03. Equivalence and Other Terms



Script:  Roy Thomas 

Pencils: Barry Windsor-Smith 

Inks: Sal Buscema © Respective

copyright/trademark holders.

Equivalence (mutual implication)

P implies q and q implies p

p ≡ q = (p É q) . (p É q)

“formal implication” thus “formal equivalence.”

It must not be supposed that two propositions which are equivalent are in any sense identical, or even remotely concerned with the same topic.

Newton was a man ≡ the sun is hot:  is true

Newton was not a man ≡ the sun is not hot: is false

Truth-Values

True if a proposition is true

False if a proposition is false

If proposition p occurs in any proposition f(p), the truth value of f(p) will depend not on a particular proposition p, but only its truth value.

if p ≡ q then f(p) ≡ f(q)

f(p) may be called a “truth function” when argument p is a proposition and the truth value of f(p) depends only on the truth value of p.

“A believes p” is a function of p which will vary its truth value for different arguments having the same truth value.

One may believe one true proposition without believing another and may believe one false proposition without believing another. This related to the characteristic of mathematics namely, mathematics being always concerned with extensions rather than intentions.  

Assertion-Sign “├”  what follows is asserted and distinguishes a complete proposition which is asserted from any subordinate propositions which are not asserted.

├ p É q   unless (p É q) is true the assertion is in error.

Inference – “├ p and ├ (p É q)” infers “├ q” –inference cannot be reduced to symbols.

To draw attention to an inference – “├ p É ├ q” may be read “p, therefore q.” this does not explicitly state what is part of its meaning, that p implies q.

This is a mere abbreviation of “├ p and (p É q) and ├ q.”

An inference is the dropping of a true premise;

it is the dissolution of an implication.

Jim Meddick’s Robotman  © Respective copyright/trademark holders.

In our dominant culture in North America, and in fact in most of the world, people follow and prefer to be ruled by laws, statutes, rules, guidelines, precepts, scriptures, principles, contracts, compacts, guarantees, covenants, commandments and all other such static recordings of behavioral intentions or requirements to govern the actions and agreements of human beings among ourselves in all matters and for every reason. It may be held that all this regulation is necessary because persons are good or bad and must be restrained from exercising their base human instincts that politicians and religions typically heap upon human character. My contention, supported by Whitehead and Russell in Principia Mathematica, is that all of this regulation has evolved from the inadequacy of language to convey abstract concepts, and the resulting misunderstandings that occur constantly and universally among all persons in dominant culture. Both from the inadequacy of language itself and more so people’s varying capacity to use the language they have, or to transliterate between one language and another.

 

Above are the beginning concepts that are baby steps towards melting away the constraints of our minds perception. The forms of functions and propositions will be repeated and expanded ahead, and the superb text will provide all the instruction a scholar requires. Concentrate on learning the material, but do not be too concerned if you can’t seem to memorize it, or bring it clearly to mind even some long way in. This is the nature of metaphysics, page after page of information with no tangible subject or story to bring it to mind. Eventually things should click if you study with diligence. Also vocabulary is crucial, and I urge you to turn to a good dictionary if any words used here are not completely clear. It can truly make all the difference.   

Script: Dave Wood; Jack Kirby  Pencils: Jack Kirby  Inks: Wally Wood 

Challengers of the Unknown © Respective copyright/trademark holders.