What then of the points that make the circle. Are they not the smallest possible straight edges? — apokrisis

Neither can a point have an edge, nor can a circle be made up of straight lines. So this idea is contradictory in two ways.

A point is the limit to a line - the zero-D terminus that has greater local symmetry than the 1D line which is having its own symmetry broken by being cut ever shorter, and eventually, infinitely short. A point is simply a line that can't be cut any shorter. — apokrisis

A point marks the limit to a line segment. It is contradictory to say that a point is a line segment which can't be cut any shorter, because a point and a line segment are fundamentally different. The two are incompatible. A point has zero dimensions, while a line signifies a dimension. A point has absolutely no spatial extension. It's relation to space is limited in a most complete way such that it cannot have any shape or spatial form. A line, despite the fact that it continues infinitely, has a very specific, and limited spatial extension, limited to what we call a dimension.

Then for a line to be either straight or curved is itself a question embedded in the 2D of a plane at a minimum. So curvature, or its lack, is determined by the symmetry breaking of a more global (2D) context. A line becomes "straight" as now the locally symmetric terminus of all possible linear wigglings. — apokrisis

I agree that a plane is two dimensional. But a line, by definition cannot be two dimensional. Therefore, "curved line" is itself a contradiction. To express two dimensions with lines requires two distinct lines. The relationship between the lines is expressed as an angle. You cannot have a curved line. That's why pi is irrational, it tries to establish a curved line, but a curved line itself is contradictory, irrational.

My argument is that it is not the curved line itself which produces the irrationality, it is the relationship between two dimensions which is what is truly incommensurate, just like the relationship between zero dimensions and one dimension, described above, is incommensurate. That is why the square root of two is irrational as well. What this indicates is that our spatial concepts, in terms of dimensions, are incorrect. The concept of dimensions of space produce an unintelligibility and therefore must be incorrect.

Straightness is defined in terms of the least action principle. A straight line is the shortest distance to connect two points. You may be familiar with that story from physics. — apokrisis

I think that the application of the theory of general relativity has proven this to be false, the shortest distance to connect two points is not actually a straight line. This is further evidence, that our dimensional modeling of space employing lines and angles, vectors, is incorrect.

They are minimal length lines. But are they straight or are they curved? Or would you say the issue is logically vague - the PNC does not apply? No wiggling means no case to answer on that score. — apokrisis

I answer this question by saying that the entire conceptual structure which models space in terms of distinct dimensions is inadequate and therefore incorrect. This conceptual structure leaves us with an unintelligible, irrational relationship between dimensions. The relationship is modeled with angles, but the concept of "angle" doesn't allow for the true nature of curvature. The "angle" is something totally arbitrary, inserted into spatial conceptions as an attempt to alleviate the described problem of an incompatibility between linear dimensions. When something fails you insert a stopgap to deal with the problem. That is the "angle", but the stopgap is supposed to be temporary. The only real thing that the "angle" represents is the limitations of linear geometry. Pythagoras was perplexed, that there was irrationality inherent within "the right angle", as right and useful as it had proven to be. In reality, as useful as it may have proven to be, no angle is the right angle because "the angle" represents nothing, it is a falsity.

Thanks Srap. This is really the difference between continuity and discrete points. You could construct a circle with points equidistant from a centre point, but this circle would be lacking in continuity, the points being discrete. If you connect the points, you cannot connect them with a straight line or else you do not have a circle, you have straight lines at an angle to each other. It is this queer aspect of the circle, that the continuity from one point to the next is not a straight line, which makes pi an irrational ratio. The continuity between one sot on the circle and the next, must always be two dimensional and cannot be represented as a one dimensioned straight line. The diameter of a circle is a straight line (one dimensional), while the circumference is curved (two dimensional), so the two cannot be measured with the same units of measurement.

You cannot measure a two dimensional object with the same units of measurement as you measure a one dimensional object because you need to allow for the defined difference between the dimensions. This is expressed as the angle. The relation between a first dimension and a second dimension is described by Euclid with the parallel postulate. The concept of "angle" is required to relate two distinct dimensions So if you measure a one dimensional object (straight line) with a specific unit of measurement, you cannot measure a two dimensional object (arc, or circle) with the same unit of measurement because the angle, which allows for two dimensions rather than one, needs to be accounted for and cannot be measured with that unit of measurement. Angles are measured by another unit.

That's funny, given a circle is the most fundamentally symmetric type of unit. It stands as the limit to an infinite regress in terms of the number of sides to a regular polygon. — apokrisis

A circle, because it has no beginning nor end, is the very same thing as an infinite regress. The circle cannot limit the number of sides to a polygon because a curved line is fundamentally different from a straight line. A polygon is made of straight lines with angels, and a circle consists of a curved line. Do you see the difference between the two, and how they are fundamentally incompatible? The curved line is not a limit to the straight line, the two are categorically different.

Consider that a circle could have whatever number of degrees we want. The choice was for 360 because it was derived from a proximity to the number of days in a year, but we could assume any number, even an infinite number of degrees to a circle. Suppose that we assume an infinite number of points around a circular line, because a line segment is infinitely divisible. Between each of these infinite number of points assume a connecting straight line. Now we have a polygon with an infinite number of sides. This is not a circle, because it is derived from an infinite number of points equidistant from a central point, rather than a circular line. So a circle does not limit the number of sides that a polygon can have. It is a completely different concept.

In math, there are at least some moves that are universally considered invalid. — schopenhauer1

My claim is that all those moves which in math are universally considered to be invalid, are based in ontological principles. The principles of addition and subtraction, just like the principle of non-contradiction, is based in ontology. So consensus on these mathematical principles requires consensus on ontology.

All that needs to occur is that a higher amount of constraints that needs to take place math than in philosophy. — schopenhauer1

I don't think you've properly elucidated the pertinent parameters. You've defined consensus in terms of constraint. However, consensus is properly defined in terms of agreement. And there are two principle parameters to agreement, one is the scope of the content of the agreement (narrow or broad), and the other is the scope of the formal aspect (the number of individual human beings engaged in the agreement). So your designation of "a higher amount of constraints' is really quite vague because it doesn't directly take into account either of these parameters. Saying that there is a high number of constraints in place doesn't say anything about the number of people engaged in each of these constraints, nor does it say anything about the scope of application of each of these constraints. For example, whether 100 instances of 20 people agreeing to some specific constraint constitutes a "higher degree of consensus" than a million people agreeing to some broad principle is highly doubtful. You cannot judge "degree of consensus" by "amount of constraints".

I could not solve a mathematical problem with a treatise on "being" for example. However, a metaphysical argument might be framed as a problem of "being", a problems of propositions/linguistics, problems of a priori synthetic knowledge, problems of empirical data gathering, etc. etc. It is framed too broadly for even a consensus on what a valid answer looks like (unless you fall within a camp with another philosopher who shares that point of view, but that doesn't negate that philosophy itself is much broader outside this compartmentalization). Thus I said earlier: — schopenhauer1

In order to even count something intelligibly, a consensus on what constitutes a unit is required. If "a unit" is understood as an individual being, then a treatise on being, and consensus on "being" is required before we can have an accurate count. This extends to all forms of measurement, consensus on the unit of measure is required. This is exposed by Wittgenstein when he claims that a metre stick is both a metre, and not a metre.

But my sentiment I'm trying to convey here is that the models and demonstrations you speak of have a lot of constraints as to what kind of methodology can be employed to solve a particular mathematical problem. Philosophy does not have these constraints (unless your philosophy is to put certain constraints on, but then the argument about what constraints to put on would still be contested and so on). There is a certain consensus in the math community about what counts as even in the realm of what is valid for an answer. — schopenhauer1

I think that this is exactly right, but you misconstrue the implications, the conclusions to be drawn from this situation. Philosophy is less constrained than mathematics, as you say, but the constraints of mathematics are really derived from philosophical constraints. So when the philosophers produce consensus on ontological principles, mathematical constraints are derived from this. The overriding constraint, "what is valid", is a philosophical principle, not a mathematical principle. So there cannot be any consensus on particular mathematical principles without consensus on "what is valid".

But this is because the very nature of philosophy is how unconstrained it tends to be. — schopenhauer1

But philosophical constraints exist. And if they are not produced, or created by philosophy, where do they come from? You cannot accurately say that philosophy is unconstrained, then look at something like the law of non-contradiction, and dismiss this as non-evidential of constraint. Furthermore, what you do not seem to apprehend, is that these philosophical constraints are what bear upon the world of mathematics, as the foundation for mathematical constraints.

Remember that in maths, a unit is defined by the identity element - a local symmetry that can't be broken by whatever operation broke the global symmetry. — apokrisis

No, no, this definition of "unit" must be rejected as circular, or an infinite regress, and therefore not a definition at all. If a symmetry is a unit, and we refer to a prior symmetry-breaking to define that unit, then we have defined that specific unit, by allowing that there was another unit, and referring to this other unit, which is prior to that unit. You have defined "unit" by referring to the unit which birthed it. Therefore there is no definition of "unit" here, just a circle a circle, defining unit with unit, which if pursued would lead to an infinite regress of units. Such a definition is inherently contradictory, because the unit is referred to as a symmetry, but you move to define it by referring to a symmetry-breaking. Therefore what is defined is not the unit, (the symmetry) but the annihilation of the unit (symmetry-breaking).

So geometry begins with the fundamental thing of a zero-d point. Dimensionality cannot be constrained any more rigorously than a dot, a minimal dimensional mark. Having found the stable atom, the concrete unit, the construction of dimensional geometry can begin. — apokrisis

As I said, mathematics could be based in "zero", but this entails a negation of the concept of "unit". When the unit is eliminated, annihilated by symmetry-breaking as you suggest, to base the mathematics in zero, then we need a clear and precise definition of what "zero" refers to. We nave no more "units" to base this mathematics in, only the assumption of "zero". Without a clearly defined "zero", all this mathematics employs completely arbitrary zeroes (concepts of zero), and is just random nonsense.

So in the mathematical realm where 1 is the identity element - the unit that is unchanged by the kind of change that more generally prevails - it is both part of that world and separate from it. It has that incompatibility which you point out. And that is because it is a re-emerging symmetry.

Globally, a symmetry got broke by the very notion of a division algebra. Division, as an operation, could fracture the unity of the global unity that is our generalised idea of a continuous wholeness - some undifferentiated potential. But then divisibility itself gets halted by reaching a local limit. Eventually it winds up spinning on the spot, changing nothing. A second limiting state of symmetry emerges ... when our original notion of unity as a continuous wholeness finally meets its dichotomous "other" in the form of an utterly broken discreteness. — apokrisis

Your global mathematics here is based in "zero", symmetry-breaking, the annihilation of the unit. You also refer to a local mathematics based in units. Instead of attempting to work out this incompatibility, by establishing a properly defined relationship between zero and the unit, you simply introduce contradiction into these two with the necessary implication that symmetry breaking, annihilation of the unit, is derived from symmetry, the unit, and the constraints which constitute local unit are somehow derived from local freedom, lack of constraints.

If mathematical physics tells us that existence is the result of broken symmetry, then who are you to disagree? — apokrisis

It is not mathematical physics which tells us this, it is a simple ontological assumption. As I explained to Schop1 above, the mathematics follows from the assumptions. There is no inherent need to describe existence in terms of broken symmetry, that's a choice.

However, the claim still remains- demonstrable results and consensus make mathematical creativity/novelty different than philosophical creativity. — schopenhauer1

I don't think complete consensus is ever possible in mathematics until the complete nature of reality is completely understood by everyone. Then everyone will agree on which mathematical principles ought to be applied to which aspects of reality. Until then, we will each have our own metaphysics, our own ontologies, and apply mathematics as suited to these various ontologies.

Since consensus on mathematical principles is dependent on consensus of ontology, it is impossible that there could be a higher degree of consensus on mathematical principles than there is on philosophical principles.

I asked them (21yrs old and 18yrs old) if they would support the reimplantation of the draft if necessary. After a bunch of defining who, what, where and why it came down to one simple factor. They would agree with the draft but those drafted would only serve on our shores. The future generation is not buying into nation building or arms races. It is about self preservation through a mutli layer system of defenses. — ArguingWAristotleTiff

There is a very real need for serving in your own land, as we need a rapid response to natural disasters, terrorism, and other possible problems which sometimes require large resources of human commitment. In the area where I live, some of the high school jurisdictions have adopted a program whereby students are required to submit a specified number of volunteer hours in order to graduate. This type of necessary volunteerism, in which one is required to volunteer, but may choose the type of work volunteered for, could produce an army of forced volunteers, and this may make a good replacement for the old draft system. It would be a shift away from the focus on foreign to service, toward more community service at home, though the option of foreign service would still be available to those who choose it.

Or put otherwise: there is no 'ultimate symmetry', the breaking of which explains individuation; it only seems that way after-the-fact, once you've illegitimately abstracted the concept from the conditions which gave rise to it; Symmetry is always-already broken in some way: there are generalities and particulars, and even stratified hierarchies of such divisions, but they develop from the 'bottom-up', even if, once so developed, the higher levels attain a consistency of their own (e.g. category theory as a 'response' to problems in algebraic topology). Explanation occurs in medias res, and not sub specie aeternitatis. — StreetlightX

This is the important first choice of applying mathematics, right here, the defining of "individuation". If we assume that the multitude, the many, or all, are one (the universe), as a bounded object, then we must assume that this bounded object has a value, a finite number, or else the multitude, the many, produced by division is unreal. Any division which allows for infinite division of a bounded object is a completely arbitrary division. This form of individuation denies the possibility that the many, in thje sense of the real, true many, is infinite, and the possibility of infinite numbers, in any real sense, is excluded. But if we define individuation such that we allow that the individual is a real object amongst the many, then the multitude is real, with the real possibility of infinity. However, then we need support for the assumption that the individual is truly the individual, in the sense of indivisible.

In reality we must accept the two distinct choices, each as valid choices, each with incompatible ontological implications. The incompatibility has to do with how we define "one", and is inherent within the concept of numbers. Does "one" signify an indivisible unit, or does it signify a divisible unit? Numbers like 2, 3, 4, represent divisible units, 2 representing a unity which is divisible into two distinct units. But 1 when understood in this way must be indivisible. If we allow that 1 is divisible, we undermine the meaning of unity. But we need to allow that one is both a unity and is divisible, so we allow two incompatible, contradictory concepts to coexist within one, being signified within one symbol. The number 2 for example, signifies a unity (one), which cannot be divided without negating the unity which is signified by the numeral. However, at the same time, it signifies two distinct unities. So each number signifies a type of divisibility and a different type of indivisibility, both at the same time.

(1) Measures of length (every number corresponds to a measurable length, like a table-leg) and
(2) Expressible as ratios ('every number can be expressed by a ratio, like x/y'). — StreetlightX

I think that the premise of B&C is a little inaccurate with (1). The basis of the number system, and the foundation for Pythagorean idealism and Platonism is that the numbers signify units, not necessarily units of length. I believe Plato describes how the Pythagoreans held that unity was the fundamental concept of mathematics, and the concept of numbers is developed from the distinction between one and many. The ordering between one and many is not a matter of choice, because we cannot count backward from an infinite number, to one.

Number is a measure, but not necessarily a measure of length, and the B&C article assumes number to be a measure of length, not a measure of the difference between one and many.

This is an important point to uphold, because the incommensurability which gives rise to the irrational numbers is only produced when the numbered units are units of measurement. This implies that the incommensurability is not a feature of the numbering system itself, but of how the numbers are applied toward measuring dimensional space. The incommensurability between the two perpendicular sides of a square (the square root of two), probably really indicates an incommensurability between the two distinct dimensions of space.

However, the B&C problem can be reintroduced in a much more comprehensive way by considering the introduction of zero into the numbering system. The zero acts to negate the unit, and all units, such that if we assume that the numbering system is based zero then it is no longer based in the distinction between one and many. Zero is more like the potential for unity, or units. From the assumption of zero we have all sorts of choices for defining unity and ordering the one and the many. The proper inquiry might be as to whether numbers should be based in zero, or in the distinction between one and many. The former giving us choice, the latter necessity. The problem with starting at zero is that we have no rational way to produce units from nothing, so zero cannot represent nothing, in any real way, for the production of a numbering system. Therefore we must determine what zero actually represents.

Further, among the points that B&C stress is that it is not at all 'discovery' that is at stake, but what they call - following Wittgenstein - concept-determination: "what is going on here is best described neither as ‘discovery’ nor as ‘invention’ of something entirely new. There are facts to be revealed, and creativity to be exhibited, but what is crucial is the opening up of different aspects of something ... which prompts a choice that sooner or later ‘catches on’... and proves fruitful." — StreetlightX

Aristotle resolves the issue of discovery/invention with the distinction between actual and potential. The act of the mind of the geometer who "discovers" the principles through constructing geometrical figures, actualizes these mathematical principles. If they exist prior to being actualized by a mind, they exist in potential only. He then uses the cosmological argument which demonstrates that nothing potential could be eternal, in his famous refutation of Pythagorean and Platonist idealism which insists that these principles existing separate from human minds, must be eternal.

the 'choice' to allow imaginary numbers (the square root of negative numbers, like √-1 — StreetlightX

By way of a footnote, the discovery and acceptance of the concept of zero was resisted by Western mathematicians for a long period of time, for religious and philosophical reasons. As is well-known, the incorporation of zero into maths - indispensable for decimal notation - was first accomplished by Indian (or possibly Chinese) mathematicians, who had no such inhibitions. — Wayfarer

We have numerous choices as to what zero actually represents, and this is evident if we start to look at the difference between the different representations of zero, like the number line, in which zero represents a count of one unit, or in some cases zero represents the point of separation between positive and negative. Then there is the representation of imaginary numbers, in which I don't quite know what zero represents.

Are you familiar with the method of Platonic dialectics?

Sometimes we have an idea of what a word ought to mean, how it ought to be used, and this preconceived notion clouds our apprehension of how the word is really used, what it really refers to. The Platonic method is to determine the nature of what the thing is which is referred to by the word, by examining usage, rather than accepting some preconceived notion of what the word ought to mean. So for example, in Plato's Theaetetus, they approach "knowledge" with the preconceived idea that knowledge must exclude falsity. However, in all the various ways that knowledge is described, none of them can exclude the possibility of falsity. Therefore it is demonstrated that the word "knowledge", in how it is commonly used, does not refer to something which excludes falsity. Knowledge, which is the thing referred to by the word "knowledge" does not really exclude falsity.

Now, we could argue that everyone misuses the word "knowledge" and they ought only use it when the possibility of falsity has been excluded, or we could allow that the preconceived idea that knowledge must exclude falsity is wrong, and start a new inquiry into what sort of thing knowledge really is, without that preconceived notion.

With respect to the topic of the op, uncertainty, if knowledge cannot exclude the possibility of falsity, then uncertainty rather than certainty is the essential, or integral part of knowledge.

To me? There is no "fair share" in helping others and maybe that is a fault of mine, that keeps me from seeing what you are seeing. — ArguingWAristotleTiff

That's exactly what I think. That's why when people are talking about the fair share, in respect to military expenditure, they are not talking about helping others, they are talking about a joint venture.

This as I noted is one of the downside risks of helping others but I don't know that it is a result of being duped so much as it is that expectations are set up for others. The expectations are based on our own beliefs mixed with those who are fighting to be free and often times the two do not survive without the other there. Which is why I believe the USA should maintain the DMZ long after the two nations peacefully become one. — ArguingWAristotleTiff

I know what you mean, It's actually a very complicated issue which I presented in a sort of simplistic, one-sided way. In reality, different cultures have very different structures of beliefs, so if we base our judgements of what others need, on our own beliefs, we're bound to get some things wrong. Ungratefulness is hard to swallow, but for anyone intent on helping others, it has to be an expectation.

I will ask her your question and report back to you the honest answer I receive. — ArguingWAristotleTiff

I'd appreciate that, I honestly believe opinions are valuable. If we don't share our opinions they reach in separate ways, and "we" is divided into us and them. There's two directions, toward division and toward unity. If we don't share opinions there is no hope of unity. But even when opinions are discussed sometimes division is required. Why?

May she safely return home to her family after she returns a home to another family in that "distant land". — ArguingWAristotleTiff

Yes, I hope that's the way it works out.

In the expression "It is certain", what does 'certain' add to the statement if not some attitudinal report, otherwise what's the utility of word 'certain', you could just say 'It is'. — Cavacava

You might say that "certain" is redundant here. But redundancy is useful to emphasize something to add strength to the statement. The utility of the word "certain" here is to emphasize that this is not an attitudinal report. In no way can it be interpreted as adding attitudinal report, as the intent in the usage is to emphasize that this is not an attitudinal report. Therefore the utility of the word is to emphasize that this report not be interpreted as an attitudinal report.

think your position is untenable. We are talking about certainty and uncertainty. How things are in themself can't be known, no objective viewpoint is possible. — Cavacava

I agree that it is very possible that how things are cannot be known. However, some people don't agree with this, and it is those people who use "it is certain..." to express how things are. I think my position on this is very tenable, the OED bears me out. It is those people who are using "it is certain" in this way, whose position you think is untenable. You might try to convince them of this, and make them stop using "certain" in that way, but I think that would be a futile effort. It's like an atheist who sees people using the word "God", and thinks the theist position is untenable, and therefore they ought not use "God". I am just describing what is going on, people use "certain" in this way, like people use "God" in that way. If you think that the things referred to by these words is non-existent, then that's a different argument. It doesn't make my position, my argument that people use these words in that way, untenable.

Think of "we" as a meeting point between "us" and "them", or "you" and "I" where we can agree or disagree with one another on some points but "we" agree to go forward. — ArguingWAristotleTiff

I agree that you and are "we". I just don't like it when "we" becomes us, as opposed to them, when others do not agree with what we agree to.

But that is not the prevailing thought that guides the average American, as I consider myself to be, nor the average soldier of which I have family. My feeling is that we are not "owed" anything, when we willingly offer help to whomever around the world needs help in fighting for their freedom. — ArguingWAristotleTiff

It's hard to say how prevalent this attitude actually is. I've heard it expressed as if it were common place, especially amongst soldiers. And president Trump seems to express this attitude, that America gives more than its fair share militarily. But what is the fair share is dependent on whether America is fighting to protect its own interests, or whether it is fighting for the freedom and liberties of others.

I do not agree with you that the only reason we "invest" our own blood and toil, is for a financial profit. — ArguingWAristotleTiff

I guess you have a different understanding of "invest" than I do. We ought not use that word then.

I know that some find it hard to believe but Americans actually do believe in helping others fighting for their own freedom, for their own liberty. — ArguingWAristotleTiff

I do not find this hard to believe at all. The problem I referred to though, is the problem of Americans who are duped into believing that they are helping others, fighting for their freedom, when really the fight is for some other reason. When this happens, the others who are supposedly being helped, may prove to be ungrateful, and those who are believing that they are helping the others cannot the ungratefulness.

On a personal note, my Uncle willingly served the United States Army for 33 years beginning with enlisting for Vietnam and ending with Desert Storm. He certainly didn't choose to devote his life to fight for the capitalists of any region. No. He served for one reason and one reason only and that is his dedication to help those fighting for liberty. — ArguingWAristotleTiff

Do you think that the average soldier in the US military knows the reasons why those who make the decisions to send them into battle in some distant land make that decision? Sure, an instance like Afghanistan after 9/11 is somewhat obvious, but after WWII "to help those fighting for liberty" was more like a catch phrase carried over from that earlier war, than a real reason. What if there's a difference in reason for being there, between those calling the shots (to protect our interests), and those firing the shots (to help those fighting for liberty)?

No, I don't see this, since as I pointed out, what is going to count as impossible is going to change depending on the circumstances just as much as what is possible. — MetaphysicsNow

Right, so knowing what is impossible requires knowing the circumstances. The circumstances dictate what is impossible, and knowing what is impossible allows one to say what is possible. Do you see how impossibility, according to circumstances, makes possibilities true and intelligible rather than infinite and unintelligible?

The criteria for what is possible does not change depending on the circumstances. Nor does the criteria for what is impossible change depending on the circumstances. But particular things which are impossible are determined according to the circumstances, and by determining these impossibilities we can limit what is possible, to less than infinite. Without such limiting, possibility is just meaningless nonsense, unintelligible. So this is the point, we bring possibility into the realm of intelligibility by limiting it with "impossible".

Firstly, the criteria I mentioned for possibility are not random in the least. One set of criteria constrains the possible within the bounds of the known laws of nature. Another set releases that restriction but applies the laws of classical logic. Those are not random criteria, but clear and precise ones. — MetaphysicsNow

Your first set of criteria restricts possibility according to "known" laws. This is ambiguous, and not a true restriction. What is "known" varies from one individual to another, such that what is possible for me is different from what is possible for you, under the same circumstances. And, what is truly possible under those circumstances is completely different from either of these, due to the failings of human knowledge in general.

Your second set is just a more ambiguous form of the first, allowing that an individual when determining possibilities may have disregard for the laws of nature, as known by that individual, and only have respect for the fundamental laws of logic. These possibilities are likely less true than the first.

Those two sets of criteria offer no approach to true possibility.

Secondly, nothing you say about the impossible rules out their being infinite impossibilities. — MetaphysicsNow

I don't know what you mean by "infinite impossibilities". That is itself an unintelligible phrase. That something is impossible is a determination made by a mind, a judgement. A mind cannot make an infinite number of judgements. That is the first impossibility which we can determine. It is impossible that there are infinite impossibilities.

Possible" and "impossible" are terms that come together as a package or not at all. — MetaphysicsNow

This is not necessarily the case. Logicians who speak of infinite possibilities necessarily imply possibility without impossibility. That is the gist of the point I am making. Possible and impossible do not necessarily come together as a package. We can premise possible without impossible, and this gives the appearance of an acceptable premise. However, it is a false premise so we must deny it and insist that possible cannot come without impossible.

This is precisely the issue in reverse though - what are the criteria for impossibility? Are we talking about physical impossibility, logical impossibility.... Each will have different criteria presumably, just like "possibility" under my contention. — MetaphysicsNow

I don't think this is the case, so long as we stick to customary definitions when determining logical impossibilities. We describe physical things with words, and our definitions are based on those descriptions. So logical impossibility, which is based in contradiction is a derivative of physical impossibility. It is one coherent set of criteria.

When we approach from the other way, "possibility", we have all sorts of random criteria as to what constitutes possibility, allowing for infinite possibility. This is why we must approach from "impossible" rather than "possible". Do you see that one of them "impossible" is a principle of constraint, while "possible" is inherently unconstrained? The unconstrained is unintelligible, while constraints are intelligible. So we proceed in obtaining certainty in knowledge by determining what is impossible, because "possible" can't give certainty but "impossible" does.

Propositional attitudes are reports using attitudinal verbs like believe, hope, is certain, in 'that' sentences. I tell you that I am certain or uncertain can you deny my report? Sure you can deny the "that" part of it but not the attitudinal part, no? How things are as they are, can't be known, Kant showed this, so then reports of this type have to be how they are for the reporter. — Cavacava

My point is that in the phrase "it is certain", "is certain" is not attitudinal. Is this not obvious to you?

You appear to have proceeded with faulty logic. You say, Kant has convinced me that how things are cannot be known. Therefore when people talk in a way in which they claim that how things are is known, they cannot actually mean that how things are is known. So, you conclude that what they really mean when they sat that how things are is known, is that how things are to them is known. In reality though, they really mean that how things are is known.

Do you see the problem? People are claiming that how things are is known. You say that it is impossible that how things are is known. So you conclude that they are not really claiming that how things are is known. But just because it is impossible that how things are can be known, this does not mean that it is impossible for people to claim that how things are is known. And despite your false conclusion, people go on claiming that how things are is known, though this itself might be a falsity.

there is no need to replace any word of mine with a word you "twisted" to find more fitting. — ArguingWAristotleTiff

The problem I see is this. "Communism" was presented to the American people by the government and media, many years ago, as a threat to the freedom and rights of the people of any country which might fall to communist revolution. In reality, communist revolution was a threat to American capitalists who had investments in those regions. The pinko commie hippies of America saw through the fake news so they demonstrated against the war on communism. They claimed that that the war against communism was a war against the people of those regions, aimed at oppression for capitalist purposes, rather than a fight for the freedom of those people.

Now we have the fallout from this anti-communist propaganda, this fake news of the communist threat. We have millions of Americans, including some in high military positions, and probably in positions of political power as well, foolishly believing that those people in those regions, owe America for its war against communism. But these people with this opinion, misunderstand the situation. By your own words, America has been "heavily invested" in blood and toil for the past 60 years. But this investment was not for the sake of those people, in those regions, it was for the sake of the capitalists of this region. That's the intent behind investment, profit. So the people of those regions owe America nothing, the blood and toil was for the profit of Americans. I'm sure you know what invest means, as that's the word which you used.

You use "we" as if you've fallen for the deception, that "we" signifies a unity of everyone, "us and them"; "we will all profit from the war against communism". But it's really nothing more than a thinly disguised separation of "these people" from "those people". And what is that but an "us" and "them"?

In other words, successful CEO's are Master Delegators and lead as a "We" not as an "I". Hence the well thought out choice of bringing Giuliani on board and the power of Bolton's intimate knowledge, of the very chaos he has been put in the position to manage and to that degree, I can see that as Peninsula dominance until we leave. We have been heavily invested in blood and toil for the past 60 years so we need to distrust but verify and that could take a decade or more. Together, as a United Front, there is no world issue that cannot be entertained AND understood by the Executive branch of our current government common as well as the common man. And that is appreciated. — ArguingWAristotleTiff

This attitude of "we" is the deceptive attitude. "We" is ambiguous, as no individual is necessarily in or out. The "we" is synonymous with "us", and the us is always against them.

Further, these people have no understanding of "equality" in the sense of states or countries co-existing in a fair and equal relationship. The underlying attitude now is that America has already done what is necessary (the 60 years of blood and toil you refer to) to demonstrate that it deserves privileged status. This is the real meaning of "make America great again" for this sort, to produce that privileged status, which twisted minds believe was the reason for that blood and toil. The blood and toil was for the purpose of giving "us" privileged status. It is a twisted belief because privilege is given to you out of respect, which is derived from a demonstration of equality, and there is no demonstration of equality in the attitude of entitlement. So if the others, "them", don't see that the privileged status is deserved, then deception is the means by which one gets what one honestly believes oneself to be entitled to. I don't think that the attitude of entitlement is a good one for international politics.

What's the point in doing philosophy in that way; where instead of changing your theory to fit the evidence, you deny the evidence which is inconsistent with your theory? It is only yourself that you are deceiving.

The difference in meaning between "I" and "it" was not at issue; the question was whether "certain" means something different in "I am certain" than it does in "We're every last one of us certain". — Srap Tasmaner

We're not talking about the meaning of "certain". We are talking about the meaning of "certainty". "Certainty" means "it is certain" rather than "I am certain". The distinction between these two is a distinction of meaning, as "I" means something other than "it".

I noted the pragmatics issue, that "I am certain" might count as a report. I don't think we'd want to say that by being used in such a report "certain" gets a different meaning. What should we say about the difference between a report and, I guess, "an observation"? — Srap Tasmaner

I don't see how that's relevant. The issue is whether certainty is an attitude. The meaning of "certain" in "I am certain" is irrelevant, if the meaning of "certainty" is other than some form of "I am certain". Which it is.



As I said, it's the most common use around here. My OED has it as 1 a) "an undoubted fact", where b) is "a certain prospect (his return is a certainty)".

"Certain", on the other hand is defined as 1 a) "confident, convinced (certain that I put it here)", and b) "undisputable, known for sure (it is certain that he is guilty).

Why do you insist on denying this difference in usage, the split in usage expressed by the difference between 1 a) and 1 b) of "certain". Surely you are familiar with this distinction between "I am certain that..." and "it is certain that ...". Why not just go with where the evidence naturally leads us, rather than trying to pigeonhole things to fit some preconceived idea, which appears to be incorrect?

Certainties are not undoubted facts. — Banno

I just took the definition from the OED. You can take that up with them, if you don't think they're making an adequate representation of usage. In my part of the world, that's exactly how "certainty" is most commonly used. Perhaps the usage is different over in your neck of the woods?

You've shown there's a grammatical difference, in the same way there's a grammatical difference between



Socrates is wise
Wisdom is instantiated by Socrates


Nowhere did you show there's a difference in meaning. — Srap Tasmaner

What? You think that when I say "I", there is no difference in meaning from when I say "it"? These two indicate the same subject to you, such that there is no difference of meaning between "I am certain" and "it is certain"?

If that's your argument then I see no point in discussing this with you.

A little like jkg20, I'm beginning to get a little lost, since what is unknown is not commonly what is unintelligible. Supposing I don't know what my birthday present is because it is wrapped in paper. Suppose that what is wrapped in that paper is the latest iPhone. That I do not know that my birthday present is an iPhone does not make either the iPhone nor the fact that it might be my birthday present unintelligible to me (indeed I may even hope or imagine that my birthday present is an iPhone) . — MetaphysicsNow

It's no wonder you're getting lost, you're inverting what I said. What I meant is that we speak of the unintelligible as an unknown. This implies that the unintelligible is an instance of the unknown, it does not mean that all unknowns are unintelligible. Therefore, that you provide an example of an unknown which is not an unintelligible, is really irrelevant, it just means that you misunderstood what I said.

jkg20 said of me, more or less, that when I use the word "possibility" in the abstract, it just stands for "criteria for what is possible". That's pretty much correct, and I do not see how it commits me to the unintelligibility of possibility or possibilities. The criteria will vary in varying circumstances - sometimes we will be interested only in what is physically possible (i.e. the criteria will include the idea that whatever is possible has to conform with the known laws of nature). At other times, perhaps when writing science fiction, we may want to think beyond those constraints, but still wish to insist that what we are imagining is a possible future, and in that case our criteria would be limited to excluding only logical contradictions (at least, to exclude obvious logical contradictions, some logical contradictions can be deeply buried). In both kinds of cases, laying down the criteria of possibility allows for an indefinite number of perfectly intelligible possibilities. Perhaps it also allows for an infinite number of possibilities, I don't know, it doesn't seem to me to matter much one way or another. — MetaphysicsNow

What you describe as the "criteria for what is possible", I find to be unintelligible. It seems completely arbitrary. You seem to be saying, that with varying circumstances, the criteria for what is possible also varies. How can this be the case? We've identified a type of thing which is "a possibility" and we want to know how to recognize a possibility when we apprehend one, so we need some clear criteria for recognition, and identification. You say, depending on the circumstances, the criteria varies. How is this any sort of realistic way to recognize or identify something, to say that it always appears differently, it fulfills different criteria, in different circumstances? What kind of criteria is this? Can't we find something consistent from one instance of possibility to the next, such that we know we are dealing with the same type of thing, a possibility? Or do we just make up the criteria, however we wish, according to what we want from the circumstances? That doesn't make sense, because we would be very likely to designate something which is really impossible, as possible, if we do not have the proper criteria. Since it is possible that we could confuse the impossible with the possible, then it is impossible that the criteria is arbitrary, as you seem to imply. Therefore there must be some real principles which could be used to distinguish the possible from the impossible in each and every circumstance. Don't you agree?

I suggest we start with very simple and straight forward criteria. Whatever is not impossible is possible. Do you agree? If something, for whatever reason, is determined as impossible we know that it is not possible. Likewise, if we know that something is not impossible then we know that it is possible. If we do not know whether or not it is impossible, then we do not know whether or not it is possible. Do you agree?

As a matter of English usage, you might be right, but even if you are, it's only for the nouns: the adjective that goes with both "certainty" and "certitude" is "certain".

I still don't see a philosophical point. — Srap Tasmaner

Sure the adjective "certain" is the same. But it means a completely different thing to say "it is certain" than to say "I am certain". Call it "objective" and "subjective" if you want, it's just the reality of the usage, these phrases mean completely different things. So it is a mistake to reduce "it is certain" to a variation of "I am certain", because when someone says "it is certain", they clearly mean something completely distinct from "I am certain".

No, but then again I don't think "how things are" can be known, only how things are for us can be known, which is where propositional attitude comes into play. What can or can't be subsumed as attitudinal in a proposition. — Cavacava

I don't see what you mean by "propositional attitude". An attitude is the property of an individual. My attitude is different from your attitude. On this premise, I assume that my attitude toward any given proposition is different from your attitude toward that proposition. If "how things are" is a matter of propositional attitude, how do you jump to the conclusion that there is such a thing as "how things are for us"?

I tend to think it is b) and, if the only thing that can't be doubted is that every thing is absolutely contingent, then contingency itself is non-attitudinal...I guess my thought is that if anything is absolute, it is absolute de re. — Cavacava

I agree with you here, because this is the point I am arguing. What we refer to as a certainty, something which cannot be doubted, is something non-attitudinal. Whether there is anything which fulfills this condition is another question. However, if there is nothing, then what justifies the attitude of certitude? And if this attitude cannot be justified, then the attitude of uncertainty is the justified attitude.

He never holds back his opinion, he trusts few and he cannot be bullshitted. — ArguingWAristotleTiff

Isn't there a contradiction in there? How can one who only trusts a few, never hold back his opinion? If you were prone to distrust, wouldn't you actually hold back your true opinion, revealing only a false presentation of your opinion? I think Bolton's past speaks loud and clear for what he is not: he is not one to be trusted. His real intentions are unclear, but appear to be along the lines of US world dominance.

You suggest that certainty is an undoubted fact, but what does that entail, what is an example of undoubted fact. I doubt any undoubted facts, I think all facts are contingent, that all facts could have been otherwise. If so, does this reduce all certainty to certitude and does this mean that un-certitude is also an attitude. — Cavacava

I agree with you that if certainty means "undoubted fact", and "undoubted" means doubted by no one, then there may very well be no such thing as a certainty. The point I was making to Banno is that we most commonly use "certainty" in this way, so it is incorrect to say that certainty is an attitude because we often use "certainty" in this way, which refers to something other than an attitude.

If one desires to argue that there is no such thing as certainty, in the sense of an undoubted fact, and so we ought to use "certainty" to refer only to an attitude, then that argument needs to be made. Until then, and probably even if that argument is produced, I think people will continue to use "certainty" to refer to an undoubted fact, and Banno's claim that certainty is an attitude is just a ruse.

I think all facts are contingent, that all facts could have been otherwise. If so, does this reduce all certainty to certitude and does this mean that un-certitude is also an attitude. — Cavacava

Perhaps I am not interpreting correctly what you mean by "contingent", but if a contingent thing is something which could have been otherwise, this does not mean that it is not as it is. So if a contingent fact comes into being, through some human choice, or the necessary efficient cause required to bring it into being, this fact still cannot be otherwise, despite the fact that things could have been otherwise.

In any case, I don't see how this is relevant to the distinction between the attitude of certitude about how things are, and certainty, as the undoubted fact of how things are.

By "contingent" are you trying to say that there is no such things as how things are? I don't think that word serves this purpose.

But if you think that possibility is completely unintelligible, then given that what is unintelligible cannot be meaningfully talked about, you seem to be commiting yourself to have been talking nonsense whenever you discuss modality. — jkg20

I don't see your problem. We mention the unintelligible commonly, it is thought of as the unknown. We don't know if it's apparent unintelligible nature is due to deficiencies in our capacities, or it is inherently unintelligible itself, but we apprehend it as the unknown, and approach it as if it is for some reason unintelligible, that's why it's unknown. This does not mean that we cannot speak of it.

I outlined to metaphysicsNow, three different approaches to this sort of unknown, which we call the possible. One is to assume that the possible violates the law of excluded middle. The second is to assume that the possible violates the law of non contradiction. The third, which I called a radical metaphysics is to assume that the possible violates the law of identity, and therefore we cannot even speak of it. You have chosen this radical position.

Possibilities are real to the degree that some logic, some principle of intelligibility, constrains an unformed potency. — apokrisis

We seem to actually have some agreement on this point. As I argued, the only "real" possibilities, what I now call "true" possibilities, are constrained possibilities, therefore "infinite possibilities" does not refer to something real, and cannot be part of a true premise.

One can start with the premise that if one were omniscient then no logical fallacies would arise in the reasoning process of a person or entity.

Therefore, every logical fallacy arises due to gaps in knowledge.

Thus, the best method at our disposal in discovering objective truths is science. — Posty McPostface

This conclusion concerning science doesn't follow from your premise. Logical fallacies arise from mistaken logical process. Science is not the appropriate field of study to determine correct and incorrect logical process.

But, science cannot discover the truth or validity of highly subjective ethical or moral claims.

Then, what method is the most appropriate at discovering the truth and validity of ethical claims, which philosophy is best known for? — Posty McPostface

Morality is concerned with what is right and what is wrong, in general, and so this extends to include right and wrong in various logical processes. So the field of study which deals with correct and incorrect logical process, and acts to determine logical fallacies, is a subcategory of morality. This is why Socrates had to ascend all the way to "the good" in order to establish a foundation from which to attack the fallacies of the sophists. The method which supports this ascent is Plato's dialectics. This method involves an analysis of the use of words in argumentation, to determine improper use and the fallacies which follow, in an effort toward producing true definitions.

Now what's the point you're making? — Srap Tasmaner

Banno said:

The first thing to note is that certainty is an attitude. — Banno

I said:

I think there is a distinction to be made between certitude, which is an attitude, and certainty, which is an undoubted fact. — Metaphysician Undercover

As you pointed out, only 2), "I am certain the earth is flat", is an expression of an attitude. Therefore "everyone is certain the earth is flat" is not an expression of an attitude. And it follows that "it is an undoubted fact the earth is flat" is not an expression of an attitude because "undoubted fact" means doubted by no one. Furthermore, it follows that "certainty", which means "an undoubted fact", is not an expression of an attitude either.

That is the argument I use to support my claim that there is a distinction between certitude (an attitude) and certainty (an undoubted fact).

Both are attitudes. So now we are in agreement. — Banno

No, one is an attitude while the other is a generalization concerning many attitudes, stating that everyone has the same attitude. Do you not recognize the difference between an attitude and a statement saying that two people have the same attitude?

I have an attitude, and you have an attitude. The statement that we both have the same attitude is not itself an expression of an attitude.

An attitude is a property of an individual person. I have an attitude toward a given proposition, and you may have a different attitude toward that proposition, being born and raised under different conditions. "Undoubted" implies that everyone has the same attitude toward that "fact".

So the distinction I refer to is the difference between something which I, you, someone else, or even a group of people, have an attitude of certitude toward, and something which everyone has an attitude of certitude toward.

There seems to be some element of talking past each other here between you and MetaphysicsNow. Perhaps you are right that because there are infinite possibilities we (as finite beings) cannot survey all of them at once. However, I think MetaphysicsNow is suggesting that this is to some extent irrelevant because it does not impact our abilities to entertain any specific possibility. — jkg20

The issue though, is what type of thing is a possibility. If we cannot produce a description of what a possibility is, then we cannot distinguish between a true possibility and a false possibility, therefore whether or not a thing actually is a possibility is unintelligible. I will use "true" and "false" instead of "real" because there seems to be ambiguity with "real".

"Possibility" is ambiguous between your two usages. For you it appears to be the sum of all possibilities. For MetaphysicsNow it appears to be just that which defines something as being a member of that group of infinite things. — jkg20

I think that what is ambiguous between us is the use of "real possibility". MetaphysicsNow seems to believe that if something is logically possible, then it is a real possibility. My argument is that logical possibilities are necessarily derived from premises, and if these are false premises, then they are not true possibilities.

Further, I argue that the assumption that there are infinite possibilities is itself a false premise. And, it is this premise, which is derived from mathematics, that defines "possibility" in such a way so as to exclude "impossible". If there are an infinite number of possibilities, then nothing is impossible because an impossible thing would limit the amount of possibilities. This move excludes "falsity", because the false thing is the impossible thing. Something which is false is something which is impossible. Following this move, we now have no basis for a distinction between true and false, because the possibility of falsity has been removed. But this is itself inherently contradictory because to remove the possibility of impossibility is to remove a possibility, and leave possibilities as less than infinite. Therefore the idea of infinite possibilities is inherently contradictory, and unintelligible, because it would require excluding the possibility of impossibility, which would leave it less than infinite. So if this is really what MetaphysicsNow is arguing, it is impossible that "possibility" is what defines something as being a member of an infinite group, because this is self-contradictory, a contradictory definition.

MetaphysicsNow is perfectly correct that possibility is intelligible if he means by "possibility" what I believe he means. — jkg20

No, if MetaphysicsNow is saying what you claim, this is not perfectly correct, it is unintelligible because "infinite possibilities" is self-contradictory, so we ought to stop talking in this way. In mathematics we have infinite numbers. But when a logician takes the concept of "infinite", and applies this to the concept of "possibility" to create the premise that there are an infinite number of possibilities, the logician creates a contradiction because "impossible", by definition already limits "possible", so the logician is trying to make unlimited that which is already, by accepted definition, limited. To avoid the contradiction, the logician must give "possible" a new definition which is not opposed to "impossible". But now the logician has excluded "impossible" from the allowable lexicon, leaving us without a true definition for "possible", and without the capacity to designate something as false, impossible. This definition of "possible" is itself unintelligible because it is not opposed to impossible. It really has no meaning. being simply an undefined term.

Would you both agree with that? — jkg20

I do not agree to those terms because I think that MetaphysicsNow's use of "possible" is completely unacceptable. My argument is to demonstrate that this is an unacceptable use of the term. You propose that we each go on using the term each in our own way, with some indication to separate them, but this is a proposal to continue talking past each other. The whole point we are trying to work out, is that we need a description of what a "possibility" is, in order that we have something intelligible to work with. If we cannot agree on a description, then we continue talking past each other. If we continue talking past each other, then "possibility", therefore what qualifies as "a possibility" remains unintelligible to us.

You can have a fully consistent theory of modality that retains the law of excluded middle. You can also have one that rejects the law of excluded middle, but retains the law of non-contradiction. Let's call the former kind of modal thinker a BigEndian and the latter a LittleEndian Concerning the example for Aristotle, BigEndian and LItteEndian are totally in agreement that we cannot know or decide which of the statements "There will be a sea battle tomorrow" or "There will not be a sea battle tommorrow" is true the day before the event. The BigEndian will simply insist that this is only an epistemological fact, and does not entail that neither one nor the other is in fact true. Certainly, this requires a particular brand of realism about future events, but then BigEndians (and generally speaking everyone who favours classical logic) will be a realist about most things. The LittleEndian has a (perhaps more sophisticated) view of the interplay between epistemology and metaphysics that ties together in some way what can be known/decided and what exists. There is no simple way to decide whether the BigEndian or LittleEndian is correct. — MetaphysicsNow

This is the ontological difference which I alluded to. The "fully consistent theory of modality that retains the law of excluded middle, also excludes what I call "real possibility". The theory of modality accepts only epistemic possibility, logical possibility. But as mathematics demonstrates these possibilities are infinite, and this give us no means for differentiating between what is physically possible, and what is physically impossible. So we have here a problem because many things which are logically possible are physically impossible. We need a way to deny this designation of "possible" to those things which are physically impossible, because they are really impossible.

From my ontology, the BigEndian 's position is based in a false premise. The BigEndian would allow that things which are physically impossible are really possible, simply because they are logically possible. I argue that there is no truth or falsity to the statement "there will be a sea battle tomorrow", because this is an ontological reality, a physical fact, rather than an epistemological fact.

The difference being that the BigEndian is committed to determinism, I am not. If it's simply a matter of us not being able to know the outcome, what will happen tomorrow, but there is a truth or falsity to it, then it is necessarily predetermined. The LittleEndian, will argue that there is no truth or falsity to this matter because it has not yet been decided, and it could go one way or the other. Of course there is no simple way to decide which is correct, that's why metaphysics is not a simple subject of study, it is extremely complicated. However, as I've demonstrated in a most basic way, the BigEndian's position is based in a false premise, allowing that impossible things are possible.

In all cases, a modal realist is not going to allow the existence of non-real possibilities: all possbilities for a modal realist are equally real, although they might not all be equally likely. — MetaphysicsNow

This is just a matter of how you define "real". I explained what I consider as a real possibility. If a modal realist premises that all logical possibilities are real possibilities, I think that this is a false premise. I think that many logical possibilities are physically impossible. Therefore it is only by changing the definition of "possible", such that it is no longer opposed to "impossible", that one can label something as "possible" which is also impossible, without contradiction. My definition of "real possibility" avoids this contradiction without resorting to such nonsense.

Your points about infinity and possibility are not clear to me - modal realists of any kind can quite happily accept the idea that there are an infinite number of possibilities and that does not render possibilities unintelligible. — MetaphysicsNow

But that's exactly the point, infinite possibility is unconstrained possibility, and this is unintelligible. So if modal realists allow infinite possibilities, then this leaves "possibility" itself as something unintelligible. Possibility is something which is infinite, and an infinite thing is unintelligible.

No, because the margin of error is an average, so it doesn't mean that each time is 99% sure.. And there could be other factors involved which are not being measured.

We can play around with the level of certainty we want in knowledge - 70%, 80%. 90%. 99%.

Uncertainty is inescapable but levels of certainty can be achieved. — TheMadFool

How would you be certain that the level of 70%, 80%, or 90% had been achieved? Or would you be 90% certain that 70% certainty had been achieved, etc.?

and the universe will chug along just fine without perception. — Marchesk

The universe will chug along? What does that mean?

Possibility does not pose a problem for intelligibility if what is possible is constrained by the laws of whatever logic you happen to prefer. — MetaphysicsNow

But possibility isn't thus constrained, this is demonstrated by the fact that mathematics always leads to infinity. That's the problem. You can produce a logical system which deals only with constrained possibilities, that is not a problem, but this logical system may not be operating with an accurate representation of possibility, because possibility may be infinite as mathematicians assume.

Here's the issue. For the sake of argument, let's assume that possibility is real. It appears to be inherently infinite, as demonstrated by mathematical principles. We could create a logic which would constrain possibility, but unless the logic is based in some true premises, these principles of constraint would be purely arbitrary. Therefore these constraints on possibility would not be real constraints on real possibility. So we must seek to represent real constraints on possibility, and this requires that we assume that there are real constraints on possibility, and we seek them for our premises. This means that the possibility which appears to us in mathematics, as infinite, cannot be considered to be real, because we have now assumed that there are real constraints on possibility.

If you want to proceed in this way, to argue against mathematical principles which accept infinite possibility, then you must do so from a principled position. We need to state some acceptable principles which would demonstrate that possibility is not infinite. This requires that we create a real, true description of "possibility", and utilize this to produce our premises. The description, if it is correct, and accurate, would indicate what possibility really is, thus constraining it to the terms of the description. Mathematics has no description of possibility, so possibility can be absolutely anything.

What I propose, as a description of real possibility, is that it is a function of time. Things in the past cannot be changed, but with respect to the future, there is real possibility. From this, we can proceed to produce a relation between future and past, whereby the possibilities of the future are constrained by the actualities of the past, thus providing the foundation for real constraint on possibility. Do you agree with this approach, or would you prefer a different description of possibility?

How? Are you confusing actuality with reality? They are different notions - indeed it is precisely the difference between them that modal realists like Lewis take advantage of. — MetaphysicsNow

No, I distinctly said "real existence of possibility", so I did not mean the "actual existence of possibility", which could quite possibly be interpreted as contradictory. For example, consider there is a chair in the other room, and I say to you that it is possible that the chair is red, and it is possible that the chair is green. These are not real possibilities, they are fictitious possibilities, made up by my mind, because there is a real description of that chair, which would exclude all other possibilities as false, unreal possibilities. There are no real possibilities concerning that chair, just an actuality, because the chair itself is an actuality These unreal possibilities are the type of possibilities which mathematics deals with, and that's why they allow infinity. They allow whatever fictitious, unreal possibilities that the mind can come up with.

An example of a real possibility is when we reference a future event which requires a human decision to bring about that event, like Aristotle's famous example of the possible sea battle tomorrow. As he describes, there cannot be any truth or falsity to that statement that there will be a sea battle tomorrow, because it hasn't been decided yet. Further, when tomorrow passes, and the event occurs, or fails to occur, we cannot look back, and say that at that prior time, one or the other was true. There simply is no truth or falsity to the statement that there will be a sea battle tomorrow. With this as a description of "real possibility", do you see how the law of excluded middle is violated? With respect to a future event, which may or may not occur, and this is the basis for my description of "real possibility", it is neither true nor false that it will occur. The dialetheists, dialectical materialists, might argue that it is both true and false, that the event will occur.

Keep on inventing things I never said. I'll sit back and watch you win arguments that are just against yourself. — apokrisis

OK keep watching then. I'm pretty good at it, maybe you'll learn something.

You didn't state an argument to support your premise:

It all starts with habits of constraint on degrees of freedom. Then it adds the twist that logic - information - is also "real" here. — apokrisis

So I had to provide one for you. Got a better one? My contention is that habits must be formed, therefore it is impossible that it all starts with habits of constraint. Have you a solution to this problem? Maybe logic is really prior to habits of constraint?

I argued that either further more particular constraints decide the matter, or it then becomes an accidental outcome. — apokrisis

So there is no final cause, or intention behind the general feeling of hunger? It is not there for the sake of anything, it is just an accidental outcome? The feeling of hunger is clearly more general, and therefore not a more particular constraint, so this leaves us with "an accidental outcome".

I take it that you are arguing that the feeling of hunger is not essential to the human being, it's just accidental. Is this what you are arguing? This would require that not all human beings experience hunger, it's something that some experience and not others. I suppose that if a human being keeps up with its preprogramed activity of eating, it would never feel hunger. Only those whom for some reason decide not to keep on with this activity, or cannot do it, actually ever feel hungry. So hunger is accidental, the result of a failure to stick with the program, eating. How do you think eating ever came into existence in the first place?

and provided that the law of non-contradiction holds, possibilities are always going to be intelligible. — MetaphysicsNow

No, that's the problem, the exact opposite is the case. So long as we allow that possibilities are real things, there will always be something inherently unintelligible about them. Do you recognize that you cannot comprehend a possibility by referring to the logical categories of what is and what is not? How would you class possibility, neither is nor is not, or both is and is not?

No I do not see that, because it is a contentious position you cannot just help yourself to. — MetaphysicsNow

How is this a contentious issue? Clearly the real existence of possibility violates at least the law of excluded middle, if not the law of non-contradiction and the law of identity itself. Where is the contention?

Perhaps we can do without the law of excluded middle (intuitionist logics for instance) but the law of non-contradiction is a great deal more difficult to do without and provided that the law of non-contradiction holds, possibilities are always going to be intelligible. — MetaphysicsNow

The problem is that the three fundamental laws of logic are all tied together. So if the real existence of possibility causes a problem for these laws, there is also potentially a number of different ways to deal with this problem. One individual might say that possibility is accounted for by allowing an exception to the law of excluded middle. What is possible neither is nor it is not. However, another person might argue that possibility is accounted for by allowing an exception to the law of non-contradiction. What is possible both is and is not. Are you familiar with dialetheism, and dialectical materialism, which is derived from Hegel's dialectics of being? Whether one takes the position that we ought to allow exceptions to the law of excluded middle, or we ought to allow exceptions to the law of non-contradiction, to deal with the reality of possibility, makes a huge difference metaphysically. There is an even more metaphysically radical position which holds that things within this realm of possibility cannot even be identified (they cannot enter into the realm of logic because they cannot pass the law of identity), so we ought not, or "cannot" even talk about them.

Your hypothesis is that (i) there is a thing called the will, (ii) the will is not subject to causal laws (iii) the will causes human action. This is a substantive hypothesis, it is not an apriori truth by any way shape or form. — MetaphysicsNow

It's pretty simple. What I claim is that if your "causal laws" exclude the will as a cause of human action, then your causal laws are incorrect. So if your process of analysis which seeks to understand human activity according to your causal laws proves to be deficient, then this is evidence that my claim is correct. Therefore a procedure which changes the applied causal laws and approaches with different causal laws may be of assistance.
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The question, then, is in any given case what leads up to the will causing a given human action or prevention of human action (nb, there is also the question how the causal mechanism between will and action works, but that is a different question). — MetaphysicsNow

Why is this a relevant question? If the will is a start of physical action, and not a continuity of physical action, then what point is there in considering the physical conditions prior to the actions of the will? Further, we have already dwelled on the psychological, and determined that there is no necessary connection between the intelligible decision, and the act of the will. We ought to be stymied right here.

However, I propose we look at the realm of the unintelligible, which is related to the intelligible, as opposed to it, but still within the same category, as hot and cold are within the same category. So we are in the category of the psychological rather than the physical, but the "decisions", the cause of action are not conscious decisions at all, and therefore not intelligible. The unintelligible is characterized by an inapplicability of the laws of logic. So for example, "possibility" refers to something in which the fundamental law of excluded middle does not apply, and is therefore unintelligible. Do you see that? So as much as we try to make possibility intelligible through probabilities and modal logic, there is something about it which remains inherently unintelligible.

Now let's approach your question. Let's say that there is a relationship between will, and possibility, and this is what "leads up to the will causing a given human action". This is why we cannot go to "physical conditions", because a possibility is non-physical, and we cannot refer to conscious decisions of the intellect which utilize "causal laws" because these are laws of necessity, based in physical observations, so they do not apply.

You also seem to be implying that there is no rational account for that either. That seems to rule out any kind of research program into how the will is supposed to get in on the act. — MetaphysicsNow

Does what I have said above, qualify as a rational account? I have not ruled out "research", but directed the research in a particular way, and that is toward the nature of "possibility". Do you think that this is the right direction? The conscious intellect wants to understand the world in terms of logical necessity, and produces concepts like cause and effect. It wants to know with certainty. However, the world keeps giving the human being possibilities, and forcing the will to act, in a way which the intellect cannot keep up with. Actions are required very rapidly as time passes, and the intellect is not capable of keeping up to, and making a decision for every act which is required. So the will may act in a way which is unintelligible to us. This is made necessary by the existence of so many millions or billions of miniscule possibilities which the conscious mind cannot even fathom.

(nb, there is also the question how the causal mechanism between will and action works, but that is a different question). — MetaphysicsNow

This is an interesting question, because it approaches the question of what type of thing the will is, and this goes to the heart of the mystery of life, what is the soul. But as you say, it is a different question, and I don't think we even have a way to approach it without an understanding possibility. In Aristotle's biology the forms of life are described according to their capacities, and the capacities are described as potencies which are based in possibilities, potential. This is a different perspective from modern biology which tends to proceed through physical descriptions. I think there is a need to unite these two perspectives, i.e., such and such physical description corresponds with such and such capacity, which corresponds with such and such possibilities.