How Scalar-logic Becomes Vector-logic

[Juvenis]

In PHYSICS, speed is a scalar, or 0-vector, measure of motion. Standing in the

middle of a street, you see a car racing at (the speed of) 50 mph. But it makes

a difference as to whether it is coming toward you or going away: DIRECTION was

missing in that "50 mph" statment. Adjoining DIRECTION to SPEED creates a

(1-)vector measure of motion</I>. I argue we've a similar problem in relating

LOGIC to everyday speech. "It was raining at the Washington Monument, 4/12/08"

is A POSITIVE SIMPLE DECLARATIVE SENTENCE CAPABLE OF VERIFICATION -- qualifying

it as a STATEMENT (a.k.a. proposition) in STATEMENT LOGIC (a.k.a. 0-ORDER

PREDICATE LOGIC). But "Was it raining at the Washington Monument, 4/12/08?" does

not qualify, being not in DECLARATIVE MOOD. INTERROGATIVES, SUBJUNCTIVES,

IMPERATIVES, PETITIVES all fail to qualify -- IN SCALAR LOGIC. But we can fit

them into VECTOR LOGIC, by PROVIDING FOR THE MOOD OF STATEMENT as well as

STATEMENT. STATEMENT LOGIC IS TRUTH-FUNCTIONAL, meaning that THE TRUTH-VALUE OF A COMPOUND STATEMENT DEPENDS ONLY ON THE TRUTH-VALUE OF ITS COMPONENTS, not

ORDER or CONTEXT or "whatever". My VECTOR LOGIC CONSERVES TRUTH-FUNCTIONALITY,

as follows. In STATEMENT LOGIC, we may denote a STATEMENT by a single letter,

say, S, a form which mathematicians call a "1-tuple". Now, in our initial form

of VECTOR LOGIC, we introduce a 2-tuple, [M, S], wherein SECOND COMPONENT, S,

IS A STANDARD ASSERTION, and the FIRST COMPONENT IS AN ASSERTION THAT SPEAKER

SPEAKS IN MOOD "M". Let's adopt Bertrand Russell's "turnstile" symbol, |-, for DECLARATIVE MOOD, and standard question mark, ?, for THE INTERROGATIVE MOOD. Thus, we transform the discussion above into: "It is raining at the

Washington Monument, 6/12/00.": [|-, S]</FONT>. "Is it raining at the Washington Monument, 6/12/00?": [?, S]</FONT>. We can write the IMPERATIVE "Go to the store!" as [!, S]</FONT>, where, now S denotes "You are going to the store." We can write the SUBJUNCTIVE "Would that you were going to the

store." as [%, S], using "%" to denote THE SUBJUNCTIVE MOOD. We can write the PETITIVE "Please go to the store." as [*, S]</FONT>, with "*" denoting THE PETITIVE MOOD. (Other "mood operators" can be introduced.) Please notice that EACH VECTOR COMPONENT IS TRUTH-FUNCTIONAL: [The speaker speaks in mood M, The speaker makes statement S]. Using VECTOR LOGIC, we BYPASS THE LANGUAGE PROBLEMS OF SCALAR LOGIC, and ENCOMPASS MUCH OF DAILY SPEECH! American mathematician-logician-philosopher, Charles Saunders Peirce, founded SEMIOTICS:

STUDY OR THEORY OF SIGNS: SYNTACTICS (SYNTAX) IS THE THEORY OF SIGNS WITHOUT

REFERENTS. SEMANTICS: THEORY OF SIGNS ADJOINING REFERENTS TO SYNTACTIC SIGNS.

PRAGMATICS: THEORY OF SIGNS THAT CONSIDERS THE SIGN-USER. Most people indulge in two confusions here. First, that Peirce promulgated "pragmatic philosophy": MEANING IS IN USE. He did not! And was so upset at this nonsense that he said he might change his term to "pragmaticism", since "no one would steal such an ugly term". Secondly, people say that two people "have a semantic difference", instead of saying that it's "a pragmatic difference". Thus, our VECTOR LOGIC IS A PRAGMATIC LOGIC. Vector-Logic resolves a long-standing problem in formulation of programming languages in BNF ("Backus-Naur-Form", first developed to define

terms in ALGOL programming language. (Elsewhere, I show how to use BNF to develop

a Methodocopoeia for teachers.) All of a programing language can be formulated

in the DECLARATIVE mood, fitting BNF, except for assignments, which are IMPERATIVE. (In the C Programing Language I used for 12 years at the Naval Research Laboratory, "x = 2" is an assignment, hence, IMPERATIVE; "x = = 2" is

an equivalence, HENCE, declarative.) But vectored BNF eliminates the problem in

scalar BNF, by simply changing the "mood" component. Thus, a "hole" is removed.

vector-Logic also resolves an even more famous problem. In the 1960's, many argued that COMPUTER TRANSLATION OF LANGUAGES would greatly simplify the publication of technical or literary-dramatic literature. But only a very limited success was ever achieved for years. (Note: a universal language for publication

once existed: Latin. Even the great Karl Friedrich Gauss -- considered "greatest of all mathematicians" and a skilled linguist -- wrote in beautiful Latin, and his works could be read all over the world, including in China. But 19th century NATIONALISM "killed" Latin as a universal language. Result: It costs our

Government and Universities and Publishers millions of dollars a year to fight the translation problem, and they still can't keep up!) Critics of "machine translation" bandied an Enlish problem: "Time flies." This has the usual meaning

that "Time gets away from you if you're no careful." But a computer translated it into a matter of "measuring the flight of certain insects". However, this ambiguity only arises in scalar logic, as used in English Grammar. In

Vector-logic, the two obviously differ: [|-, "Time flies."] for the first version; [!, "Time flies."], for the second version.--The Austrian logician,

Gotthold Frege, in effect, treated statement logic as zero-order predicate logic and created first-order predicate logic, second-order predicate logic, tc. He did so by creating two QUANTIFIERS: The UNIVERSAL QUANTIFIER ("for all instances or members of the given set"), denoted by capital "A" turned upside down. The EXISTENTIAL QUANTIFIER ("ONE INSTANCE EXISTS"), denoted by capital "E" turned left. The VECTOR-LOGIC thus described can be carried over into "the predicate calculus".--Frege also noted that a NAME has two linguistic ROLES in language: USE, as in "Boston is a busy town", for the name "Boston". And MENTION, as in "'Boston' is a 6-letter word. (Note that the latter distinction can be made, in written form, by putting the term in quotation marks, showing that we are talking about the NAME rather than USING it.

VECTOR-LOGIC also invokes these distinctions. The "extra" component we introduced plays a USE ROLE: THE SPEAKER IS USING A MOOD IN SPEAKING. However, in the spirit of Frege, we can also invoke the MENTION ROLE: THE MODES OF SPEECH. That is, "The sign-user mentions statenent S is mode D", using this letter for "mode", so as not to confuse it with "mood" -- MODES OF DISCUSSION, viz.: ALETHIC MODES or MODES OF TRUTH are, principally, necessary, possible, impossible, contingent. (For purposes of discussion below, let's adopt, A, as the alethic mode operator.) TENSE MODES enable TEMPORAL aspects of sentences. (Aristotle considered this problem: a declaration which is TRUE at a given time, and FALSE at others. I avoided this by putting time into my sentence about "raining".) Let's denote the temporal mode operator as "T". DEONTIC MODES deal with obligation, can, may, etc. (This is the MODE

used in ETHICAL and MORAL discussions, as well as LOGICAL and THEOLOGICAL ones.) Let's denote it by "D". EPISTEMIC MODES deal with terms such as knowing, believing. Let's denote it by "E". The PREFERENCE MODE is needed in economic and political discussion. Let's use "P". The FREE MODE allow fictional imagination to "roam free". Let's use "F". Etc.--VECTOR-LOGIC via MODES enables us to RESOLVE A CLASSICAL PARADOX: "The Morning Star Paradox", often stated in SYLLOGISTIC FORM as in "All men are mortal. Socrates is a man. Therefore, Socrates is mortal. The "Morning Star Paradox" runs: "The Shepherd knows that Venus is The Morning Star. The Morning Star is The Evening Star. Therefore, "The Shepherd knows that Venus is The Evening Star." Then this would follow, in scalar logic, by TRANSITIVITY: "V = M. M = S. S = V." But the Shepherd may not actually know this. In terms of Vector-Logic, it would take the mood-form: [|-, "V = M"].

[|-. "M = S"]. [|-, "S = V"]. And transitivity would support it in the 2nd or syntactic component. But in the MODE form: [A, "V = M"]. [A, "M = S"]. [A. "S = V"]. In both cases, the 1st component is CONSTANT ("a parameter"), which shifts the logic-question entirely to the 2nd component-argument, which is VALID in Scalar-Logic. However, the "Morning Star Paradox" must be considered only in the mode-form of

Vector-Logic and we must invoke the epistemic mode, for which we adopted (above) the operator, E. Using our two mode-operators, we have: [E<, "V = M"]. [A, "M = S"]. [E, "M = S"]. The mode shift is epistemic ("knowing") to alethic to epistemic -- or E to A to E. Lack of tranitivity

shifts the burden to the 1st component, with NOTHING LOGICAL TO SUPPORT A SHIFT OF MODE. Therefore, THE ARGUMENT IS INVALID, hence, NO PARADOX! Other ambiguities and paradoxes could be resolved similarly.

(Somewhere, in the "time capsule" of my past cluttered files, there was a C Programs I wrote years ago, automatically translating from well-formed English sentences into Vector-Logic, and vice versa. If JAVASCRIPT had existed then, it would have been easier and more might have been accomplished. I CHALLENGE you to TAKE UP THIS WORK! And invite comment/argument.

[Graviphoton]

Ooooo... this is messy... you should clean it up... it just looks like a big slab of words

[antimatter]

Ooooo... this is messy... you should clean it up... it just looks like a big slab of words

 

Agreed. He should also attempt to hide his fetish for caps a little more.

I only got about half way down before my eyes got tired.

[Graviphoton]

I left at the third...

 

That is after i scrolled down to find it was all pretty much the same fasion

[Dave]

Yeah, I'm classifying this as junk until it gets cleaned up. Please re-post only if you fix it to make sense.