StrictlyLogical

Additionally, given my later, more considered examination, I should take back my earlier, imprecise statement: “Galt’s Speech confined itself to what a person needs for an integrated full framework for living in the modern world.” Rather, that confinement is what remains of GS when one sets aside “psychologies and motives of religionists and of materialists (e.g. Marxists, Behaviorists) / psychologies of savages and of dictators.”
I said also earlier in the reflections in this thread that the doctrines in Galt’s Speech “suffice to cover all the essentials of the philosophy. (Amplifications of those essentials Rand subsequently published could also be taken as part of the essentials.) Additionally, all points in OPAR for which an endnote is attached that gives a source in remarks of Rand that she did not publish are not points essential to the Objectivist philosophy.” I want to expand further on the amplification idea and to amend the not-published-by-Rand resort in source found in endnotes as a criterion for chucking into the bin Non-Essential.
Concerning amplifications, I’m thinking of post-Atlas writings such as Rand’s essays “The Metaphysical versus the Man-Made” and “Causality versus Duty.” Another candidate would be David Kelley’s argument that essentials of Rand’s philosophy beget benevolence as a major moral virtue. Each such candidate would have to have it’s argument outlined and its beyond-GS premises, if any, studied to assess whether the candidate is an essential part of the philosophy. (In the twentieth century, I recall seeing proof of a theorem about circles in the Euclidean plane which was a new discovery of a truth in Euclidean geometry, notwithstanding the external circumstance that Euclid had died a long time ago—truths of Euclidean geometry can come to light without Euclid having ever known anything about them.) Such assessments of candidates as amplifications of essentials in Objectivism will be left to the labor and sagacity of the reader as interest in a particular amplification candidate might arise.
I notice it also seems possible that the essentials of Objectivism or some natural portion of them might have a significant reformulation of them, rooted in writings of Rand, that is equivalent to the formulation expressly given them by Rand. This would be analogous to the equivalence of the epicycle model and the eccentric model that astronomers in ancient Greece used in capturing certain patterns of celestial bodies moving over the earth through a year.* I’ve seen a couple of efforts gesturing in this direction, but among the writings of Rand they draw upon are ones that are beyond GS and its implications, and their equivalence in resulting formulation to (portions of) Rand’s essentials are not entirely worked out.
The amendment I should add to counting as inessential any points supported by citing solely a saying or writing of Rand that she never chose to publish is: If the point can be argued anyway from essentials in GS by a deduction, then we can count it an essential. I make such a particular deduction myself in my paper “Existence, We” to be published in JARS next month (p. 88), and I then quote the conclusion also as an oral statement of Rand’s that she had never chosen to publish.
To locate the places in OPAR where Peikoff cites in support of a point words of Rand she did not chose to publish is easy. Just look down the Endnotes for ones citing only the Appendix to ITOE (1990) or only a private journal note of Rand’s or only a private letter of Rand’s. Compilation of the theses to which these Endnotes are attached and determination of whether they can also be reached by argument from essentials of Objectivism in GS, will be left as an exercise for the reader and maybe not this one who is the writer.
There is something not about OPAR in general, but a point within it, I’d like to comment on, particularly in connection with Aristotle and Bolzano. So there’s at least one more post coming.

My summarized take after reading all your responses:
The Benevolent Universe Premise describes an attitude that views man as empowered to survive in an intelligible universe: he can discover facts, causal connections and the unknown. He is equipped with a tool that, when applied correctly, allows him to build an ever-growing context of knowledge which, rather than being threatened by new knowledge, is strengthened by it.
It's also helpful to make a few distinctions that clarify thinking about the kind of world we live in: (1) the metaphysical vs. the man-made; (2) the unknowable vs. the unknown;
With respect to distinction #1: The differences between men and objects are consequential enough (a badly styled outfit is capable of being visually irritating, a badly developed soul is capable of murder) to separate them out for analysis.
 
 With respect to distinction #2: A quote from John Galt's speech describing the feeling of living in an unknowable universe:
 
Actually, this is something I had in mind originally too. According to the quotes below we consider “accidents” as not being the essence or the “norm” of human life. It’s still not really clear to me what kind of conceptual stepping stones I need to jump over to be fully convinced of this. I can see that we have a tool to discover the unknown, but there is still the unknown—and the unknown can include causes of negative, deadly consequences and this fact is "in the nature of existence." I don’t think I’ll get an answer until I explore lots of real-world examples of how men actually dealt with the unknown, e.g., the case of discovering blood types compatibility and how that unfolded. This is what Greg pointed out with exploring “positive reinforcements” too.
Some quotes:
With respect to distinction (1), the man-made:
Rearden reflecting in Atlas Shrugged:
“The Inexplicable Personal Alchemy:"
With respect to distinction (2), an unknown as opposed to unknowable universe:
Leonard Peikoff's lectures:
 

This could bring new meaning to kangaroo court.

"Fictional problem", in the sense that a "paradox" must involve some disconnect with reality.  Reality has no problems, the problems are thus fictional. 
No hypothetical shape, event, situation, process, system, etc. which is obvious and behaves exactly as "expected" or "intuited" was ever called a "paradox".   Neither was anything which was judged too new or too complex to understand. Differential geometry is not a paradox to a musician, it's just something he/she does not have training in and does not understand, but he has no reason to suspect "paradox".  A paradox requires an experience that something is amiss... but there are no contradictions in reality (no matter how many opposing forces, collisions or disagreements) there is only existence and existence is identity.
So the "problem" is fictional, in the same way an illusion introduces a fiction... reality is what it is, but something about what we see, and should understand, is off kilter, and we know it. At least for those who experience the particular paradox...  the feeling of paradox requires a certain thinking process to get a person in the wrong place to sense that disconnect, and in truth, different people are often led in different directions...
 
I think in a sense the more something appears or seems opposite of what one assumes it obviously should appear or seem like, the more paradoxical it is.  Since reality is NOT at fault, our sense and assumptions of what things obviously should appear or seem like, IS.

Yesterday, while pursuing my current series "Prime Movers, Immovable Movers, Self-Movers", I came across the following in Plato's Laws. In rotary motion of a disk there are "points near and far from the center describ[ing] circles of different radii in the same time; their motion varies according to these radii and is proportionately quick or slow. This motion gives rise to all sorts of wonderful phenomena, because these points simultaneously traverse circles of large and small circumference at proportionately high or low speeds---an effect one might have expected to be impossible." 
There is something fascinating and, as SL termed it earlier, unexpected that the Greeks experienced in thinking about rotation of a disk, even at this elementary look mentioned by Plato. I notice the words "wonderful" and "expected to be impossible." Archytas was a personal friend of Plato, and Plato may well have seen the puzzle #24 and could have it in mind as among the "wonderful phenomena" stemming from rotating disks. The sort of showman talk of Plato and of the author of Mechanics reminds me a lot of Galileo's way of presenting mechanical things---here's an amazing thing, and I have the secret of how it comes about.
I suppose "paradox" covers a pretty wide variety of puzzles. I gather that the paradoxes of Zeno and pals were not put forth as problems having solutions, but as absurdities one enters when one denies the doctrines of their master Parmenides (doctrines folks outside that school find absurd). Those paradoxes---deeper perhaps than the wheel one we've look at---continue to be analyzed today. I've books with various resolutions to paradoxes of Zeno, but I've never pulled them all together and made an assessment.
The wheel case seems to have an element of deception to it, but I don't think it was put there in an effort to trick. Rather, there was something naturally tricking most any mind thinking about the setup. This problem involves perception/imagination, but also trains of thought. It is among cases that when intellectually resolved, understood, the illusion is dispelled. That's not true of our purely perceptual illusions, I've noticed. We continue to see the sun and moon near the horizon as larger than when they are high in the sky, even though we know they do not change size. The illusion, the dependable experience itself, is not altered by our knowing it to be an illusion (by reasoning and by taking a photograph). Also, I do not get robbed of the pleasure of that illusion, by knowing it to be an illusion; and I expect the illusion and the pleasure would continue all the same if I learned some definitive explanation of how the illusion comes about in the human visual system.

What I find fascinating about this wheel issue, is that a full enough description of the actual motion of the wheel and its parts relative to the ground and its frame of reference is, arguably (theoretically), all that is required to dispell the apparition of paradox from the mind of one capable and willing to understand fully, for when the confusion at issue is removed and reality laid bare... what else needs to be said?
There are different descriptions of that reality with different focii and different levels of completeness, which nonetheless will be sufficient to dispell the misgivings, depending upon the mind in which the irksome feeling of "paradox" resides, the particular form the paradox takes, and the particular sum of integrated and connected knowledges and intuitions of the person, which allows them to, by thier own routes, untie themselves from the Gordion knot.
It's fascinating to note that minds differ so much they will argue endlessly whether or not some particular truth told in a certain way about the non paradoxical thing (in reality) is in fact enough to dispell the misapprehensions.  That there is so much disagreement over which truth among many "really works" points mainly to the way paradox and misapprehension, errors of the mind, lodge themselves, they must be of widely varying natures and magnitudes. 
Who am I to say your realization has not led you out of the labyrinth?  When I see that I require mine to escape.
Many are the different ways our minds are each led astray and knotted up, and so too, many are the different ways which work to lead us each aright and unknot our thinking.
 
 

"Fictional problem", in the sense that a "paradox" must involve some disconnect with reality.  Reality has no problems, the problems are thus fictional. 
No hypothetical shape, event, situation, process, system, etc. which is obvious and behaves exactly as "expected" or "intuited" was ever called a "paradox".   Neither was anything which was judged too new or too complex to understand. Differential geometry is not a paradox to a musician, it's just something he/she does not have training in and does not understand, but he has no reason to suspect "paradox".  A paradox requires an experience that something is amiss... but there are no contradictions in reality (no matter how many opposing forces, collisions or disagreements) there is only existence and existence is identity.
So the "problem" is fictional, in the same way an illusion introduces a fiction... reality is what it is, but something about what we see, and should understand, is off kilter, and we know it. At least for those who experience the particular paradox...  the feeling of paradox requires a certain thinking process to get a person in the wrong place to sense that disconnect, and in truth, different people are often led in different directions...
 
I think in a sense the more something appears or seems opposite of what one assumes it obviously should appear or seem like, the more paradoxical it is.  Since reality is NOT at fault, our sense and assumptions of what things obviously should appear or seem like, IS.

The difference is in the attempt to apply a linear dimension to both circumferences and equate them with the distance traveled. Only the outer diameter rotates where the relationship between the angular progression and the circumferential engagement are 1:1. The inner diameter goes along at 1:1 with regard to the angular progression.
There may be some quibble with the terminology, but it appears that a paradox is contrived by trying to combine unlike terms.

The author of Mechanics, or Mechanical Problems, does not regard #24, which is the problem discussed in this thread, as unresolvable, only wondrous, and he offers a solution. I gather his solution fails; he's just spinning his wheels. The author is not Aristotle, all agree. A good argument has been made that the author was the famed Archytas, who was a contemporary of Plato.

You are at an intellectual advantage, whether by nature, nurture, or self made and you’ve shown that once more.
I do begin to wonder whether as a compliment or adjunct to philosophy (perhaps it already forms part of it) the study of what leads the mind astray, causes confusion, gives rise to the appearance of paradox etc should not have a more prominent place, perhaps even outranking epistemology (maybe it’s a small subset of epistemology) in importance … it seems to me that 
insufficient knowledge was never the cause of all the woes of a man or mankind but the over abundance of false impressions and ideas masquerading as knowledge.
 
Perhaps the study of fools is the path to wisdom?
 

Thank you Boydstun & StrictlyLogical for clarifying this. Here is my summarized understanding after having read both your replies.   The assumed context here is that man survives by a particular method of thought and action.You cannot evaluate an object when it is obtained by irrational action because it is moral principle that sets the context (a commensurable standard) for evaluating that object in relation to your other values. You can evaluate the method as good or bad, i.e., this is for my life or against my life, but not the object. Similarly, in epistemology, a proposition accepted on faith cannot in some sense be evaluated on its own, but in terms of method.    An example with StrictlyLogical's breakfast:  If I obtained the breakfast by cheating a shop keeper and he later hits me with a rock does it make sense to say the breakfast was good because I enjoyed it while it lasted? Or what about if I suffered no immediately perceivable consequences but began obtaining more things in the future through fraud? In either case I can't really make sense of the situation by looking just at the breakfast (evaluating the object in terms of my other values) but only by looking at how I obtained it (against moral principle, bad when evaluated in terms of action or method).

This example was reminiscent of this quip by Albert Einstein, without the hearing of the ticking, or the hope of ever understanding exactly how it works:
In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way to open the case.

I have the book and have read it through.  I'm not sure I am completely satisfied with the level of detail reached.  Nor do I believe there is quite enough of an integration/reconciliation (this is in reference to the article) with a persistent dichotmously and disparagingly labelled "material world" (label used not in reference to the article).
 
An undecided mind is still roving over the possibilities... narrowing in on the choice, the freedom from being wholly determined I would assume must extend continuously until it has been made.  Whatever choice is, if one is ever definitively made and if it is of only a choice of one of many alternatives, then the alternatives I assume must somehow be eliminated  in the process, thrown out of consideration, until literally only one remains.
 
I suppose rather than looking at this process empirically as merely refining one's ideas of about freedom of choice, we could simply use it to define the moment of choice.
A free choice has been made, by definition, once the factors present to make it free, are all in the past.  This freedom shrinks (if one could assign a magnitude) as one approaches the choice, and simultaneously becomes 0 as it is made.
That does not mean one can not make another choice, quickly countermanding the previous... but that is a further choice, not an extension of the first, nor an illustration that the first choice was or was not free.
There may be a "deciding one has chosen" factor which shuts the freedom down, at least for that choice, or for some temporary period afterward... to avoid endless dithering in the mind.
 
I do like your softening of classical determinism, and your reflections about genuine contingency, with processes which (like QM) exhibit multiple outcome causality.  I think it is a sort of multiple outcome causality which for any particular starting identity of the universe and itself, would exhibit a probability function (if it were possible to repeat reality) in the Hilbert space of all choices and actions, which would typify free will.  It has enough identity (the probability function is specific... maybe you'll choose Italian Food over Thai 80% of the time) so that it is not purely random, but it also is not wholly determined.
 
Here's an aside:
Of course if we shrink free will, or the free aspect thereof, i.e. if we restrict it ONLY to the choice to focus... well we have a different story.
Once you make the choice to focus or not everything else would be determined... and so then alternative futures are all about the randomness with which you choose to focus. 
IF you so happen to be such that you choose to focus 100 percent of the time you'd be deterministic. 
If you so happened to be such that you choose to focus 0 percent of the time you'd be deterministic. 
If you so happened to be such that in each and every particular context you always made the same decision to be focused or not, say 100% whenever you are in a car and 0% whenever you are on a boat, you would be deterministic.
There has to be some appreciable number of contexts, realities in the moment, at which point you could choose to be focused or you could also choose not to be in focus, that alternative futures are even possible.
 
If follows, that in accordance with Objectivism, your ability to choose to go out of focus is crucial to your having fee will.
[As you can likely see I am not of the view that free will must be so restricted]

A worthwhile set of schematics to think with, I’d say, SL, at least to get started. I notice that internally, there are random processes that affect a human life in a deterministic way, such as the appearance of a cell mutation (truly random at first cell alteration) we call cancer. It could deterministically become, say, non-Hodgkins lymphoma. In the particular case of person having it, though in advance of therapies, we might say it’s a matter of chance whether the therapy will be effective in this case; that is just our ignorance, and when the particular outcome eventuates—say death from the cancer—we sensibly say that this outcome was a matter of objective, determined fact from the time the therapy had begun. With the same stage of cancer and the same age of life when the therapy would begin, different patients would make different yes-no choices over whether to undertake the therapy. Each patient could weigh all sorts of common and uncommon factors in coming to a decision. It might become clear enough to a patient which way she should go, or she might end very unsure and decide to let a coin-flip decide which way. But I’d say each person of mature sound mind freely comes to their decision.
One thing that seems key in my current thinking about this is that alternatives as alternatives on what to do are not something merely out in the world without their being an agent confronting the world. The thinking agent is able to generate alternatives, and though they are drafted over what all is in the world, the more powerful at generation, the more free is the agent in the sense of having organized outputs more distant from, more deliberately organized than, immediate-emergency fight or flight response (I’ll pose the latter for William O’s deterministic case). And so long as the thinking agent’s conscious, purposive control system has been in the overall control, greater freedom seems also to go with greater distance from random acts, or anyway acts without large purpose, such as acts of someone who has lost their mind (which I’ll pose for William O’s randomness case).

This is very insightful.  I agree.
It might be that after eons of observation and study of brains (ours, animals, and possibly artificial ones), once unimaginable technological innovations which allow us to see the brain at work in real time in all its complexity have been achieved, we might be able to see or confirm the riddle of free free will from a third person perspective, only by determining and distilling (controlling and isolating) those aspect of some pattern in ourselves when we are actually engaged in the use of our "free will"... by hook or crook will require the teachings of millions of years of evolution exhibited by our vast and complex minds being what the brain is and does.
Whatever that is, whatever aspects, patterns, clues, it produces, will then be how we see and measure it in animals or machines we may wish to create.

ET, concerning your original question of this thread, I notice that if one is looking at various objects and their actions or behaviors or if one is interacting linguistically (as here or as in the Turing Test setup), one knows by one's thinking sort of looking that one has some freedom in directing that inquiry. Then too, one's bodily movements, the ones the medical folk would call voluntary, seem to straddle the external and the internal. One might know little about how one is directing from the brain to one's finger movements on the keyboard, but one has at once direct access to both (the internal) the directing thoughts and a sense of some freedom in bringing them together and (the intimate external) the movements of one's fingers and appearance of text on the screen. I wonder if determining whether some entirely external object has free will necessarily requires, by hook or crook, determining its likeness to oneself.

Volition is associated with free will, rather than mere "purposefulness".
 
Free will is a crucial concept not because it deals with "will", but because it posits that that will is "free".
What does "free" mean?  Free from what? 
 
Certainly not entirely "free" from "reality".  That is impossible.
Certainly not entirely "free" from the "identity" of the entity exhibiting it.  Impossible.
Certainly not entirely "free" from the context surrounding the entity exhibiting it.  A non interacting thing unaware of its surroundings is "oblivious", not "free" in the intended sense.
 
"Free" includes "at least" being free from absolute determinism, in this sense:  the entity could have done otherwise ... hypothetically speaking.  Given the exact same entity and reality ... the same entire universe... same IDENTITY, the entity could do X or could do Y and does do X or does Y.  If we could turn back time, it would do different things... because we define it as being free from absolute determinism.
If we characterize or concretize the doing as choosing, we locate the freedom with "will", and therefore we define free will as requiring (at least) hypothetically, an entity which could have chosen otherwise, even keeping IDENTITY of all of reality the same, as the control...
of course we cannot actually set the universe back to the same moment in time to test this.  In fact, some might say wording the hypothetical in this way is incoherent.  But it is literally all we have which makes sense.
 
 

I guess my argument for objective morality would go like this:
First, establish objective reality. If your audience doesn't accept that, then there is no reason to continue.
Then, I'd do the "argument from the hamster":
If you want to keep a hamster alive and thriving, you have to follow certain rules. The same thing is true if it's a human instead of a hamster, although the rules are more complex. (Humans don't thrive in cages.) The same thing is true if the human you are trying to keep alive and thriving is yourself. That argument should be sufficient to demonstrate that an objective morality exists. It doesn't say what the rules are, but that can be the next step.
p.s. I'm aware that this argument takes it for granted that the purpose of morality is to keep yourself alive and thriving. It's possible to explain why that is the proper purpose, but I'm not doing it in this post.

The case for an objective morality can be made much more easily than Objectivist Morality.
For one thing, if you have to say this is from Ayn Rand, you will be seen as a mass murderer.
But that aside, the summary of Objectivism does not do it justice and you can't ask them to read multiple books essays etc., because they want it in a nutshell.
The summary of Objectivist Morality is not that easy to communicate, otherwise the population of Objectivists would be far higher.
The case for morality is not going to be morality defined as the guidebook for life but morality as in "right and wrong".
They believe that "right and wrong" has no basis in reality or logic. It is an invention like religion.
The case can be made that "right and wrong" can be Objective, knowable, determinable. Not priviledged knowledge for only a few to know.
In this way, the case for an Objective "ought to" is far more easily done than the totality of Objectivist morality.
It can be shown that if you want X, you are obligated to do "something". That you have to, the moment you want.
That you ought to, because you want. That you must, because you want.
If you don't, you lose, you fail, you do what is wrong based on that.
If you don't want, then the obligation goes away too.
At it's basics, the case has always been simple with cybernetics, or missile technology. If you have a target. There is a right way to hit it.
This right way is knowable, it can be figured out. It's objective (with all the definitions of objective)
That's all it takes to show that an Objective morality can exist.
The part that becomes far more complicated is "what is the target and why".

Except when he is drowning..

 
[I agree btw]

First Objective does not mean Universal
Second, without the choosing of life, there is no ought.  Only with an aim can you ought do something “if” you want to bring about your aim.
A human being, if he wants to flourish long range is bound by reality and his nature.  Everything flows from that.  Just recognition of facts of reality in the form of principles.
Morality is not intrinsic.
 

Although I believe I have addressed this already, since I had something to add I felt responding to this might be appropriate.
Notice for "socialist" ethics (yes that is an anti-concept) or "communist morality", the field in question is akin  to the realm of what WE ALL must (notice invocation of force rather than choice) DO, which as judged by individual members of the body politic will often conflict.  This is in the sense of the ONE commune being forced to be of ONE mind, it cannot be split into myriad directions no matter how diverse its individuals.
Social metaphysicians, who almost ALWAYS think in WE and US, when thinking about relationships and the State... will always see collisions, because no matter what they think, they cannot on some level, know that the individual person IS free and independent in action and thought and is the unit by which to conceive of humanity.  The illusion of conflict is a result of their mystic notion of the ONE mob, the public good, and the State... that field in which "either or" arises.

Thank you.
[PS I've edited many times ... if you read this after an hour since posting it should be stable]
The reason I bring up commensurability or field is because it narrows down our thinking to referents of concepts to which the idea of conflict is somehow possible.
A "conflict of interest" in a person IS possible precisely because a person is of ONE mind, the one mind being the field for the two opposing interests, a single mind cannot be FOR and AGAINST the same thing and in the same respect, at the same time.  The presence of a single field guarantees the "either or".  It guarantees the impossibility of the two things.
If two things are wholly independent of one another, do not affect one another, or depend on each other, then ANY interaction, let alone "conflict" or any requirement of "either or" between the two things, as such, is impossible. 
My taste (as such) in music has no common arena to conflict with your taste (as such) in music.  No matter whether your love for Baroque or heavy metal wanes, increases or disappears, my love for tiddlywink continues on its trajectory without any concern for what happened in your mind.  Now we could literally get into a fist fight over my displeasure that you like different music from me, but that is not a conflict between our musical tastes, our tastes are not fighting, WE are.
Anyway this might be getting too concrete, but I think you get my general idea. 
Collision is the the perfect metaphor.  Here we have a field, space, in which the things "solid objects" have an either or relationship: solid objects cannot occupy the same space, or pass through one another.
So, there being a field (not space) and things (not solid objects) which cannot both be in the field at once and in the same respect at the same time: i.e. there is an "either or"  we probably can best label it as a collision or conflict or contradiction.
 
There is a lot here I agree with.
I like the vehicle analogy it is a start.
 
Consider these claims:
A. Blind airplanes can collide.
B.  Seeing airplanes always avoid each other and cannot collide.
 
The air is the field, and the conflict or "either or" is physical collision.  The question raised about claim B is whether the seeing airplanes are infallible, otherwise it is possible they can collide.
 
I take your point that generally collision being possible is in a sense a foil for the claim of something more specific being an example of collision not being possible.
 
Consider now:
There are an infinite number of paths an airplane can travel on.  Let's divide them into two classes (which are not mutually exclusive)
I) Paths blind airplanes take
II) Smart Paths seeing airplanes should take
 
Now, consider this statement:
X) there are no conflicts between the Smart Paths.
Here, the field is no longer the air, it is the "abstract space" of paths, and the "either or" (conflict) is "crossed paths". Now random sets of paths generally do cross.  X proposes there exist smart paths the airplanes should take which never cross.  Note that this is not a statement about what paths seeing airplanes actually take but is primarily a statement about what paths they should take.
 
Without getting ahead of myself I think Rand is identifying something more about what "rational interests" are, as opposed to what so called "rational men" do.  Attributing too much of the statement as directed to men, who are fallible and never always rational, is a redirection from the profound statement therein about what "rational interests" are.
 
Now, my last examples of airplanes is of course simplistic.  A path through life, is vastly more complex than a path through the air.
Consider, however, that a rational path through life is guided by rational objective moral principles which includes being long range and respecting individual rights, and everything else which comes with Objective morality.
Although the consequences of such paths, and whether we can identify and follow such paths, are questions of knowledge, prediction, and capacity.  Sometimes in context we can predict, know,  and follow such paths... sometimes we cannot. 
BUT as Objectivists, I do NOT believe we can deny the existence of such paths.
 
The next step, if you agree is to look closely at the nature of these paths, and why they do not conflict (or why they can and do) 
Unfortunately, commensurability and the definition of "either or" raises its head again here, my path through life cannot AS SUCH conflict with your path through life.  Arguably, we could end up fighting over the physical paths, or bump into each other (rather clumsily) in following our dreams... but why couldn't I walk around you in physical space on my way back from fishing (my passion), while you are walking toward the lake to paint it (your passion)?  Our intelligent walking around each other represents no change or impediment to the life path either of us is on in following our respective passions.  I would argue that following the rational path INCLUDES and MEANS walking physically around one another in such a context.
I'm starting to wonder whether "conflict" should mean something more like "gives rise to a conflict", in that although the paths per se don't conflict, they might arguably give rise to a conflict between the people who follow them.  But the focus here is still on the paths themselves... and whether the rational paths necessarily give rise to conflict between those who follow them, if they could fully identify and follow them.
... I'm getting ahead of myself.

You seem to not like the simplicity of your analogies while I value it very highly.
I had initially put in this half baked question responding to your original post regarding "a field" and I took my question out, afraid of confusing the issue, but I was pleasantly surprised to see you are using the word "path" like I was drawn to it. I had written:
"For now, I am wondering if the field guiding your actions is a "field" of paths. A field of "methods". A field of "ways" (as in ways of doing). A field of possible actions which can also be seen as a field."
I included this because of amusement, you can ignore it, will respond later to your posts.

As I find more material about the subject matter I include it. This is from Atlas Society:
"This principle of the harmony of interests is key to the Objectivist view of ethics and politics. Objectivism’s ethics of rational selfishness is not an ethics of dog-eat-dog because of the harmony of interests. A political system based in individual rights to freedom—i.e., capitalism— does not pit the “haves” against the “have-nots” because of the harmony of interests."
"The bottom line is that conflict is good for us, in context, when participating is to the benefit of everyone involved."
https://www.atlassociety.org/post/how-can-one-create-a-harmony-of-interests-among-people