Possibility, Necessity, and Contingency...

Possibility, Necessity, and Contingency; from IEP...

To expose the mistakes in the deterministic arguments, we will need some tools of modern logic. Some elementary symbols will help to illuminate the concepts at play in the deterministic arguments. However, all the formulas that will be used, which incorporate these symbols, will also be expressed in English prose.

Symbol	Its meaning	Explanation
P, Q, R, …	propositions	See (see Sec. 2 of Truth)
~P	it is not the case that P	Example: It is not the case that copper conducts electricity. (Note: “P” and “~P” have opposite truth-values – whichever is true, the other is false.)
P ⊃ Q	if P, then Q	Example: If she is late, (then) the meeting will be delayed.
gKP	God knows that P	Example: God knows that the Mississippi River flows north to south.

Next we need three concepts at the heart of modern modal logic. The symbols are:

Symbol	Its meaning	Explanation
◊P	it is (logically) possible that P	Example: It is (logically) possible that the United States was defeated in World War II. (Note: Whatever is not self-contradictory is logically possible.)
☐P	It is (logically) necessary that P	Example: It is logically necessary that every number has a double. (Note: If Q is not logically possible, then ~Q is logically necessary.)
∇P	It is contingent that P	Example: It is contingent that the United States purchased Alaska from Russia. (Note: A proposition, Q, is contingent if and only if ◊Q and ◊~Q.)

These latter three concepts require further elaboration.

P is possible (symbolized “◊P”). A proposition, P, is possible if and only if it is not self-contradictory. All propositions that are true are possibly true. In addition, some false propositions are also possibly true, namely those that are false but are not self-contradictory. Some philosophers like to explicate “P is possible” in this way: “There are some possible circumstances in which P is true”. And some philosophers, adopting the terminology popularized by Leibniz (1646-1716), will substitute “worlds” for “circumstances”, yielding “P is true in some possible worlds”. Examples of possibly true propositions include:

1. Ottawa, Canada, is north of Washington, DC.
2. The Great Salt Lake is saltier than the Dead Sea.
3. The Dead Sea is saltier than the Great Salt Lake.
4. John Lennon was the first songwriter to travel in a space capsule.
5. There are three times as many species of insect as there are species of mollusk.
6. 2 + 2 = 4
7. All aunts are female.
8. Some pigs can levitate.

Understand that prefacing a proposition, P, with “◊” does not ‘make’ P possible. What it does is to create a new, different, proposition, namely ◊P, which, in effect, says that P is possible. If P is possible (for example, suppose “P” stands for “Gold was first discovered in California in 1990″), then (although P is false), ◊P is true. Or, suppose “Q” stands for “2 + 2 = 7″. Then prefacing “Q” with “◊” does not ‘make’ Q possible. It produces a new proposition, “◊Q”, which is false. Q is, and remains, impossible whether or not it is prefaced with “◊”.

Everything that is actual (or actually true) is possible (that is, possibly true). But if a proposition is actually false, then it is impossible only if it is self-contradictory; otherwise it is a false contingency, and all contingencies, whether true or false, are possible.

We may ask “What color did Sylvia paint the lawn chair?” We look at the chair and see that she has painted it yellow. Thus it is demonstrable that it is possible that she painted the chair yellow. And its being yellow implies it is false that she painted the chair blue. But the falsity of the proposition that she painted the lawn chair blue in no way precludes that she could have done so. Even though false, it still remains possible that she painted the chair blue.

P is necessary (symbolized “☐P”). Necessarily true propositions are those that are true in all possible circumstances (/worlds)—that is, are not false in any. Necessary truth can be defined in terms of possibility, namely P is necessary if and only if its negation (that is, “~P”) is impossible. In symbols (where “=_df” stands for “is by definition”):

☐P =_df ~◊~P

Examples of necessarily true propositions:

1. 2 + 2 = 4
2. All aunts are female.
3. Whatever is blue is colored.
4. There are either fewer than 20 million stars or there are more than 12 million. (This statement may be unobvious; but if you think about it you may come to see that it cannot be false.)
5. It is false that some triangle has exactly four sides.

P is contingent (symbolized “∇P”). A proposition, P, is contingent if and only if it is both possibly true andpossibly false. Contingent propositions are those that are true in some possible circumstances (/worlds) and are false in some possible circumstances (/worlds). Contingency can be defined in terms of possibility, namely:

∇P =_df ◊P & ◊~P

It is essential to understand that “◊P & ◊~P” does not mean “P is true and false in some possible circumstances (worlds)”. No proposition whatsoever is both true and false in the same set of circumstances (law of non-contradiction). To say that a proposition is contingent is to say that it is true in some possible circumstances and is false in some (other!) circumstances.

Examples:

1. The Boston Red Sox won the World Series in 2002.
2. It is false that the Boston Red Sox won the World Series in 2002.
3. Steel-clad ships can float in the ocean.
4. It is false that steel-clad ships can float in the ocean.

Modal terms and modal status

Terms such as “must”, “has to”, “cannot”, “is necessary”, “is impossible”, “could not be otherwise”, “has to be”, “might”, “could be”, “contingent”, and the like, are known as “modal” terms. All of these are definable in terms of “possibility”.

Every proposition is either logically possible or logically impossible. And no proposition is both.

Drawing the net a bit finer, and dividing the class of logically possible propositions into those that are necessarily true and those that are contingent, we have three exclusive categories. Every proposition is exclusively either necessarily true, necessarily false, or contingent. That is, every proposition falls into one of these latter three categories, and no proposition falls into more than one.

Just as the expression “truth-value” is a generic term encompassing “truth” and “falsity”, the expression “modal status” is a generic term encompassing “contingent”, “necessarily true”, and “necessarily false”.

Finally, no proposition ever changes its modal status. We will call this principle “The Principle of the Fixity of Modal Status“. And for the purposes of assessing the deterministic arguments we note especially: no contingent proposition ever ‘becomes’ necessary or impossible.

6. The Modal Fallacy

From a mathematical point of view, if we arbitrarily pick any two propositions, truth and falsity can be attributed to them in four different combinations, specifically

• the first is true, and the second is true
• the first is true, and the second is false
• the first is false, and the second is true
• the first is false, and the second is false

However, it sometimes happens that two propositions will have certain logical relationships between them such as to make one or more of these four combinations impossible. For example, consider the two propositions α and β.

α: Diane planted only six rosebushes.β: Diane planted fewer than eight rosebushes.

While each of these propositions, by itself, could be true and could be false, there are – as it turns out – only three, not four, possible combinations of truth and falsity that can be attributed to this particular pair of propositions. On careful thought, we can see that the second combination – that is, the one which attributes truth to α and falsity to β – is impossible. For if α is true (that is, if it is true that Diane has planted only six rosebushes) then β is also true. Put another way: the truth of α guarantees the truth of β. This is to say

(1) It is impossible (for α to be true and for β to be false).

Unfortunately, ordinary English does not lend itself easily to express the quasi-symbolic sentence (1). In symbols we can express the sentence this way:

(1a) ~◊(α & ~β)

About the best we can do in English is to create the following unidiomatic, extremely clumsy sentence:

(1b) The compound sentence, α and not-β, is impossible (that is, is necessarily false).

English prose is a poor tool for expressing fine logical distinctions (just as it is an unsuitable tool for expressing fine mathematical distinctions^[3] ). But, as it turns out, the situation is worse than just having to make do with awkward sentences. For it is a curious fact about most natural languages – English, French, Hebrew, etc. – that when we use modal terms in ordinary speech, we often do so in logically misleading ways. Just see how natural it is to try to formulate the preceding point [namely proposition (1)] in this fashion:

(2) If α is true, then it is impossible for β to be false.

Or, in symbols:

(2a) α ⊃ ~◊~β

In ordinary speech, the latter sentence, (2), is natural and idiomatic; the former sentence (1b) is unnatural and unidiomatic. But – and this is the crucial point – the propositions expressed by (1)-(1b) are not equivalent to the propositions expressed by sentences (2)-(2a). The former set, that is (1)-(1b), are all true. The latter, (2)-(2a)are false and commit the modal fallacy. The fallacy occurs in its assigning the modality of impossibility, not to the relationship between the truth of α and falsity of β as is done in (1)-(1b), but to the falsity of β alone. Ordinary grammar beguiles us and misleads us. It makes us believe that if α is true, then it is impossible for β to be false. But it is possible for β to be false. β is a contingent proposition. Recall the principle of the fixity of modal status. Even if the falsity of β is guaranteed by the truth of some other proposition [in this case α], β doesnot ‘become’ impossible: it ‘remains’ contingent, and thereby possible.

Whatever impossibility there is lies in jointly asserting α and denying β. (See (1b) above.) The proposition “it is false that β” does not ‘become’ impossible if one asserts α.^[4]

a. The Modal Fallacy in Logical Determinism

Some persons have been deceived by the following (fallacious) argument to the effect that there are no contingent propositions:

“(By the Law of Non-contradiction), if a proposition is true (/false), then it cannot be false (/true). If a proposition cannot be false (/true), then it is necessarily true (/false). Therefore if a proposition is true (/false), it is necessarily true (/false). That is, there are no contingent propositions. Every proposition is either necessarily true or necessarily false. (If we could see the world from God’s viewpoint, we would see the necessity of everything. Contingency is simply an artifact of ignorance. Contingency disappears with complete knowledge.)”

The fallacy arises in the ambiguity of the first premise. If we interpret it close to the English, we get:

P ⊃ ~◊~P
~◊~P ⊃ ☐P

---

∴ P ⊃ ☐ P

However, if we regard the English as misleading, as assigning a necessity to what is simply nothing more than a necessary condition, then we get instead as our premises:

~◊(P & ~P) [equivalently: ☐(P ⊃ P)]
~◊~P ⊃ ☐P

From these latter two premises, one cannot validly infer the conclusion:

P ⊃ ☐P.

In short, the argument to the effect that there are no contingent propositions is unsound. Its very first premise commits the
modal fallacy.

The identical error occurs in the argument for logical determinism. Recall (the expanded version of) Aristotle’s sea battle:

Two warring admirals, A and B, are preparing their fleets for a decisive sea battle tomorrow. The battle will be fought until one side is victorious. But the “logical laws (or principles)” of the excluded middle (every proposition is either true or false) and of noncontradiction (no proposition is both true and false), require that one of the propositions, “A wins” and “it is false that A wins,” is true and the other is false. Suppose “A wins” is (today) true. Then whatever A does (or fails to do) today will make no difference: A must win; similarly, whatever B does (or fails to do) today will make no difference: the outcome is already settled (that is, A must win). Or again, suppose “A wins” is (today) false. Then no matter what A does today (or fails to do), it will make no difference: A must lose; similarly, no matter what B does (or fails to do), it will make no difference: the outcome is already settled (that is, A must lose). Thus, if every proposition is either true or false (and not both), then planning, or as Aristotle put it “taking trouble,” is futile. The future will be what it will be, irrespective of our planning, intentions, etc.

If we let “A” stand for “Admiral A wins” and let “B” stand for “Admiral B wins”, the core of this argument can be stated in symbols this way:

A or B		[one or the other of these two propositions is true]
~◊(A & B)		[it is not possible that both A and B are true]

∴	A ⊃ ☐A A ⊃ ~◊~A	}	If A is true, then A must be true. If A is true, then A cannot be false.
	A ⊃ ☐~B A ⊃ ~◊B	}	If A is true, then B must be false. If A is true, then B cannot be true.
	B ⊃ ☐B B ⊃ ~◊~B	}	If B is true, then B must be true. If B is true, then B cannot be false.
	B ⊃ ☐~A B ⊃ ~◊A	}	If B is true, then A must be false. If B is true, then A cannot be true.

In this argument, by hypothesis, either A is true or B is true, and since they cannot both be true, the second premise may be accepted as true. But none of the conclusions is true. A is contingent, and B is contingent. Yet the conclusions state that from the assumed truth of either of (the two contingencies) A or B, it follows that A and B are each either necessarily true or necessarily false. Each of these eight conclusions violates the principle of the fixity of modal status. What, then, are the conclusions one may draw validly from the premises? These:

☐(A ⊃ ~B)	or, equivalently,	~◊(A & B)
☐(B ⊃ ~A)	or, equivalently,	~◊(B & A)

So long as we remain mindful of the fact that “~◊(P & Q)” is logically equivalent to “☐(P ⊃ ~Q)” but is not equivalent to “P ⊃ ☐~Q”, the argument for logical determinism will be seen to be invalid. Our ordinary language treats “it is impossible for both P and Q to be true” as if it were logically equivalent to “if P is true, then Q is necessarily false”. But the profound difference between these two assertions is that the former preserves the principle of the fixity of modal status, the latter violates that principle. The proposition, “Admiral A wins”, is contingent, and if true, then it “remains” true. Indeed this is a trivial logical truth:

(i) ☐(P ⊃ P) alternatively, ~◊(P & ~P)

The argument for logical determinism illicitly treats this logical truth as if it were equivalent to the false proposition

(ii) P ⊃ ☐P alternatively, P ⊃ ~◊~P

If you do not let yourself be beguiled by the invalid ‘move’ (inference) from (i) to (ii), the argument for logical determinism collapses. The truth of a proposition concerning your future behavior does not make that future behavior necessary. What you choose to do in the future was, is, and will remain contingent, even if a proposition describing that choice is timelessly true.

b. The Modal Fallacy in Epistemic Determinism

Let’s recall Maimonides’s argument:

… “Does God know or does He not know that a certain individual will be good or bad? If thou sayest ‘He knows’, then it necessarily follows that [that] man is compelled to act as God knew beforehand he would act, otherwise God’s knowledge would be imperfect.”

We can symbolize the core of this argument, using “∴” for “it necessarily follows”; and “☐” for “compelled”; and “D” for the proposition describing what some particular person does tomorrow.

gKD

---

∴ ☐D

There seems to be (at least) one missing premise. [In the terminology of logicians, the argument isenthymematic.] One tacit assumption of this argument is the necessary truth, “it is not possible both for God to know that D and for D to be false”, or, in symbols, “~◊(gKD & ~D)”. So the argument becomes:

gKD
~◊(gKD & ~D)

---

∴ ☐D

But even with this repair, the argument remains invalid. The conclusion does not follow from the two premises. To derive the conclusion, a third premise is needed, and it is easy to see what it is. Most persons, with hardly a moment’s thought, virtually as a reflex action, will tacitly assume that the second premise is logically equivalent to:

gKD ⊃ ☐D

and will tacitly (/unconsciously) add this further premise, so as to yield, finally:

gKD
~◊(gKD & ~D)
gKD ⊃ ☐D

---

∴ ☐D

But this third premise, we have seen above, is false; it commits the modal fallacy. Without this premise, Maimonides’ argument is invalid; with it, the argument becomes valid but unsound (that is, has a false and essential premise [namely the third one]). Either way, the argument is a logical botch.

Once the logical error is detected, and removed, the argument for epistemic determinism simply collapses. If some future action/choice is known prior to its occurrence, that event does not thereby become “necessary”, “compelled”, “forced”, or what have you. Inasmuch as its description was, is, and will remain forever contingent, both it and its negation remain possible. Of course only one of the two was, is, and will remain true; while the other was, is, and will remain false. But truth and falsity, per se, do not determine a proposition’s modality. Whether true or false, each of these propositions was, is, and will remain possible. Knowing – whether by God or a human being – some future event no more forces that event to occur than our learning that dinosaurs lived in (what is now) South Dakota forced those reptiles to take up residence there.

Logic is the science about drawing conclusions…

Hi, well a short reply grew monstrous; again__but maybe there's a silver lining in this big cloud...(this is just a repost to keep the blog active...)

Question: How would a mind process 'the infinite number line', and the infinite energy capacity link of emotions/desires, to solve a scientific problem__unless logic herself, had an infinite capacity to do so...? Logic must somehow see some sort of infinity, to even think about it__No...? In my experience, logic even corrects wayward imaginations and dreams back into reality, but if imaginations and dreams do happen to contain infinite scenes of action__then, how does logic do the correcting back to finite realities__What's that particular 'inference path' mechanics...? See the difficulties...? If we don't know this 'inference path mechanics', yet the path does get corrected back to reality_as we certainly know it does__then, does the mind know more about how to do these corrections than us...? Is such auto-pilot 'inference mechanics' not 'background-independence', of the highest order...? Is such 'auto-pilot inference mechanics' possibly part of our existing 'a priori' bio-structured brain self-mechanics...? 'A priori' here meaning simply, 'built-in bio-mechanical functions' similar to, or the same as, how our heart and lungs function...

These are just some of the old skeptic's questions that have been asked for millennia, but they do bring the complexities into clear light, imo...

Just wade in, and see where you go... I guess that's all I can say, since it is so monstrous a reply...

Imo, you can't derive a 'came to be' from an eternal state mechanics__It's just simply always been... Any 'came to be' state is simply what science and physics has falsely been attempting and doing, over the last 100 or near so years, with the big-bang and inflation theories__And, that's why I say, "they are religions", as all 'came to be's' are 'creation myths...' I think you seem to be forgetting our most recent x-ray satellites are presently correspondingly externally filming the internal dynamics of black-holes spewing their internal guts all over space__It doesn't take a great deal of good investigative science to put this picture together, as much of that I revealed in the Universal mechanics of fs-field photons I just sent you. I think we can pretty much extrapolate most of this internal mechanics, presently... We presently still do have some information horizons(incompleteness’s), but they are fast falling__maybe not all of em, but most of em will fall__shortly, imo..."

Have you thought out the 'Many Universes' model thoroughly__As near as my logically using the entire laws of physics, nature and thought go__Such mechanics would by necessity of the mechanics produce just about exactly what we actually have. I see little difference in the mechanics of one Universe or many... If you think our the possibilities of other 'Universal Law Systems' actions being different, one's mind comes up short, as there's only a certain workable mechanics, by these very necessary laws' functions__of fundamental motions' aggregations... Do they arise, or are they integrally existing, and necessarily so__as an aggregate matrix, unit of the exist...] [Ditto__It is...] [If we have field_everywhere_nothing is impossible_tis eternally outside logic__logic also ceases to function as any possible viable mechanics, any time 'nothing' is considered viable__except as a 'not something' virtual state of reference to validate 'something'__yet we still know the impossible of 'the naked nothing'.] [You are probably meaning by 'emerge', to 'self-construct', I'm not sure__But, I might point out that infinity is an absolutely necessary requirement of logic and the exist, for any Universal and logic mechanics to function__since the opposite is 'naked finiteness' which I've many times shown to be impossible, due to such mechanics necessitating the 'something from nothing' 'creation myth' impossibilities__not even counting contradicting the very necessary requirements of the laws of physics, logic and thought... Also, even for logic to begin to recognize the all known and necessary existence of feelings and emotions, logic must have a rhetorical core of knowing intelligence, above both the 'infinite emotions'__which every finite logician has admitted, since antiquity__but, also for use to even begin to understand others who are using mixed metaphoric and rhetorical states of communication__such as, courts of law, where lawyers have to stick to strict physical evidence, and physical motives__yet, at the same time convince very subjective information processing jurors of the clients innocence, or guilt if the lawyer is the prosecutor__so, logical and rhetorical knowledge of both sides of the mind__'infinite subjective' and "finite objective' are absolutely necessary__as has always been shown by juridical logicians, for millennia... This same logically necessary 'inference mechanics' of abductive judgment, concepts, theories, hypothesis, models, etc., applies to physics as well as any subject, in the same inference requirement necessities__except possibly setting aside most or all of the 'infinite subjective' as much as necessary or possible__though, it still exists as a necessary part of our grounds of meaning and knowing mechanics__These ideas have been settled, over the last 75 or so years, by many logicians', scientists' and mathematicians' work, as well as the lesser philosophers...]

[In that case__where's the initial function of the initial forming...?__as per forming structures from fields, or even forming disorganized fields into organized fields as forms of fields...? As a case__Fields exist in dense and less dense states, and most likely always have...] [And, may I point out right here__Herein lies our 'background independences'__And, this pertains to both the 'hyper-small-infinitesimals' as well as those 'hyper-huge-infinities' we will never be able to define__but, I have also shown that such states, the smaller or larger, the further away__have less real and possible influence, the more infinitesimal or infinite they become__due to c mechanics necessities... Further 'background independencies' can be the non-isomorphics of the very laws of physics, nature and thought__that are also known to exist... I'm not trying to steer you away from knowledge__I'm trying to point out the mechanics knowledge that exists, in these 'not knowable' states__when one simply thinks our the necessities these 'not knowable' states force on us about the known possibilities, that are left to think about__these ideas simply force us to think more about the 'logical possibilities left', by eliminating such impossible influences from our theorizings...] [I don't know, but it seems we may both be trying to convince each other of the same ideas__without knowing it...?] [Maybe form + function at the same time...?] [We must be very careful here, to fully understand what is purely virtual abstract theorizing, and the real factual physical motions and forces of functions and forms...] [To me here, there's no deeper understanding than 'pure inference mechanics', as this is the only 'pure mechanics' understanding we possess of any physical actions of our Universe... Imo, all our 'inference mechanics' functions and forms must correspond to our views of actual Universal facts__or we've left the field of science and physical laws, required for real and true science... This doesn't mean we can't abstractly use 'virtual ideas' beyond such 'inference realities'__but, in the end we must bring them within scientific intelligence's scope...

[Imo, you're ignoring a lotta' scientific capacity of discovery without evidence here__We do have much scientific discovery capacity with circumstantial evidence, by aggregating and integrating exactly what is possible of such finished models__and imo, to where none of exactly what is happening at the center of a black hole is of any importance to reality__what-so-ever__as long as we generally know its conclusion and effects. This is where I and many modern thinkers part company with the deductive logicians__as the deductive only logicians are leaving the largest part of science and scientific history out of the equation, from Francis Bacon onwards. Abductive and inductive logic have and do make up by far the larger part of real science__and this is the science I use. By truly looking at the end result__the 'cosmological ontological eschatology', as I mentioned already__science can logically build the internal mechanics of black holes, in the computer labs, to show these deeper functions__if they be necessary to you. They are not necessary to my theorizing and logic to understand the Universe, as I more use the natural 'innate a priori inference mechanics' as my major guide to science's proofs. If it don't fit my 'inference mechanics'_it ain't science__but that does not stop me from conjecturing the internal mechanics of black holes__as the entire Universe offers exactly zero mysteries to me, where real necessities of function and form are required, to complete my model... The black hole mechanics I've seen is fine with me__as much of it is a known necessity to produce such metals as tungsten and uranium, or many other heavy elements__as our sun, and many bigger suns' science, has done the hydrodynamics of, is incapable of the pressures required to construct such heavy elements__Imo, that leaves the super-high-pressure of the hydrodynamics of black holes as our sound model producers of such heavy elements. Diamonds are not included here, as they grow under even Earth's low hydrodynamic pressures... Just model mechanics, but it satisfies me... The black hole results are far more scientifically important to me, than the deepest internal mechanics' processes__whereas I see that nothing than higher pressures, and the further conjectured actions such actions would produce up to tungsten, then spew it into the Universe for other forming planets, suns, moons and other rock debris to pick up, upon coalescences of...] [But, if this be true, then why do we see these massive jets of real information exiting black holes__that we absolutely know had to go in, in the first place...?_Unless your wish is some 'creation-myth black hole...?' I don't accept any of these new 'emergence myths' as valid science__as they all represent 'something from nothing' 'creation myths'__Again, imo... [I see the same here, as to real matter__on the way in, but 'matter that goes in, must come out'__'Action-reaction law...'

 [Aren't you forgetting here, there's already a pre-formed uniform model, nature has planted in our minds, of a 'general descripted Universe'__implanted since birth...? My main point asking those questions was to have you see and understand, we can't possibly process from each other’s private information processing centers__we must have a publicly agreed upon objective model__Named 1st, so's we both are on the same page... I know and agree with probably 99% of your private logical processing mechanics__but I'm yet to get a good picture of your public model__or any possible public model you are working toward. Maybe the same is true to you of my wordings, also__I don't know... It's just I hate to keep confusing these small points, when agreeing to a public model and personal goals of what one is trying to discover, may be able to alleviate the difficulties__That's all...] [I get a kick out of this dialogics that's going on between us. I'm not talking about real models of 'Infinity', as how you are evidently thinking about them__I'm simply speaking about the infinities we do absolutely know exists within our finite understandings__We do have infinite realizations of both mathematics and emotions__Neither one is possible of boxing in finiteness__Yet, what seems to be happening when I try to bring those entities we absolutely know are infinite, you somehow get the idea I'm speaking about actual infinities, of different sorts, than I am actually meaning. Let me see if I can straighten this out. Let me list a few pieces of knowledge, I've stated before about both finiteness and infinity__as these ideas are so necessary to wrap one's mind around, that I can't stress enough their importance to scientific and logical thinking...

1. Rational finiteness is all we can pertain science and logic to, and have scientific meaning about the geo-universe...

2. Rational infinity is a scientifically known reality of our bio-mental-natures...

3. Therefore, iff finiteness is scientifically restricted to eliminating rational infinity of our bio-being state__even in casual scientific conversations__it is not true scientific thought, and this is where the skeptics enter, to destroy scientific thought and conversations__so I also always dispute these mistakes of thought...

4. Scientific thought must be worded to be true to both geo- and bio-systems, or it's not scientifically true__and this is the area science has made many of its mistakes in...

5. The differences between 'True Infinity' and 'Rational Infinity' are immense__yet, science uses both, while biology mainly uses only 'True Infinity'__due to not understanding the mathematical restrictions of 'Rational Infinity', which simply means 'Extremely Large Numbers Logic...'

6. We can't scientifically quantify logic, without setting up the boogie-man of 'True Infinity' or 'Rational Infinity', to quantify finite logic against__As already mentioned, finiteness has no definition until quantified against 'True Infinity', which also exists in science, through science's knowledge of 'The Unending Number Line' and 'The Known/Unknown Unending Energy of The Universe' and 'The Known Infinite Capacity of Emotions To Keep On Giving...'

7. All the finite wishes in the world can not eliminate these infinite facts' realities, from the world of finiteness, no matter how much scientists wish for it__yet, it sets the 'Dynamics of Conflation and Confusion' in play in all dialogical conversations__which must be quantified, qualified and clarified, iff scientific conversations are to achieve real meaning and substantial knowledge...

8. This simply means, 'Exactly and Explicitly Known Models of Interpretation and Explanation' are absolutely necessary for real scientific conversations to take place, and all the parameters and axioms must be stated clearly and exactly of the ideas, hypotheses, thoughts and models used and expressed__even though I prefer only thoroughly derived axioms, and not postulated axioms...

9. In other words, 'Scientific Results Necessitate Exact Methodologies of Procedure'__Even our simplest of conversations__at these particular levels of thinkings...

I don't know if that will help, or not...]

[Well, that sounds feasible__but, the problem enters when 'simple wordings' that apply to 'parts' have 'wholes' implications__as my mind normally processes from the 'largest to the smallest' and not from the 'smallest to the largest'__as I think that's the present world's major problem within science__sending them into foolish 'somethings from nothings' theories... I can't even think of a 'part' without an 'infinite whole field' attached, whether I know of a reality of such 'infinite field' or not__as I absolutely know of the 'infinite number line' which has been known since the ancients... How can one throw away the absolute knowledge of an 'infinite number line' that all sound logical quantification is founded on, through 'modal quantification logic'__well and hard proven, over the last 60 or so years...? It just can't be done. There is a solution, but you've never liked this solution__You can be exactly accurate in your scientific wordings, to avoid the pitfalls of 'unintended subjective links' within your sentences. I know that's very difficult for someone who may not be schooled in exact scientific linguistics__but, I see no way to avoid the many 'conflations and confusions' of different levels of knowledge trying to be used. If I restrict my language to 'parts', when I don't accept the logical validity of a 'parts formed from finiteness' Universe__Such logic would negate my 'Necessary EM-Field' of 'A Highly Possible Infinity' Bose-Einstein condensing into rocks, moons, planets, stars, black holes and galaxies, etc.__which if you also look at Dave's entire model, was founded on the 'Eternally Existing' colliding spheres, as well__and iff eternal, then infinite__even though Dave entered the contradiction of finiteness into his genesis model... The simplest main point I've constantly tried to make, is the complexity of our languages, in handling the 'one-many_infinite-finite' self-generating contradictions__when not fully understood as true__as 'Both at Once...']

[Platonic numbers. It's been known since Pythagoras, and many other earlier Assyrian and Indi sources, that the number line is absolutely infinite, as pertains to the 'Law of Large Numbers'__Now scientifically, it's as simple as that__but personally, my thinking goes back to my childhood, and being raised in a constantly bickering academic family__I rejected all the finite nonsense by going outdoors, from the earliest age memorable, and simply looking up at the night sky. I knew by seeing the billions of trillions of bright lights, on the clearest of spring and early summer's clear nights__These academics' known finiteness arguments didn't make any sense to what I could see, on these clearest nights... My wife and I both, just a couple of months ago, witnessed one of these most super-exceptionally clear nights, just as we crossed the Alabama-Florida border a month and a half ago__She'd never seen anything like it, as she'd grown up in the city, where the light makes it impossible to see with such country mountain clarity__but, even I was impressed, as I'd never seen a night as clear as this, so we stopped and stared for a long time. The more and deeper we looked, the more we saw__It was exactly like the deep Hubble pictures, except we were seeing it with our naked eyes. Somebody tries to tell me these visions are absolutely known to be finite__and I just ain't buying it, no more than I did as a kid__then with age, I learned that scientific observation and facts of finiteness, with nothing but mere conjectures__at the least conjectures of mathematical models, that couldn't fully be proven to the exact curvature numbers. But anyway, getting back to why and how I choose to process from the 'wholes to the parts'__It's not only from childhood skeptical rejections of adult views, it's also my own deep investigations of the inadequacies of scientific proofs of finiteness, and then in HS when I first read Newton and Einstein, that I thoroughly rode that 'single photon' with Einstein, to see exactly what he saw__and he also only knew that the 'single photon' may have been produced by the sun, but where did the first particles come from to produce the very first star-sun...? That quests true result lead me back to the em-field, or simple photons__as the most elemental entity of the Universe. It's not a massless non-particle wave, or it couldn't form a picture imprint on film__It's a real particle-wave, with real mass, just as the father of the photon's name, Gilbert Lewis, long ago stated... I can't make it any planer___Fields and photons are absolutely required by all physical logical necessity to have real fundamental mass, or it ain't valid science__and complete scientific validity is all important to scientific logic and truth...

[I build my ideas about logical content from actual real world and universe properties, i.e., real physical particle waves, that imo, are not absolutely known, to be finite__but just may be infinite, and the bare atom of 'A Priori Inference Logic Mechanics' absolutely necessitates such most fundamental substance to be physically eternal, as such being finite would negate and contradict the laws of physics, especially the 1st law__conservation of energy and matter, of course the law only states 'conservation of energy', but matter or mass is always implied, by E=MC^2... You've gotta have mass, in that most fundamental energy, or ya don't gut' science... And here realize__The eternity I'm referring to, that necessitates infinity, is first the state of logical equivalence required, to quantify logic as having true validity, and next that the 'Universal Exist' must also 'Inference-Wise' be eternal, to exist at all__as no other 'Modal Quantification Logic' is available, as proven by Ruth Barcan, back in the forties... These are just simple logical necessities__for our logic to be absolutely free of contradictions__and I think you can believe me, as you know my extensive studies of logic, for some 66+ years of experience and reading thousands of the world's wisest logicians, rhetoricians and scientists who agree with my research results... When all the contradictions are absolutely eliminated from 'pure logic'__and that's the state of 'pure arithmetic logic arguments'__All that stands in the end, is the integration of the aggregate logical and biological truths, fundamentally based on real world 'truth-maker' objects and laws, aggregated over time, into my logic database, based in bio-physical memory...

I probably couldn't begin to explain all the intricacies of complexities of full explication of what I've above written, but maybe you can see somewhat, what I am trying to relay. I think the Universe is simple, and that relaying this simple information between two people__is the only complexity__and that's why I've often suggested positive rhetoric, to relay such information__but then again, that's another whole new field of study, to thoroughly know what it truly is, and much of the older schools of rhetoric ended, when womens' sensitivities had to be taken into consideration, when they newly started entering the male dominated colleges and schools of higher learning, back in the 1900's...

Oh, all the complexities of the simplicities...

P.s.
Here's something you might look at. I don't know if you are familiar with formal logical and scientific validity or not: anyway, here's the links:

http://en.wikipedia.org/wiki/Validity

http://en.wikipedia.org/wiki/Deductive-Nomological

The second link refers to the laws of physics, nature and thought having higher validity over even statistics...

The Triadic Maxim___Any Idea; “Arithmetically check all possible effects, against all possible premises, and the combined results will be the total actions of the idea.”

After All The Stars Go To Sleep__The Universe Awakes__A Final Theory...

After all the stars burn our, and all the black-holes, planets and moons, etc., radiate away to the fundamental substance em-field__Thermodynamics is necessarily required by all the laws of physics, logic and math__to change wave phase-state aether space Hydrodynamics__Through the cyclic mechanics of the Universal nearest absolute zero k cold__Shrinking the fs-em-aether back to re-structured matter...

The Cosmological Complexity Logic of The Prime Mover__Solved...!!!

http://en.wikipedia.org/wiki/Cosmological_decade...

QTHD__Quantum Thermo-Hydro-Dynamics' Necessity...

The proof is: Any simple ideal gas, such as liquid natural gas, shrinks when the heat is removed__and the aether being such a hyper-fine-structured ideal non-viscous fluidic gas__is also necessarily required to shrink, when all the heat goes out of the Universe__Thus turning the expansion to contraction... But, it's a trillions of trillions of years out to the re-cycle mechanics and back, and the sheer velocities and magnitudes of time/distance volume involved__Should be enough hydrodynamic force, to produce the four fundamental forces to construct another Big-Bang__as Newton's laws come into play on the return trip__Expecially Inertia__Then of course, all the Quantum and Relative Mechanics Laws...

Btw, if a LNG tanker's gas were at room temperature, a ship to carry it, would be 600 thousand feet long__as it's a 600 to 1 gas shrinkage, just by removing the heat from the gas... The largest LNG tankers are 1000 feet long, appx...

A Possible Answer of Universal Mass…

Hi L______, funny you should mention this at this moment, as I awoke this morning thinking on this very subject. To me it's the most foundational question there is, and people the world over have been trying to solve this 'Riddle of The Sphinx' since the dawn of time. What my thoughts wandered to this morning was Einstein, as I was always trying to delve deeper into his mind, to the levels he'd have been thinking, to get as deep as he did, when I realized from being pushed a bit by G___, how I'd respond to answering to the challenge of best explaining my Decay Model. Also by relating A_____'s, N_____'s and P____'s ideas to mine, I just realized it all comes down to interpreting clearly just exactly what E = MC^2 truly means. Energy and Mass are what is stated, but by my defining Energy on N_____'s thread as not an entity, but a by-product of matter in motion, it finally dawned on me that both Energy and Mass in Einstein's formula are simply measurements, and nothing more__E is simply a measurement of M__another measurement. The real substance being measured is never mentioned, so really, the whole formula as stated is just Einstein's subjective 'God' view of 'Self and All' measurement__Totally lacking the entity of foundation of the material measured. Of course, all physicists know he's intended it to measure a certain amount of matter, but by being left open and background independent, it can also oh so easily be applied to the entire Universe of all reality__and herein lies its subjective faults mixed and conflated with any objective reality, the formula is really supposed to be applied to, and very much confusing so much of the world of science, philosophy and psychology...

Now, let's look for the true foundation in E = MC^2. If it's not energy measuring mass, due to both being pure measurement of measurement, what is it? It's no more than the subjective formula of measurement of its own non-entities__Until we enter a Real Entity. The only real entity to enter into the formula is one of the elements of the elemental table, and choose any one of them you wish, but realize Energy and Mass are not even a single element of the elemental table__Therefore, the formula only makes sense when one of the elements of the table of ground are thought to be the Mass in the formula__so we finally chase mass back to its ground of at least one Real Element... Now, take Einstein's formula all the way to the Universal level, which many of us do, by seeing it as the Relativity Measure of all structured matter sped to the speed of light, and either going backwards in time, or dis-appearing through the light cone as total decay of all finiteness__But Now__Realize these are false subjective assessments of the formula, because the formula is only measureing the formula itself, in most minds, as no fundamental ground is even mentioned... Finally bring the formula back to Earth and enter a piece of matter, and ask yourself what that matter truly is...???

The answer can only be known by either using the subjective side of the formula or an objective Real Matter side of it. Let's simply life-span decay all matter to its most fundamental, and that would be a photon, so by realizing a almost infinitely huge number of photons would be required to account for all of finiteness's decay, we also in reverse thinking, would realize a very large number of photons would be required to build any even smallest piece of matter, even a tiny hydrogen atom__Now, and with the help of Ol' Man Einstein himself, we find the Bose-Einstein Condensate__on the return trip of decay, building from photons back to seeable condensed structured matter__So, the M in the formula is the Mass of real Matter, who's absolute fundamental structure is the Photon made of Real Matter__All along__and the newest standard model physicists, scientists and philosophers are finally coming around to realizing the fact that E = MC^2 must be a representation of Real Matter's Mass__to have any meaning at all__as otherwise, it's just a measurement of measurement__Mass and Energy are not Entities__They are both simple measurements of fundamental matters of mass in motion... So now, these many standard model physicists and theorists have finally realized the lil' ol' photon is absolutely required to have Both matter and mass, to build a Real Universe__Even if, a very infinitesimal amount...

Sorry, for the long off-topic post, but Your post just happened to be the first one I opened this morning, and when I saw my name, and the subject addressed, I thought it might fit...

Addendum:

There's no other Engine of the Prime Mover Motion ability, except the final phase changing state of Decay at Limit, to be the Prime Mover of The FS...

It's the simple phase-state change, demanded by wave mechanics, of thermodynamics losing heat, to turn hydrodynamic at extremely low wave frequency, which just happens to be the Universal conditions of such state, when all the stars, black-holes, planets and moons, etc., go to sleep, i.e., decay to the nearest zero k limit...

It's all the simplicity of Quantum Wave Mechanics At Limit__The Re-Cycle Limit of Thermodynamics to Hydrodynamics...

As to infinity, it's required to account for eternity's space__otherwise you have only the infinite regresses, and illogical contradictions of all the laws of thought, logic, math and science...

The Universal Topology Absolutely Requires Infinity, as Finiteness Only Occupies a Small Volume of Infinite Space, But when Space is Seen As EM-Fields’ FS__The Conundrum of Infinity vs. Finiteness Arises, and Is Only Solved by An Eternal Infinity of The FS, Even Though It's Only Provable By Modal Necessity Logic and Intuitionistic Math...

It's only a model guys__And models are mere representations of reality, but mine offers the logic and maths as proofs, of a truly fundamental foundation for the standard models__for the first time in history...

There's no conjecture__Only the necessary and fully derivable logic from the real Universe, and its laws and maths...

Iff there's no infinite field beyond finiteness's decay limit__there's no prime mover possible__and a true void is not allowed by science's necessary logics, maths and proofs__Since; "Field is everywhere"__whereas infinity exists simply by being required by eternity's necessity__plus a Universal Mechanics Necessity of Motion__or there's absolutely no foundation for Motion__So, the choice is Conjectured Eternal Motion__Or a Fully Logically Derived Motion...

The Choice is Yours...

When will the world ever learn, Energy, Mass and Time are mere measurements of FS-Space-Em-Field Matter in Motion__and Nothing More...

FS-Space-Em-Field Matter = A Single Triadic Physical Entity...

P____, there is no beginning of a "No Beginning"... Even in your own ideas, any beginning is a logical contradiction of your own ideas of eternity in infinity. Both your and my logic dictates/necessitates an "Absolute No Beginning"__to be eternal, thus infinite...

My model isn't conjecturing a fundamental motion__It's clearly stating the Absolutely Necessary Universal Wave Mechanics Function at Re-Cycle Limit, which really isn't a Limit of the Universe, but just one of its Phase-State Changes__Necessitated for the eternal Universe to have motion__It isn't created within the entire Universe__It's only a described always existing mechanics, as what's always been the Prime Mover Hydrodynamics of all existence, of the FS, and all structured matter and fields...

Peirce's Definitions of Scientific Truth...

Truth

(see also Real )(if need be, highlight this entire post to read easier, the red and gray elements)

"To say that a thing is Real is merely to say that such predicates as are true of it, or some of them, are true of it regardless of whatever any actual person or persons might think concerning that truth. Unconditionality in that single respect constitutes what we call Reality.[---] I call "truth" the predestinate opinion, by which I ought to have meant that which would ultimately prevail if investigation were carried sufficiently far in that particular direction." ('A Sketch of Logical Critics', EP 2.457-458, 1911)

"Unless truth be recognized as public, - as that of which any person would come to be convinced if he carried his inquiry, his sincere search for immovable belief, far enough, - then there will be nothing to prevent each one of us from adopting an utterly futile belief of his own which all the rest will disbelieve. Each one will set himself up as a little prophet; that is, a little "crank," a half-witted victim of his own narrowness.

But if Truth be something public, it must mean that to the acceptance of which as a basis of conduct any person you please would ultimately come if he pursued his inquiries far enough; - yes, every rational being, however prejudiced he might be at the outset. For Truth has that compulsive nature which Pope well expressed:

The eternal years of God are her's.

But, you will say, I am setting up this very proposition as infallible truth. Not at all; it is a mere definition. I do not say that it is infallibly true that there is any belief to which a person would come if he were to carry his inquiries far enough. I only say that that alone is what I call Truth. I cannot infallibly know that there is any Truth." (Letter to Lady Welby, SS 73, 1908)

"The purpose of every sign is to express "fact," and by being joined with other signs, to approach as nearly as possible to determining an interpretant which would be the perfect Truth, the absolute Truth, and as such (at least, we may use this language) would be the very Universe. Aristotle gropes for a conception of perfection or entelechy, which he never succeeds in making clear. We may adopt the word to mean the very fact, that is, the ideal sign which should be quite perfect, and so identical, - in such identity as a sign may have, with the very matter denoted united with the very form signified by it. The entelechy of the Universe of being, then, the Universe qua fact, will be that Universe in its aspect as a sign, the "Truth" of being. The "Truth," the fact that is not abstracted but complete, is the ultimate interpretant of every sign." ('New Elements', EP 2:304, c. 1904)

"... to believe the absolute truth would be to have such a belief that under no circumstances, such as actually occur, should we find ourselves surprised." ('Reason's Conscience: A Practical Treatise on the Theory of Discovery; Wherein Logic Is Conceived as Semeiotic', MS 693: 166, 1904)

"Every man is fully satisfied that there is such a thing as truth, or he would not ask any question. That truth consists in a conformity to something independent of his thinking it to be so, or of any man's opinion on that subject. But for the man who holds this second opinion, the only reality, there could be, would be conformity to the ultimate result of inquiry. But there would not be any course of inquiry possible except in the sense that it would be easier for him to interpret the phenomenon; and ultimately he would be forced to say that there was no reality at all except that he now at this instant finds a certain way of thinking easier than any other. But that violates the very idea of reality and of truth." (Harvard Lectures on Pragmatism, CP 5.211, 1903)

"Truth is a character which attaches to an abstract proposition, such as a person might utter. It essentially depends upon that proposition's not professing to be exactly true. But we hope that in the progress of science its error will indefinitely diminish, just as the error of 3.14159, the value given for π, will indefinitely diminish as the calculation is carried to more and more places of decimals. What we call π is an ideal limit to which no numerical expression can be perfectly true. If our hope is vain; if in respect to some question - say that of the freedom of the will - no matter how long the discussion goes on, no matter how scientific our methods may become, there never will be a time when we can fully satisfy ourselves either that the question has no meaning, or that one answer or the other explains the facts, then in regard to that question there certainly is no truth. But whether or not there would be perhaps any reality is a question for the metaphysician, not the logician. Even if the metaphysician decides that where there is no truth there is no reality, still the distinction between the character of truth and the character of reality is plain and definable. Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth. [---] In the above we have considered positive scientific truth. But the same definitions equally hold in the normative sciences. If a moralist describes an ideal as the summum bonum, in the first place, the perfect truth of his statement requires that it should involve the confession that the perfect doctrine can neither be stated nor conceived. If, with that allowance, the future development of man's moral nature will only lead to a firmer satisfaction with the described ideal, the doctrine is true." ('Truth and Falsity and Error', DPP 2 / CP 5.565-566, 1902)

"These characters equally apply to pure mathematics. [---] A proposition is not a statement of perfectly pure mathematics until it is devoid of all definite meaning, and comes to this -- that a property of a certain icon is pointed out and is declared to belong to anything like it, of which instances are given. The perfect truth cannot be stated, except in the sense that it confesses its imperfection. The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. [---] But whether there is any reality or not, the truth of the pure mathematical proposition is constituted by the impossibility of ever finding a case in which it fails. This, however, is only possible if we confess the impossibility of precisely defining it." ('Truth and Falsity and Error', DPP 2 / CP 5.567, 1902)

"But even if it were impossible to distinguish between truth and reality, that would not in the least prevent our defining what it is that truth consists in. Truth and falsity are characters confined to propositions. A proposition is a sign which separately indicates its object. Thus, a portrait with the name of the original below it is a proposition. It asserts that if anybody looks at it, he can form a reasonably correct idea of how the original looked. A sign is only a sign in actu by virtue of its receiving an interpretation, that is, by virtue of its determining another sign of the same object. This is as true of mental judgments as it is of external signs. To say that a proposition is true is to say that every interpretation of it is true. [---] Thus, a false proposition is a proposition of which some interpretant represents that, on an occasion which it indicates, a percept will have a certain character, while the immediate perceptual judgment on that occasion is that the percept has not that character. A true proposition is a proposition belief in which would never lead to such disappointment so long as the proposition is not understood otherwise than it was intended." ('Truth and Falsity and Error', DPP 2 / CP 5.569, 1902)

"All the above relates to complex truth, or the truth of propositions. This is divided into many varieties, among which may be mentioned ethical truth, or the conformity of an assertion to the speaker's or writer's belief, otherwise called veracity, and logical truth, that is, the concordance of a proposition with reality, in such way as is above defined.

(2) The word truth has also had great importance in philosophy in widely different senses, in which it is distinguished as simple truth, which is that truth which inheres in other subjects than propositions.

Plato in the Cratylus (385B) maintains that words have truth; and some of the scholastics admitted that an incomplex sign, such as a picture, may have truth.

But truth is also used in senses in which it is not an affection of a sign, but of things as things. Such truth is called transcendental truth. The scholastic maxim was Ens est unum, verum, bonum. Among the senses in which transcendental truth was spoken of was that in which it was said that all science has for its object the investigation of truth, that is to say, of the real characters of things. It was, in other senses, regarded as a subject of metaphysics exclusively. It is sometimes defined so as to be indistinguishable from reality, or real existence. Another common definition is that truth is the conformity, or conformability, of things to reason. Another definition is that truth is the conformity of things to their essential principles.

(3) Truth is also used in logic in a sense in which it inheres only in subjects more complex than propositions. Such is formal truth, which belongs to an argumentation which conforms to logical laws." ('Truth and Falsity and Error', DPP 2 / CP 5.570-573, 1902)

"By a true proposition (if there be any such thing) I mean a proposition which at some time, past or future, emerges into thought, and has the following three characters:

1st, no direct effort of yours, mine, or anybody's, can reverse it permanently, or even permanently prevent its asserting itself;

2nd, no reasoning or discussion can permanently prevent its asserting itself;

3rd, any prediction based on the proposition, as to what ought to present itself in experience under certain conditions, will be fulfilled when those conditions are satisfied.

By a reality, I mean anything represented in a true proposition.

By a positive reality or truth, I mean one to which all three of the above criteria can be applied, - of course imperfectly, since we can never carry them out to the end.

By an ideal reality or truth, I mean one to which the first two criteria can be applied imperfectly, but the third not at all, since the proposition does not imply that any particular state of things will ever appear in experience. Such is a truth of pure mathematics.

By an ultimate reality or truth, I mean one to which the first criterion can be in some measure applied, but which can never be overthrown or rendered clearer by any reasoning, and upon which alone no predictions can be based. Thus, if you are kicked by a horse, the fact of the pain is beyond all discussion and far less can it be shaken or established by any experimentation." (Letter to Georg Cantor, NEM 3:773, 1900)

"The question therefore is, how is true belief (or belief in the real) distinguished from false belief (or belief in fiction). Now, as we have seen in the former paper, the ideas of truth and falsehood, in their full development, appertain exclusively to the experiential method of settling opinion. [---]
On the other hand, all the followers of science are animated by a cheerful hope that the processes of investigation, if only pushed far enough, will give one certain solution to each question to which they apply it. [---] This activity of thought by which we are carried, not where we wish, but to a fore-ordained goal, is like the operation of destiny. No modification of the point of view taken, no selection of other facts for study, no natural bent of mind even, can enable a man to escape the predestinate opinion. This great hope is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. (' How to Make Our Ideas Clear', CP 5.406-407, 1878)