
P ↑ Q
P | Q
P NAND Q
P → ¬Q
¬P ← Q
¬P \lor ¬Q
Dpq
Q
01
P0   1  1 
1   1  0 
Venn1110.svg

Disjunction
NotationEquivalent
formulas
Truth tableVenn diagram
P \lor Q
P OR Q
P \leftarrow ¬Q
¬P → Q
¬P ↑ ¬Q
¬(¬P \wedge ¬Q)
Apq
Q
01
P0   0  1 
1   1  1 
Venn0111.svg

Joint denial
NotationEquivalent
formulas
Truth tableVenn diagram
P ↓ Q
P NOR Q
P \not\leftarrow ¬Q
¬P \not\rightarrow Q
¬P \wedge ¬Q
Xpq
Q
01
P0   1  0 
1   0  0 
Venn1000.svg

Material nonimplication
NotationEquivalent
formulas
Truth tableVenn diagram
P \not\rightarrow Q
P \not\supset Q
P \wedge ¬Q
¬P ↓ Q
¬P \not\leftarrow ¬Q
Lpq
Q
01
P0   0  0 
1   1  0 
Venn0100.svg

Material implication
NotationEquivalent
formulas
Truth tableVenn diagram
P → Q
P \supset Q
P ↑ ¬Q
¬P \lor Q
¬P ← ¬Q
Cpq
Q
01
P0   1  1 
1   0  1 
Venn1011.svg

Converse nonimplication
NotationEquivalent
formulas
Truth tableVenn diagram
P \not\leftarrow Q
P \not\subset Q
P ↓ ¬Q
¬P \wedge Q
¬P \not\rightarrow ¬Q
Mpq
Q
01
P0   0  1 
1   0  0 
Venn0010.svg

Converse implication
NotationEquivalent
formulas
Truth tableVenn diagram
P \leftarrow Q
P \subset Q
P \lor ¬Q
¬P ↑ Q
¬P → ¬Q
Bpq
Q
01
P0   1  0 
1   1  1 
Venn1101.svg

Exclusive disjunction
NotationEquivalent
formulas
Truth tableVenn diagram
P \not\leftrightarrow Q
P \not\equiv Q
P \oplus Q
P XOR Q
P \leftrightarrow ¬Q
¬P \leftrightarrow Q
¬P \not\leftrightarrow ¬Q
Jpq
Q
01
P0   0  1 
1   1  0 
Venn0110.svg

Biconditional
NotationEquivalent
formulas
Truth tableVenn diagram
P \leftrightarrow Q
P ≡ Q
P XNOR Q
P IFF Q
P \not\leftrightarrow ¬Q
¬P \not\leftrightarrow Q
¬P \leftrightarrow ¬Q
Epq
Q
01
P0   1  0 
1   0  1 
Venn1001.svg




Dobie Gray - Out On The Floor