Why does one state "it is not profitable for us at present to do moral philosophy", and then proceed to do moral philosophy? Do you apprehend the pretense? In extreme cases like this, it's called hypocrisy. Do you think that psychology has a better system for treating this illness, "pretense", than moral philosophy does? Why pretend that psychology can produce authenticity in a human being, when we all know that authenticity is the product of good moral training. Why pretend that psychology is required for a philosophy of morality?

Thought is incredibly calorie intensive, we have a huge network of functions designed to select and imitate others, it's just massively more efficient than trying to work it out from scratch each time. — Isaac

Would you classify imitating others as a form of pretending?

The interesting question, for me, is how people select who to imitate - but that's a completely different topic. Moral virtues and duties are usually adopted by imitation. Consequentialist moral decisions are obviously an exception, by their very nature, but the goals against which potential outcomes are measured are still virtues or duties determined by cultural inheritance. — Isaac

Aren't we taught that good moral standards involve thinking things out for ourselves, and not to simply imitate others?

Nonsense. Take the Pythagorean Theorem: a2+b2=c2a2+b2=c2

The original thought occurred millennia ago, and it has been transmitted through the intervening years both by a variety of symbols and word of mouth. It remains essentially the same in Euclidean geometry, which by and large is the world in which we live, even though there are other forms of geometry. — jgill

Symbols, and word of mouth do not transmit thoughts from one person to another. It's you who is speaking nonsense. When I write this symbol "A", do you think that there is a thought inside there, which is coming from my mind to go into your mind?

Are you familiar with the law of identity? When I read the symbols you wrote, I do not have the same thoughts as you had when you wrote those symbols. When two things are similar, like my thoughts and your thoughts, they are of the same type, they are not the same thing.

The law of the excluded middle doesn't apply to anything really, love be ing a great example (again Aristotle is wrong). — Gregory

Actually Aristotle is the one who first explained the failings of the LEM. Sophists at the time could produce absurd conclusions by adhering to the laws of logic. He found that either the law of non-contradiction, or the law of excluded middle had to be violated to adequately describe the real world of change, becoming. He insisted that the law of non-contradiction ought to be upheld, and described the types of situations which were to be considered as exceptions to the law of excluded middle. Notice in the Nichomachean Ethics he describes the various virtues, each as the mean between two extremes, the extremes being a vice.

The other possibility, of allowing violation of the law of non-contradiction, was dismissed because Aristotle felt it would lead to incoherency and unintelligibility. It's better to say "x is neither A nor B", than it is to say "x is both A and B". He seemed to appeal to intuition on this principle, but intuition he classified as the highest form of knowledge. If we say "neither A nor B", then we must find different words, a different category, to speak of this property of x. But if we say "both A and B", then we find ourselves in a logical conundrum which prevents us from saying anything intelligible about that property.

But those who read and interpret those symbols revive those thoughts and give them renewed existence. — jgill

Not quite, the readers produce new thoughts, within a new context. So if thoughts are existent things, the old thoughts of the author are different things from the new thoughts of the reader. There is no continuity of existence between a thought at one time and aa thought at a later time, so the two are not the same thing. The moon landing, along with all the thoughts involved, is a distant memory. It may be recreated with new thoughts, but the new thoughts are not the same thoughts as the old thoughts, as is evident from conspiracy theories. The thoughts which supported the moon landing are not existing.

Thus, like monks reading and reciting scripture, were an order to so illuminate and pronounce mathematical works with unflagging resolve those thoughts would exist forever.

Hemingway's thoughts exist unendingly, for someone, somewhere is reading them now. — jgill

This is a myth which science has dispelled. Symbols, which represent thoughts, might exist indefinitely, but not the thoughts themselves. And, as time passes, the context within which the symbols exist, changes. Since the meaning of any symbols is context dependent, the interpretation of the symbols changes with the passing of time.

I really don't understand your argument. You seem to be declaring what we do and then complaining that we're not doing it. I'm saying that Anscombe is saying that there are positions she will not engage with. If you want to engage with them, that's up to you. As a vegetarian, I am simply not interested in the nutritional value of meat. — unenlightened

What's the point then? Isn't this just like saying "let's discuss morality, but I have no respect for your opinion, I just want to discuss my opinion"? Ethics is not a matter of enforcing your morality onto others. There is a necessary requirement of demonstrating to others the superiority of your principles, because people choose freely. If you deny free will, and insist that people must do as you say, you won't get far. That's why platonic dialectics is the classic example of how to discuss morality. Plato at least pretends to take into account the opinions of others.

Pretense is an important issue here. Notice in my post I mentioned the poser. You cannot simply pose as a moral authority, and expect others to submit to your will. You must act the part, and pretend that you actually are a moral authority. It is truly an act, a "pretense", for the reason that god must be atheist pointed out:

This is true. Very true. The saddest part is, that ethical principles are what each person who refers to them calls them. They are arbitrary, while appearing to have a certain theme (but that is only appearance.)

Ethical principles either don't exist, or we haven't discovered them yet. Therefore the referring to ethical principles is a snow job, a wool over other's eyes, it is a pungent force of argument, without any essence or logical backing. — god must be atheist

The question might be asked, what is it, which persuades another to accept moral principles. If it's not the argument (rhetoric) which convinces, nor is there an inherent appeal within the principles (subject matter) being argued, then what is it? Am I missing something? Is it really just rhetoric, "a pungent force of argument"? If so, wouldn't we end up with truly arbitrary principles? I suggest you consider that there is an inherent appeal within the principles.

nteresting observation. My take is that the LEM applies to individuals - the thing - as you say. But at the same time, if the LEM is either-or, the fellow who gave us that, Aristotle, also gave us neither-nor.

It follows, then, that if it's true of some people that they're either male or female, and modern insights are also correct, then it's also true that there are people who are neither male nor female, in the sense just given. — tim wood

The LEM only applies when the two terms are properly opposed, or form a dichotomy. It's quite clear that "male" is not a proper opposite of "female", so the LEM does not actually apply, though many of us might like to claim it does.

The point I was trying to make is that I think we tend to see things in dichotomous terms (we have even evolved to see things in this way), because it facilitates judgement. If male and female were proper opposites, dichotomous attributes we could look at a person and say that the person is either male or female, apply LEM and say there is no other possibility. So when we see things in this way, it's very easy for us. It's easy because we don't have to ask, if the person is neither male nor female, then what is the person. Seeing them as dichotomous attributes, logic disallows anything else. Therefore it is really just this way of seeing things, (the easy way, or "lazy man's way") as either black or white, which blinds us to all the colour in the world.

Edit: artist statements are an academic notion. — Brett

It's simple, it picks out an obvious theme, and it usually tries to relate the artwork to the child in some manner. It's not altogether different from - as the OP put it - a kindergarten show and tell. — StreetlightX

I think this is right, the statements are meant to educate. There is a wide variety of reasons for the statements, whether it's to introduce children to what the artist is doing, or to explain to a wider audience, why the artist is doing it. The artist might even be trying to reach a wider audience through the medium of education.


If you think it's cheesy, then ignore the statements. Or better yet ignore the art which includes statements altogether. Isn't that what we normally do with art that we dislike?

Strictly speaking, we can only judge hypotheticals. We dont know future events and so there's nothing to judge. 'Looking backward, living forward'. We enter the future ass first. — frank

I agree that we enter the future ass first, because we are looking at things which we have seen and remembered, and that is past. ,However, a past event can be described, a future event cannot be described, that is the point. So we might judge the future on hypotheticals, but the past we judge on memories and descriptions. Neither one is more or less of a "judgement" than the other.

Well indeed. So they remain unsupported. — unenlightened

No they do not remain unsupported, we support them all the time, by referring to ethical principles. That's what I told Banno, and Banno suggested that we might just declare that courage is a virtue without reference to any ethics for support. But that's not reality, in reality we support those judgements with such references.

So MU is an anti-Peircean. That actually helps me understand Peirce. Sounds like I'm a Peircean and never knew it. — fishfry

That's not a logical conclusion.

Furthermore, I actually agree with a lot that Peirce has said. in particular his very coherent method of laying out particular epistemological problems. What I disagree with is the metaphysics he proposes to resolve those problems. He provides no real solution, only the illusion of a solution. Aletheist resorts to contradiction in an effort to support Peirce's illusory solutions, because Peirce draws on dialectical materialism, or dialetheist principles which decline ruling out contradiction. Aletheist refuses to acknowledge this.

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This simply your "take" on language. It has nothing to do with the definitions, purposes, and functionality of the idea as used by its users and represented by them in this phrase as term of art. — tim wood

It seems you didn't read my earlier posts

You would deem the mathematics "supporting" the moon landing and Mars' vehicles non-existent. You would also label the very thoughts you post here non-existent. — jgill

Right, the symbols on the paper, and on this page have existence. The thoughts which were used to produce those symbols are events which are in the past, and no longer have existence.

Morality is ultimately about judgement. It's about living with the consequences of our past actions. We head into the future with the innocent but potentially destructive desire to live. — frank

Morality is just as much about judging possible future actions as it is about judging actual past actions.

Outside of sociopathy, all humans seek to please some authority (but a better word than 'please' is needed here.) & not just any authority - an authority that is legitimate. This fuzzy idea of legitimacy (which begins in childhood) brings with it all kind of ideas of what makes someone legitimate. — csalisbury

Authority puts an end to the infinite regress of "why?", which I mentioned earlier. The child continually asks "why?", and ultimately the answers are like this, "because the parents say so", "because the teachers say so", "because the Bible says so", "because the laws say so" etc..

There may be a need to inquire as to why we are often observed to submit to authority, "seek to please", but there is an even greater need to inquire as to why we are often observed to confront authority with doubt and skepticism. This confrontational attitude is the reason why there's no longer obligation to God. And the psychological aspect is not rooted in that desire to please the other. Instead, it might be rooted in a philosophical , or epistemological attitude. The submission to authority is a respect for the knowledge of the other, and the desire to know what the other knows. So even the "seek to please" attitude can be represented as part of the desire to know. If respect for the knowledge of the authority figure ceases, then there is no respect for the posed authority, consequently not authority.

What I believe is the key point to this psychological aspect, is that the breakdown in respect is a breakdown in the respect for the posed authority's knowledge, not a breakdown in respect for the person. This is how the posed authority looses authority and is no longer an authority but a poser. However, the poser may be respected as a person, without being respected as an authority. So we have a necessary distinction to be made between one's attitude toward other human beings, and one's attitude toward the knowledge of other human beings. This separation is evident when people of high moral standard have a disrespect for the law. The gap is widened, and the problem exacerbated when those who are supporting this system of knowledge insist that the knowledge itself is the authority rather than the person who poses. This only provides the people with disrespect for the law more principles of separation, to support the position that one may have high moral standards (respect for other human beings), yet great disrespect for the law.

Understanding this principle reveals the disarray and incapacity of the current socio-economical-epistemological system in relation to morality. The individual who has contempt for that system might still be a loving, caring, moral individual, because disrespect for any given system is not the same thing as disrespect for any human being. I can have great respect for you as a human being, while still not liking your way of doing things. But other individuals who adhere to the principles of the system, as if the system is the authority, cannot apprehend the person who has disrespect for the system, as anything other than immoral. Therefore the gap widens.as the supporters of the system increase efforts to present the system as a "person" to be respected (i.e. as an authority figure).

If I have a corrupt mind, I will have corrupt ethics and make corrupt calculations. This much must surely be accounted for, as one has ample evidence for its occurrence in the world. "I am an exceptionally fine fellow, and therefore anything that helps me is a good thing and anything that hinders me is a bad thing." I don't need to name names do I? — unenlightened

This is exactly the separation I refer to. The exemplified person has a corrupt mind, corrupt ethics, and makes corrupt calculations, in relation to the principles established by the system. Such allegations of "corrupt" can only be supported in relation to the principles of some system. Now figure into your calculations the fact that many people might have a similar general disrespect for that same system, which validates the designation 'corrupt", for a vast variety of reasons. The exemplified person, demonstrates nothing but flagrant disregard for this system. So the person is propped up by others as a symbol of general disrespect for the system, then sacrificed to the system, in the attempt to damage it. The real personality of that person is completely irrelevant because the person has now been thrown into the system, become a part of it as an opposition to it, and is therefore not considered as a person. This person (who is no longer a person) is a symbol of the separation between the people and the system. It's an inversion of the "scapegoat", which may have been perfected by Jesus and his disciples. There is a goodness associated with opposition to evil within a system. The people gather together all this goodness and sanctify someone (Jesus, or your exemplified person) with this goodness, and sacrifice the person to the system.

Once you make the backbone of morality the idea that you're culpable for any consequence of your actions that could be foreseen, you set up, perhaps despite yourself, a moral situation where people develop a system of calculating consequences in advance. What may have started as possibly reasonable (taking into account consequences) metastasizes into something like insurance companies predicting risk. It turns morality into something totally different, something approaching plausible deniability (to your conscience, but the same principle: youre your own pr guy to yourself) — csalisbury

I don't see how this is a problem. Human actions, by their very nature are means, they are never ends in themselves. All we have, as evidence, to judge a person's morality, is the person's actions. They keep their intentions to themselves, and if they claim to reveal them, the revelations may not be truthful. If a person is responsible for the moral character of one's own actions, regardless of one's intentions (the end cannot be used to justify the means because the end cannot be proven), then it is of the utmost moral importance for the person to calculate the possible consequences of one's action prior to acting.

This does not turn morality into "something totally different", it simply provides a realistic representation of what morality is, instead of hiding it behind some idealistic veil. We, as adult human beings, are responsible for our actions regardless of what might be our intentions. If our actions bring about unintended results, we cannot justify those actions by simply claiming it's not what I intended, and I forgot to consider all the possible consequences ("sorry mom, it was an accident").

Banno suggests we simply deem "courage" as a virtue, and get on with it, without defining what courage is. But if we allow rashness to enter into the nature of courage, such that people are encouraged to act in a reckless manner with complete disregard for possible collateral damage, then how can we say that this type of "courage" is a virtue?

He won't weigh the intrinsic badness of an action, but focus on the consequences. — csalisbury

By the way csalisbury, I think you must have misrepresented this idea, because the way you have presented it is oxymoronic. There cannot be "intrinsic badness" of any particular action because the goodness or badness of an action is a judgement based on a description of the action. A description of an action is itself a consequence of the action. So the suggestion that we might separate the "intrinsic badness" of an action, from the consequences of that action, is in fact an oxymoron.

One might describe the act as good, or one might describe the act as bad, either way the description of the act is consequent to the act. We cannot describe the act before it occurs, for the very reasons given. Prior to its occurrence it is apprehended in terms of possibilities and we cannot foresee them all. We must respect the uniqueness of every particular act, such that a prescribed general type of act cannot serve as a description of the particular act, in order to judge an act prior to its occurrence. A general type is not the description of any particular. Therefore, "this act will be x type of act" cannot serve as a description of the act. And judgement of the act requires a description of it. It is only 'type' which allows "intrinsic badness", when badness is a property believed to be essential to that type. But the particular act cannot be judged as a specific type of act without a description of the act, which can only be provided after the occurrence of the act.

Assuming that by "foundations" you mean the acceptable accumulated knowledge and practices up to any particular moment of mathematical history. Weierstrass and Cauchy laid the critical foundations for my interests, above and beyond what came before. — jgill

I think "foundation" refers to principles which "the acceptable accumulated knowledge and practises" are based in, built upon. So Weiersfass and Cauchy produced some new principles and also built upon some existing principles, and this would be the foundation. Notice that no conceptual structure is completely new, in an absolute sense, it's always built with some already existing principles. Because of this, there is an appearance of an infinite regress in the creation of such principles, y, as a principle, was created using x, but x was created using w, and so on.

The infinite regress of dependency was avoided by the Pythagoreans by assuming that the principles are eternal, have always existed (platonic realism), and are simply discovered rather than created. But since these ideas or Forms are necessarily dependent on a mind for their existence, this conceptual structure is closely tied to the idea of an eternal soul. So Plato describes the discovery of the principles as remembering what is already known (Platonic theory of recollection, "Meno").

From the principles of modern science, we reject the eternal soul, along with the eternal Forms, and Plato's theory of recollection. This puts us back toward an ontology of mathematical principles which describes them as actively evolving. The problem though, as described above, is the appearance of infinite regress, because there must always be something which supports the changing structure, the underlying kernel (what I call the foundation). So when a new type of structure is created, such as in your example of what interests you, it is not a completely new creation, it is still supported by underlying principles which have already been tested by practise.

If we follow this type of evolutionary theory, rather than platonic realism, we might consider that there was a first mathematical idea created. We see that other animals don't use mathematics, and human beings evolved from other animals, so there must have been a time when mathematical ideas were first thought up. It might be a first group of ideas which we could call the first mathematical ideas. So at some time, mathematical ideas were thought up for the first time. Would you agree that these first mathematical principles would also have some underlying principles, being not mathematical in nature, but already tested by practise, and these non-mathematical principles would support the first mathematical ideas? We could say that these principles are the foundation for mathematics.

Why are the "in-betweens" so hard to find? The vast majority of human beings are either male or female, and there's very few in-between. There's a similar situation with species. We have one species and other species, and evolution theory tells us that one evolved from the other. Shouldn't there be a vast array of in-betweens? The discreteness appears to be very real.

Consider the fundamental laws of logic, either the thing has the specified property or it does not, there is a law of excluded middle which dictates that there is no other possibility. So we make judgements based on the assumption that there is no in-between either the thing has, or has not the specified property. Wouldn't allowing the real existence of in-betweens impair our capacity to judge? So we have evolved in such a way so as to minimize the existence of in-betweens, because the existence of in-betweens impairs our ability to judge.

It doesn't work though, because it doesn't explain how I'm here when no one's looking. So my real, true existence, is not supported by that fiction. That it is, is a delusion.

Nothing really exists because there are no entities of sufficient purity that they are not compositions of things, many of which fail to exist themselves. — jgill

Right, how could a thing which is composed of parts which do not exist, itself exist? This doesn't mean nothing exists, only those things composed of fictional parts do not exist.

quote="jgill;380008"]Seek help, my friend. You limb is but a twig.[/quote]

Size is irrelevant. What matters is that it provides support. Non-existent things provide no support.

History demonstrates otherwise, as fishfry has pointed out. — aletheist

Actually history has not demonstrated that. You and Fishfry have simply made the assertion that history has demonstrated this. I demonstrated how that assertion is illogical..

The axioms of pure mathematics are neither true nor false, and claiming otherwise is a category mistake. — aletheist

Another assertion without justification.

One assertion after the other, without explanation or justification, together with an ignorance of logic; you just reminded me of how difficult it is to hold a discussion with you.

Typically what we end up selecting is either the least expensive solution or the one that in our judgment properly balances cost with risk. — aletheist

"Risk" here means the possibility of a law suit against the engineering firm. Real risk contains unknown factors which cannot be assessed. What we really end up with "typically", is an extremely expensive building designed to protect the engineer from lawsuits. The exorbitant expense is not balanced by the building's owner being protected from risk, because the real risk, the unknown, has not been assessed.

In other words, the "best" foundation can only be determined relative to a specific purpose. Why would philosophy be any different? — aletheist

As I said already, the purpose of philosophy is truth. I don't try to disguise the fact that this is a "specific purpose". But if we justify the use of false principles on the basis that false principles may still be useful for some other purpose, this particular usefulness would be inconsistent with the specific purpose of philosophy, being truth. Therefore they would be rejected by good philosophers..

A philosophy of mathematics identifies the foundations that have already been established by the practice of mathematics. Most people who use mathematics, including most professional mathematicians, have little or no knowledge of its foundations--and little or no need to have such knowledge. Likewise, most people in general have little or no knowledge of philosophy in general--and little or no need to have such knowledge. — aletheist

That people have little knowledge of the foundations of mathematics, is not an argument supportive of fishfry's claim that mathematics precedes its foundations. As you explain, the design is prior to the structure. If people move into houses, having no knowledge of the design or blueprints, or even that there were blueprints, this does not mean that the house is prior to the design.

The practise of mathematics itself, requires that a foundation already be laid in order for that practise to occur. These are the theoretical principles employed in the practise. So it is a mistake to say that the practise produces the foundation. In reality, the theory which provides the principles for practise, is the foundation.

In other words, philosophy is useful in relation to the goal or end of knowing for the sake of knowing. Well, so is pure mathematics in relation to the goal or end of knowing what follows necessarily from certain axioms, purely for the sake of knowing it. — aletheist

Do you see what happens when you qualify "knowing" with "what follows necessarily from certain axioms"? The goal of philosophy is an unqualified sense of knowing, and truth is implied by "knowing". If the axioms involved are false, then what follows from them cannot be sound conclusions. Therefore we cannot even call this a form of "knowing". This problem becomes very evident in the use of counterfactuals in logic. Even when we recognize the counterfactual as false, it is doubtful whether the use of counterfactuals provides us with any real knowledge.

We stipulate what is the character, or nature, of a bad act. It is harmful to another, or it infringes on another's rights, something like that. A virtuous act is not simply the opposite of a bad act.

Rubbish. — Banno

Well, I thought I'd add my two cents worth to your thread. As expected, you've deemed it not worth two cents. You owe me nothing though, because I offered it freely, and gifted it, as a virtue act. Virtue does not impose debt. I'm sure you are acquainted with the Christian use of the word "love". There is nothing owed for an act of love.

However, the fact that you think we can simply "step over" the infinite regress involved in justifying particular virtues, by suggesting that virtues do not need to be justified, is an indication of the pathetic state of modern moral philosophy.

Why not just say that courage is worthy of cultivation - and if you disagree, that's not a fact about courage, but a fact about you. — Banno

I hope you can see, that in order for the saying "courage is worthy of cultivation", to be accepted, we need a description of what constitutes "courage". And this description must cast the described thing, which is to be called "courage", in a positive light. That way it is acceptable as something which is worthy as cultivation. This is why Aristotle produced 'the doctrine of the mean', as a way of showing how to give the named virtue a positive description, making it something worthy of cultivation. Notice that not only is the courageous person not cowardly, but is also not rash. Otherwise "courage" might be conceived as rashness and therefore not something worthy of cultivation. So his technique, which may or may not be adequate (notice that "mean" has now developed bad, vicious, connotations) was to place the virtue between two extremes each being a vise.

Well, the point of virtue ethics was to avoid rules, so... — Banno

Can't you see that this is futile? Just like we need rules of definition, to determine what constitutes a punishable act like "murder", or "theft", we also need rules of definition as to what constitutes a virtuous act. The real difference is that it is a far better enterprise, to determine rules concerning what is "good", and encourage people to act accordingly, then to determine rules concerning what is bad, and punish people accordingly. The former gives us guidance, encouraging us to stay away from bad behaviour while the latter gives us punishment for bad behaviour without any guidance. The problem, is that it is easier to determine the essence of a bad act than the essence of a good act.

Knowledge of the history of math.

But it's the same in any discipline. There's science, and then there's the philosophy of science. One can and does do science without regard for its philosophy. That's true in every field. X precedes the philosophy of X. — fishfry

The claim was that math precedes foundations. But math consists of concepts, and concepts require foundations, so it is impossible that math is prior to foundations. It should be obvious to you, a structure is built on foundations, not vise versa. The fact that the philosophy of math follows math is irrelevant, because it is not the philosophy of math which produces the foundations. The philosophy of math might study the foundations, but it does not produce the foundations.

The task of the philosopher is to explain how it comes to be that math and science are abstract yet useful. — fishfry

You don't seem to grasp the problem. "Usefulness" is judged in relation to a goal or end, and that goal or end may be contrary to truth. When principles are used in a way which is contrary to revealing the truth (i.e. hiding the truth), this is deception. The philosopher seeks truth, so the task of the philosopher is to prevent such deception. Principles of math, axioms, might be useful for obtaining truth, or they might be useful for deception, if they are produced without any goals whatsoever. Since the philosopher seeks truth, the mathematical principles which are not useful for revealing truth, and are only useful for hiding the truth,(i.e. deception), ought to be rejected.

You seem to be under the illusion that if mathematical principles are useful they ought to be accepted by the philosopher, simply because they are useful. But you misunderstand philosophy, which seeks to distinguish truth from mere usefulness. The philosopher seeks to know, without regard for the usefulness of that knowledge, knowing for the sake of knowing.

He rejects the idea of taking math on its own terms; insists that it must refer to something outside of itself. Nobody believes that, not about pure math. Why does Metaphysician Undercover believe that? What is the basis for his ideas? — fishfry

Look, just above, you refer to the "usefulness" of math. "Usefulness" of something is determined by relating that thing to something outside itself. That's what usefulness is, it's putting the thing, as a tool, toward a further end, something outside itself. So, if philosophy to you, is explaining how something like mathematical abstractions might be "useful", you need to apprehend how mathematical abstractions relate to things outside of mathematics. This is what it means to be useful. If you assert that no one believes mathematics ought to relate to anything outside of mathematics, then all you are doing is denying that mathematics ought to be useful. Then your philosophical dilemma, of how it is that math is useful, is self-imposed by your faulty belief, that math does not relate to anything outside itself. By this belief mathematical abstractions cannot be useful because usefulness requires relations to other things..

However, true philosophers take for granted that math is useful, because the evidence is everywhere. Therefore we take for granted that mathematical abstractions relate to things outside themselves. Then we can proceed to analyze these relations, instead of denying that there is such relations and wondering how it is that math can be useful when it doesn't relate to anything outside itself.

On the other hand, the ideas/concepts represented under the name "empty set" certainly do exist. They're functional and purposeful. So also is my imaginary hippopotamus friend: he exists too, but also not at the store. — tim wood

The problem is, as I demonstrated, the concept of "empty set" is self-contradicting. Sure, a contradictory concept is functional and purposeful, but that purpose is nothing other than deception.

What do you say of a chair? "Chair" is certainly an abstract noun. Actually, all nouns expect for proper names are abstract. Where do you go with that? — tim wood

I told you already, abstractions do not exist as objects. That is the oversimplification of platonic realism which Plato himself demonstrated as false. Abstraction is an activity of individual human minds, and the proposition that there is "an abstraction" which is created by numerous human minds, is dependent on both a category mistake and a composition fallacy.

First, abstraction is a process of the human mind, there is no evidence that it produces an object, called "an abstraction". There is recollection of the image, representation with symbols, and application, but no evidence of an abstracted object. The proposition, that abstraction does produce an object, "an abstraction" is a falsity intended to simplify reasoning. It is a convenient falsity, accepted because it produces efficiency, but false because it is based in the category error that mental activity, "abstraction", can be represented as an object, an abstraction.

And, even if we are fooled by the category mistake, and accept that mental activity produces an object, "an abstraction", we have to get past the composition fallacy involved with the proposition that there is "an abstraction" common to numerous human minds.

So, the idea of "an abstraction" is supported by a double falsity. Some human beings might argue that two wrongs make a right, because a double negation is a positive, but that assumption as well, is based in faulty principles.

I would say that the laws of Mathematics and Logic are normative principles pertaining to conduct regulation so as to make the world easier to describe and manipulate.

These normative principles cannot be given a logical justification on pain of circularity, rather their justification stands or falls with their general overall usefulness. — sime

At least someone here has a reasonable perspective. Still, there is a problem basing justification in "overall usefulness", because deception is a valid intention. So unless we allow that "useful for the purpose of deception" is valid justification, we need further principles to judge "overall usefulness". I think it is necessary to exclude "useful for the purpose of deception" as a valid justification.

Think of mathematicians sitting around a table and creating a game, discussing the pieces that are played, the environment in which they are played, and the rules that are agreed upon. Once done, would you then say, "The game does not exist."? You fail to recognize that math is a social endeavor, frequently deriving from observations of the physical world, but just as frequently not. — jgill

Saying "the game exists" has the same problem as saying "the rules exist", or saying "the concepts exist". It is an over-simplification made to facilitate communication. Each of these terms, "game", "rules", "concepts", refers to a complexity of physical objects, symbols, and mental interpretations of the symbols. To make communication smooth and swift we refer to those complexities with simple words. The problem is, that common language use which is an habitual activity, clouds our minds as to what is really behind those terms. Because we use the language as if there is an existent thing referred to by "game", "rule", or "concept", we fall under the illusion that there is such existent things.

But a careful, clear, and rigorous analysis of what is actually referred to by these words reveals that there is no such existent things. Each of these words is used to refer to a massive complexity of social interactions which we do not properly understand how to represent. So, we have a word, we assume that the word represents an existent object, and we go about our business ignoring the fact that the word does not represent an existent object, it really represents a massive complexity of social interactions which is not understood. In philosophy though, we seek to unravel these mysteries of the misunderstood, and that is why I insist on recognizing the reality that there is no existent objects referred to by these names.

From this perspective, would you say the rules are the axioms? I would say no, there are ill-defined patterns of thought that precede the establishment of the rules, and that might be the subject of study and formalization at a later time - as is the case of the foundations of mathematics. — jgill

If I understand you correctly, you are suggesting that the axioms are like proposals for rules. Each axiom is presented by a mathematician as a proposition to be accepted, or rejected, by the others. The various mathematicians will then take these proposals and try them out, relate them to each other, combine them with each other, etc., in a sort of trial and error fashion, and after some time of doing this some axioms will emerge as "the rules". I accept this representation, it's similar to the way we do science, hypotheses are presented, they are related to each other, tried and tested with experimentation, until certain theories emerge as "the rules".

Here's something we ought to respect though. The proposals don't ever change their inherent nature as "proposals", despite the fact that they get accepted into the fold as "rules". Therefore we ought not change our attitude toward any proposal just because it has obtained the status of "rule". In reality, things change, human beings and their social structures evolve, so the "rules" change accordingly. Therefore we cannot allow that a proposal, long ago accepted into the status of "rule", is beyond reproach.

Physicists thought one day there must be atoms. Then they discovered the atoms are made of protons and electrons and neutrons. Then they discovered the protons are made of quarks. Now they think the quarks are made of strings. Do any of these abstractions exist? Yes they do, in the sense that they are part of an abstract mathematical theory that explains the experiments we're capable of doing at any moment in history. — fishfry

The problem here is that you assume "they are part of an abstract mathematical theory", when there is no such unified "theory". There is a multiplicity of theories, related or connected to each other in various different ways, dependent on an individual's interpretation. So this assumption is misleading. It is the belief that the abstractions are all part of one overriding theory, which gives credence to the claim that they exist. Once we recognize the falsity of this assumption, the assigned unity is lost, and the entire structure which depends on the reality of this unity, falls apart into individual ideas in individual human minds. The assumed reality of these ideas, as existing "abstractions" is dependent on this unity of "an abstract mathematical theory", which is not supported or justified.

Physicist invent new existing things all the time. And de-exist things to. The luminiferous aether was once regarded as existing, till Michelson and Morley couldn't find it and Einstein did away with its necessity. — fishfry

Again, to call these things "existing" is an over-simplification designed to facilitate communication. That we say at one time X exists, and later x does not exist is an indication of this. At one time we are comfortable using these theories, that is the convention, so we talk as if they exist, at another time we are not comfortable using them, they have become unconventional, so we talk as if they do not exist. Using the word "exist" is just a convenient fiction to refer to what is and isn't conventional. But if we take that fiction literally, and assume that because a conventional idea "exists", it is therefore an object, and we try to treat the idea as an object, we have been misled down the path of misunderstanding.

A scientific entity has existence when it's a necessary ingredient of a successful physical theory. — fishfry

Again, you are over-simplifying, referring to a "physical theory" as a unified object. Every theory is interpreted in numerous different ways, by numerous different people, and one interpretation may be demonstrated as unacceptable while another one is acceptable, so there emerges a conventional interpretation.

I gather you call "real" only what is "really out there." But if the 20th century taught us anything, it's that the existence of such a thing as "real things out there" is an assumption and not a fact. I believe if I'm not mistaken this is called scientific realism. It's only an idea. We could kick it around. But you have no logical basis for claiming it's true and everybody else is wrong. The days of Euclidean geometry and Newtonian physics are gone. Now we know the world consists of probability waves that are everywhere at once till we measure them. What can that mean? We don't know. But you claiming that you personally know what things are real, is a delusion on your part. Since you called me delusional the other day, which I can live without. — fishfry

Sorry, there was no ill intent with the word delusional, and it wasn't meant to single you out. I think we are all delusional, it's a function of where our institutions and conventions have misled us. You might think that science has guided us to the ontology of model-dependent realism, meaning that there are no "real things out there", but this necessitates also that there are no "real things in there". So this form of "realism" is not a realism at all because it cannot validate anything as real. That's why we're deluded, we base reality on usefulness and eloquence, having dismissed truth as unreal. But without truth, eloquence is useful for, and justified through, deception.

t's apparent from discussion elsewhere that infinity holds a terror for you that I, and I think most others, do not share. — Banno

It's not a terror at all, it's a respect for the reality of it. Infinite regress is an unintelligibility which is repugnant to a rational mind. A healthy philosophical mind, with the desire to know and understand, will not accept the proposition that some things are unintelligible, because that proposition is contrary to the philosophical desire to know. A mind which accepts that a thing be described in terms of unintelligibility is not a healthy mind. And an unhealthy mind puts a scourge on virtue.

Arguably Aristotle sort to promote, say, courage because it presented a path to eudaimonia; but I don't see why we could not simply accept courage as worthy in itself. — Banno

It is unreasonable to simply accept a proposition as true, without a reason for accepting it. You might call this the justification. The reason why this proposition is true is that if we accept as true, any such propositions without any justification, we will be deceived and taken advantage of by those with an ulterior motive.

One can step over the pit of regress. — Banno

What you describe is not stepping over the pit of regress, but actually turning away from it, as if in fear of it.

Isn't it possible to have an ethical outlook that is not law-bound, and yet still hasa philosophical infrastructure?

Isn't that what virtue ethics is? — Banno

The problem with virtue ethics is the appearance of infinite regress. Plato introduced "the good", which Aristotle described as "that for the sake of which" an action is carried out, what he called the "end", and we call the "purpose" of an act. Aristotle set out to put an end to the infinite regress. Notice the use of the word "end". The problem is that whenever we assign a purpose or "end" to an act, that purpose is justified by a further purpose, and so on, creating the possibility of infinite regress. So Aristotle posited happiness as the end which justifies all ends. Ultimately, he suggested all things are done for the sake of one's happiness. But "happiness" is just an arbitrary designation based in a principle of self-sufficiency, it's not properly supported.

What emerges from Aristotle, and is followed in Christian ethics is a distinction between the real good, and the apparent good. All goods (anything for the sake of which an action is carried out), must be justified as real goods rather than merely apparent goods. So to take the example of what a person "owes", the purveyor of goods is only owed if the goods supplied are true, not spoiled, not something other than what was requested, etc., as there are many reasons why one might reject the burden of debt. The burden of debt is dependent on the reality of the goods. The reality of the goods is justified by reference to further principles and the infinite regress rears its ugly head. In Christianity there is an assumed end to the infinite regress, as God provides the real good, and the means for reconciling the apparent good with the real good. You might say that God objectifies the good, but in reality the Euthyphro conundrum kicks in, and the real good is enveloped in a vicious circle of thought. This is expressed in Aristotle's ethics and metaphysics. The highest virtue is described as a thinking, thinking on thinking. This type of thinking (contemplation of the true good) suspends decision making, incapacitating one from acting. This portrays virtue ethics as turning back on itself. By recognizing the irrational nature of the infinite regress, and upholding the effort to end the infinite regress, the most virtuous act becomes the act which suspends action.

nd what is completely absurd is an otherwise educated individual who cannot grasp that there are terms of art, and what they mean as terms of art is just what the people who use them as such say they mean, period. — tim wood

Trying to change the subject to distract from the fact that you're wrong? If so, you're unsuccessful because you're still wrong. The critics determine the value and meaning of the piece of art, not the artist.

For example, I have a chair. By your standards, that's incoherent because "chair" is an abstraction.... — tim wood

It seems like you misunderstand "instantiation". From Wikipedia: "The instantiation principle, the idea that in order for a property to exist, it must be had by some object or substance; the instance being a specific object rather than the idea of it".

"I have a chair" is not incoherent, but we need to respect the fact that it may be false. You might not really have a chair when you say this, and then you would be deceiving us. What fishfry has finally started to realize above, this principle: "if mathematicians say it exists then it exists", is a faulty principle.

o, sounds like you do not agree w/ Zelebg that a robot operating 100% deterministic on its program is acting out 'free will' because it actions are necessitated by the thing it is responding to. is that right? — Sir Philo Sophia

Right, I'm not even in the same ballpark as Zelebg. You and I might have some things in common

So, would you say that human type/level of 'free will' is pretty much equal to the 'free will' of, say, a bee? Why so or why not? — Sir Philo Sophia

Yes, I would think so. Free will only requires an agent to make a decision on the possibilities which are apparent. I would think that a bee does this. I think that even plants might make decisions, but their decisions are made much slower, depending on weather, nutrients in the ground, etc., and we don't really know very much about many of the actions of plants

The difference with human beings is that we have developed our consciousness in a way which aids us in comprehending possibilities, and assessing possible outcomes from our actions. So not only am I capable of apprehending a much wider variety of possibilities than a bee, I can also foresee the possible outcomes from my potential choices. This, I think, is where self-consciousness starts to play a role, when I realize that my decisions have consequences.

The actual meaning of mathematical existence is that it's whatever working professional mathematicians say it is. You don't accept that, but that is how it works. — fishfry

I hope you see the problem with this. You're saying, if we (mathematicians) agree that it exists then it exists, without any definition of what it means to exist. In any other field, no one would agree that such and such "exists", unless there was a definition of "exists" and some evidence to show that the thing actually exists. For example, would some biologist come in with a fictitious life form and ask the other biologists, can we agree that this life form exists, so that it can be a real existent life form? Or would a physicist propose the existence of a fictitious particle?

What I think is that "existence" is just a facilitator. The mathematicians realize that if they posit the existence of these things, they can treat them logically as we would treat objects, and this makes things much easier. A symbol represents an object, nice and simple. The problem though is that we can't really treat these things like objects. So the mathematicians have created a wall of illusion which separates them from reality. And now, they do not even know how to properly deal with these things which they have assumed to be objects, because they have spent so long wrongly assuming that they are objects, that they have no understanding of what they really are any more.

You have the same objection to football, baseball, Chinese checkers, and whist? You reject playing poker because the only Queen you know is Elizabeth? Nihilism. Childish rejection of the very concept of abstraction. — fishfry

What I reject, is not the concept of abstraction, but the childish notion that an abstraction is an existing object

The empty set comes quite naturally from two principles:
(1) The ability to state what elements sets have in common.
(1a) The elements that sets have in common must always be equal to a set.
(2) That two sets might be disjoint. — fdrake

(1a) would be better stated as, "if" two sets have elements in common this must be a set. There is no reason to interpret a situation where two sets have nothing in common, as meaning that this nothing ought to be a set. That is arbitrary, and actually illogical. If two sets have nothing in common, then why must this nothing be a set? That's nonsense, by the described situation, they have "nothing" in common. Why try to make nothing into something (a set)?

Maybe - maybe - we can sharpen this with an example. What is a warehouse? If you hold that a warehouse is a place where goods are stored, then there can be no such thing as an empty warehouse, and if you say there is, then I reject the entire idea of warehousing. — tim wood

A set is not analogous with a warehouse where things are stored, or any such container, because there is no separation between the set and its elements. Unlike a warehouse which has an identity as a warehouse, with the potential to store things regardless of what is actually stored within it, a set is identified solely by its elements, and is therefore inseparable from its elements. That's why an empty set is contradictory nonsense.

but you each end up saying that math itself is flawed therefore there's no empty set. There must be a name for such an argument. You want to argue a very narrow technical point and your only argument is to blow up the entire enterprise. — fishfry

Don't cast this in the wrong light. I don't say "math itself is flawed therefore there's no empty set". I say "there's no empty set therefore math is flawed". I point out the specific flaws to justify the more general claim, that math is flawed. So it's not the case that I am arguing that math by its very nature is inherently flawed (what you call nihilism), I think the very opposite, that math by its very nature is perfect, "ideal". And, because it has this status of being ideal, we must hold it to the highest standards of perfection. Therefore we are obliged to reject any imperfections.

Math precedes foundations. Not the other way 'round. — fishfry

How could you conceive of this?

are you saying that the standard definition/meaning of "free will" does not require an agent? — Sir Philo Sophia

I do not believe that "agent" requires self-consciousness. For example there are conscious agents which are not self-conscious.

is that a bad example? I mean, are you saying that breathing is an example of carrying out our 'free will'. That example actually makes my point, that is breathing is a pre-programmed part of the agent's system so cannot be part of the agent's free will. If you believe otherwise, please try hard to use your will power to stop breathing for more than 5 (or even 10) minutes and let us know how successful 'you' were at that test of 'free will'. I'm sure you have the 'will power' to do so... If we do not hear back from you anymore then we will assume you were right and you have ‘free will’ the way you say you do. — Sir Philo Sophia

The point is that one can choose without knowing oneself to be choosing, just like one can breathe without knowing oneself to be breathing. There is nothing intrinsic to "choice" which makes it necessary that a person know that they are choosing in order to make a choice. If you are presented with possibilities you might choose one without knowing that you are choosing. A child makes choices before knowing what it means to choose. We do not wait until we know what "choice" means before we start making choices. So we make choices before we know that we are making choices. We choose without knowing ourselves to be choosing.

'free will' is not about only about anything that makes a choice. If it were then you can say the Earth is an agent and it has 'free will' to make weather of its choice. If the choices always happens automatically then no 'choice' by an agent is ever made at all. If you disagree with that then everything like inanimate objects have 'free will' according to your (et. al.) definitions and you've thereby reduced the term to be meaningless wrt how it is used for humans. — Sir Philo Sophia

Free will is about making free choices, notice the word "free". If an automatic response is called a "choice" (and no one in their right mind would call it that), it is not a free choice, because it is necessitated by the thing it is a response to.

And once again, the point is that a person does not need to know oneself to be making a free choice in order to actually be making a free choice. So you've just gone off on a tangent here.

The point is that I do not accept your argument. You seem to be proceeding from the false assumption that only a self-conscious being can act freely. That's an assumption which begs the question. You are limiting, restricting what it means to "act freely" by defining it in a way which supports your metaphysics. If we release your restrictive definition, and proceed solely on descriptive principles you'll see that all sorts of beings "act freely". It is unreasonable to enact your restriction, saying that only self-conscious beings can act freely, just because it supports your metaphysics.

Why do you think it is that "choosing" requires that the individual be conscious of the fact that one is choosing? Does breathing require that one be conscious that one is breathing? Do you see what I mean? There is a term which describes the thing being done, "choosing". Why do you assume that the person must understand what it means to be "choosing", in order to be actually choosing?

The one I particularly enjoyed delved into the nature of mind and consciousness. — jgill

What do you think "rule" signifies?

Does the knight's move have chess existence? The other day you said you reject chess because it doesn't refer to anything in the real world. That's extreme nihilism. You can't get out of bed in the morning with a philosophy like that. How do you know it's your own bed? Property's an abstraction. — fishfry

What I said, or at least meant, is that I refuse to play chess because I find it irrelevant to my endeavours, so it's a waste of time. What could you possibly mean by "chess existence"? Let's say that the game consists of some physical pieces, and some stated "rules". What you have referenced is "a rule". How do you think that a rule exists? Does it exist as the symbols on the paper as the stated "rules of the game"? If so then these rules require being read, and interpreted, understood, in order for someone to actually play the game. Then the person's play is dependent on the person's interpretation. If the rules exist as the interpretation, within someone's head, then who's interpretation is correctly called "the rule". Consider President Trump's, impeachment trial. Who's interpretation of what is required for impeachment constitute the actual existing "rules"? And if it's what's written on paper, that is the existing "rule", how does it have any meaning as a "rule" without being read and interpreted?

Because I have not seen any resolution to these questions, I would not say that a "rule" has any existence at all. I think it is a simplification of something we do not understand. There is a subject of human behaviour, habituation, etc., which is not well understood, and some people like to represent it as understood, so they say there are "rules" which human beings are following. The use of "rules" creates the illusion that human behaviour is understood. The human being follows rules, just like matter follows rules of physics. Use of the term "rule" is just a convenient fiction, used to hide the fact that this subject is not well understood. It's a fiction because it doesn't represent any real, existent thing, it just creates an illusion. So when I get out of bed in the morning (hopefully it's the morning), I am not following rules, I am acting on my own terms. That's what it means to be a free willing human being.

Your "proof" of inconsistency, as I just said before, is not something that contemporary mathematics would accept as valid. — Mephist

I went through this already. You cannot use the logic derived from the axioms to judge the axioms of the system, because valid logic will not allow one to produce a conclusion which is inconsistent with the premises. Therefore we need to refer to some other principles, and philosophy provides us with those judgements and proofs. If you're not interested, that's fine, but the assertion that such proofs are not valid in mathematics is not a sound rebuttal. I'm demonstrating to you, that the premises of your logic are false, and you reply, that doesn't matter because for me, and for everyone who uses my system the premises are true, and unless you can prove that they are false, by starting from the premise that they are true, you have no argument.

When I challenged you on this point, you admitted that it's not only the empty set, but set theory in its entirety that you object to. — fishfry

Of course, the nature of the empty set is essential to understanding what a "set" is, and if a theory has contradictory premises, then I object to the theory in its entirety, it needs to be reformulated

So, according to your definition, have I not invented/created a robot which has 'free will'? — Sir Philo Sophia

I wouldn't say that this robot has free will, it is determined to act according to the parameters of your program. This is an age old problem for theologians. How is it possible that God could have created us, and yet we have free will? This requires a separation between the agent (each of us), and the creator (God), such that there is no necessary relation between the agent and the creator. The necessary relation would allow the creator, to be able to figure out, and always know the agent's act, denying the possibility of free will. Free will would be an illusion. the agent would only be responding according to its program. The omniscient God would always be capable of knowing each agent's choice, demonstrating that the agent really does not have free will. To avoid this, we need a separation between the agent and God, the robot and its creator, such that the thing created is not a necessary effect of the act of the creator, more like an accident. But allowing such an accident denies the omniscience of God.

Does the smiley mean that you don't actually believe what you wrote but that talking to Metaphysician Undercover has caused you to lose your grip? — fishfry

Mephist seems to have no rebuttal to the arguments which demonstrate that the "empty set" is a contradictory concept, and unlike you, seems about ready to face the reality of this.

When I put the same question to Metaphysician Undercover, he admitted that it's not the empty set he objects to, but rather the entirety of set theory. That's a nihilistic position but at least it's a position. You have none that I can see. — fishfry

What I object to is the claim of "existence" for objects which have a contradictory description. This is not nihilistic, but a healthy skepticism. The attitude demonstrated by you, that we might assign "existence" arbitrarily is best described as delusional.

Our friend Metaphysician Undercover is a special case. — fishfry

Thanks for the compliments. The biggest stumbling block between us is your concept of "mathematical existence". The proof that something has mathematical existence is really meaningless unless we have a rigorous definition, or convention, concerning what "mathematical existence" means. If it simply means to be consistent with some set of axioms, and we have no standard as to how an axiom might be justified, then all sorts of fictions may be proven to have mathematical existence. And, if mathematical existence is not consistent with "existence" in the more general, philosophical sense, then it's not even a type of existence at all, and use of the term "existence" is misleading. Then we'd be better to replace "mathematical existence" with "pseudo-existence", or "crackpot existence", so as to be less misleading with our terms.

Maybe you are right: sets cannot be empty. — Mephist

What this means is that zero is a very strange type of number, unique and different from the other numbers. So we ought to be careful in the way that we use it.

nept? Maybe incomplete. Not inept. — tim wood

No, a description which contains contradiction is inept.

"null" is an attribute of "extension": an extension can be "null" or "not null". A set can be defined as something having extension (following your definition). null extension => empty set; not null extension => not empty set. Maybe this is a trick of sophistry, but it avoids the contradiction. — Mephist

Yes, I would say it is a trick of sophistry. To say of an attribute that it is "null", is to say that the attribute is non-existence. So to say that the attribute of extension is null, is to say that the attribute of extension is not there. So all you are saying is that the thing has the attribute of extension, but the attribute of extension is not there because it's null. Of course that's contradictory.

A segment is defined by giving two points. if the two points are coincident (the same point), then it's the same thing as only one point. If the two points are distinct, the length is the measure of their distance from each-other. I don't see any problem with this definition. — Mephist

Do you not see, that if the supposed "two points" are really one point, then they are not two points at all, they are one point? That's directly from Leibniz' identity of indiscernibles. So if they are really one point, then there is no segment.

Yes, that's the same thing: you don't define what a set is, but just give some properties that any set should have, and one of the attributes of a set is the fact to be empty or not: this is just an attribute of any set: no need to define the word "extention". — Mephist

OK, we could take this route, but I think I've followed it before. Perhaps you could lead me to something new. Let's say that a set does not necessarily have extension, extension is not an essential feature. We'll say that a set may have extension or it may not have extension. Let's define "set" then. Isn't a set a collection of objects? Doesn't it appear contradictory to you, to speak of a collection of objects with no objects? If we define "set" as a possible collection of objects, such that the set is the defining terms rather than the actual objects, then no sets would actually have any objects and they would all be empty sets.

In my opinion to say "A line is length without breadth" is like saying "A line is a rectangle with zero width". He means that real objects have 3 dimensions, but a line is like a real object that has only 1 dimension. The other two dimensions are missing. — Mephist

Wow, I find that a very strange way of looking at this. Instead of imagining a line exactly how it is defined, length with absolute purity, no width, you imagine a wide long thing, then subtract the width off it.

Well, we could do the same with sets: adding properties instead of subtracting
- an "point-set" is a set with no parts
- a "line-set" is an extension of the "point-set" that introduces a new property: the number it's parts.
For me, that's the same logical construction. Why this should not be allowed?
At the end, they are all similar ways to do the same thing: attach some properties to an object to describe it without giving an explicit definition in terms of other objects! — Mephist

As I explained above, a set with no parts seems contradictory, and this is due to what a set is. Do you see the difference? A point is defined as having no parts. But a set has parts, according to what a set is, so the set with no parts doesn't make sense unless we changed what a set is. If a set is something other than a thing with parts, what is it?

Right, the universe does not consult with our laws of logic, but we must follow these laws if we wish to make a coherent description of the universe, it's convention. So here's is the problem with your "point". The fundamental laws of logic apply to our descriptions of the universe, they do not apply to universe itself. If a person's description fails to follow these laws, it is an inept description. Your description, "light acts like a wave when looked at as a wave, and otherwise as a particle" suffers that problem.

If I ask you, is your car green, and you say sometimes it looks green, but other times it does not look green, you have given me an inept description.