What I am claiming is that the measure of moral value is the ability of free, rational agents to understand and make their own choices. By "their own choices" I mean choices over those things that belong to them, their minds, bodies and property. — Dan

I really do not think that this could suffice for a foundation of "moral value". It requires a determination, or judgement as to what qualifies as "one's property". This begs the question of the right to ownership. This would place laws and government, which determine ownership, as logically prior to moral principles. The principles which determine ownership would be amoral, being outside of morality. Then those with power would dictate who owns what.

I mean, a choice being "difficult" in that sense is morally irrelevant. It's not a real restriction on the choice. — Dan

I don't know about you, but I find that difficulty is a very real restriction on choice. If there is a very easy way, and a very difficult way, to achieve the same end, no one would choose the difficult way. Clearly the degree of ease or difficulty is a real restriction on one's freedom of choice. Look, if I apprehend something as so difficult that it is impossible, the restriction becomes virtually absolute, I will not choose to do what I know is impossible.

Again, laws restrict our freedom because they come with threats attached. If laws didn't carry the threat of punishment, they wouldn't restrict our freedom either. — Dan

I know, but you are not paying attention to the way that threats can restrict freedom of choice. The threats only act to deter the deciding agent, through the person's mind, via thoughts. The threat of punishment makes me think twice about stealing your car. It is this activity of thinking, I might get caught, I might get punished, which is what really restricts my freedom of choice. Threats of punishment don't deter, and therefore don't restrict the freedom of, the person who doesn't care, or who doesn't think about getting caught. Therefore it is not the threat of punishment which restricts freedom, but the thinking of the person who apprehends the threat of punishment, which restricts the freedom. This is no different from the restriction of freedom involved with the choice about something which is difficult to do. One restricts freedom with the thought of "I can't do that, I might get caught and get punished", while the other restricts freedom with the thought of "I can't do that, it's too difficult".

Note: it is platonism with lower case, we are not talking about Plato when the discussion is modern mathematics. — Lionino

OK, I was unaware of that convention. We are definitely not talking about Plato, but modern day platonism (my spell check does not like the lower case).

But nominalists deny that mathematical objects are real, some think they are useful fictions. — Lionino

If the so-called mathematical objects are fictions then they are not really objects, but fictions. Therefore we cannot correctly refer to the tools of mathematics as "objects". If we're nominalist we'd say that anyone who speaks about mathematical objects is speaking fiction; fiction meaning untruth, because abstractions are simply not objects for the nominalist. And to call them objects would be false by the principles of that ontology.

That is a deep topic in itself and, though related, distinct from the metaphysics of mathematics. — Lionino

The point though, is that if we reject platonism, then we need some other ontology to support the reality of rules. We cannot defer to "intersubjectivity", because that makes a rule something between subjects, therefore outside the subject, and this external existence of rules is just a disguised platonism. Therefore we need to properly locate "rules" as properties of subjects, internal to thinking minds. I have my rules and you have your rules. Then the reality of agreement, convention, needs to be accounted for, and pragmaticism is designed for this purpose.

Application, just like 2000 years ago. — Lionino

So truth for you is pragmatic then?

He said they are mathematical objects, not platonic objects. — Lionino

I don't see how one could ever distinguish between these two. When an idea is said to be an "object" this is Platonism, by definition. Platonism is the ontology which holds that abstractions are objects.

The two key words you used. Social rules are (inter-)subjective because, as soon as we die, they are not carried out, the "rules" of physics are carried out independently of an observer. — Lionino

It appears like you are confusing descriptive rules with prescriptive rules. This is why we need a good definition of what a rule is. The laws of physics describe the way things behave. Social laws prescribe the way we ought to behave. The latter requires an agent who understands, and intentionally conforms one's activity to follow the law, the former is an inductive conclusion derived from observations of how things behave.

Some philosophers mix the two, so that a social rule is just a descriptive principle of how people behave in general. I think this is done to avoid the fact that people choose to follow rules. But this is problematic, because many people step outside the bounds of social rules, so it would be faulty induction.

If that is the case, I think MU's argument simply dissolves and rules are subject to the same debate of nominalismXplatonism as numbers. — Lionino

Tones is arguing that rules are Platonic objects just like numbers are. If that is the case, then formalism does not escape Platonism, it is a deeper form of Platonism, just like I said.

To pull this structure out of TIDF"s Platonic cesspool, and give it a nominalist foundation, you need to address the problems which I stated above. How do we get beyond arbitrariness? What makes some rules more acceptable than others. This commonly leads to pragmaticism

As these references to pragmatic theories (in the plural) would suggest, over the years a number of different approaches have been classified as “pragmatic”. This points to a degree of ambiguity that has been present since the earliest formulations of the pragmatic theory of truth: for example, the difference between Peirce’s (1878 [1986: 273]) claim that truth is “the opinion which is fated to be ultimately agreed to by all who investigate” and James’ (1907 [1975: 106]) claim that truth “is only the expedient in the way of our thinking”. Since then the situation has arguably gotten worse, not better. The often-significant differences between various pragmatic theories of truth can make it difficult to determine their shared commitments (if any), while also making it difficult to critique these theories overall. Issues with one version may not apply to other versions, which means that pragmatic theories of truth may well present more of a moving target than do other theories of truth. While few today would equate truth with expediency or utility (as James often seems to do) there remains the question of what the pragmatic theory of truth stands for and how it is related to other theories. Still, pragmatic theories of truth continue to be put forward and defended, often as serious alternatives to more widely accepted theories of truth. — https://plato.stanford.edu/entries/truth-pragmatic/

No, I am saying that only the freedom to make certain kinds of choices is morally valuable. Specifically, the choices over that which belongs to the person, their mind, their body, and their property. — Dan

No, no, no, this is not true at all. The most morally valuable choices we make are concerning others, when we help them, or choose to hurt them. You know, like "love thy neighbour". The choices derived from that principle concern other persons.

You can characterize them as neural pathways if like, but a reinforced neural pathway does not prevent a person from choosing to think differently. — Dan

Remember, I didn't say that a habit restricts freedom in an absolute sense, it restricts in the sense of facilitating one specific decision at the expense of others. It doesn't make it impossible to choose otherwise, as will power, and the will to break a habit demonstrate. It restricts by making one choice the easy choice and anything else much more difficult.

People are able to act against their habits and, in some cases, they are morally required to do so. Knowing the right thing to do and not doing it does not show that you were unable to do it. — Dan

I've been through this already. I'm not talking about absolute restriction, making something impossible. I am talking about restrictions in the same sort of way that laws restrict us. Laws don't make criminal activity impossible, yet they are understood to restrict our freedom.

No, I am not saying that being "under the influence of habit" affects whether a choice belongs to a person at all. I am saying that habits are not a relevant factor because they don't restrict freedom. I am also saying, seperately, that the only freedom that is morally relevant is the kind over those things which belong to us. These are two seperate claims. — Dan

You are inconsistent, because you say that laws restrict our freedom, but habits do not.

If any rules at all, the idea that every rule we may come up with is a platonic object is silly, especially when so many rules are absolutely dependant on us being around. If you are talking about rules of logic and mathematics, then wonder why it is only such rules that get a special status. — Lionino

Yes, I think this is the issue, why would some rules get special status, and if they do, how could we know which ones deserve that special status. For example if we say some rules are objective, and other rules are subjective, what would distinguish the two?

? Those are set up by convention. — Lionino

So it appears like you want to start with the basic premise that rules are fundamentally arbitrary. Why should we agree to some rules and not to others then? Why would we want to start with something like "truth tables" as the primary rule?

It seems to me, that rather than jump right into the process of deciding which rules to accept, and which not to accept, we ought to first determine precisely what a rule is, When we have a complete understanding of what a rule is, then we will be much better prepared for making such a choice, by having some understanding of what the consequences of that choice might be. So rather than start from a truth table, as the basis for which rules to accept, we should start with the definition of a rule, as the basis for which rules to accept.

No, I don't imply that you shouldn't make that choice (though in this case you shouldn't). What I am saying is that your freedom to make that choice is not morally valuable because that choice doesn't belong to you. My freedom to keep my car on the other hand is valuable because my car does belong to me. — Dan

Now you've lost me. You appear to equivocate with "belong". Your car belongs to you. A choice which I freely make has no moral value because it does not belong to me. Are you insinuating that a choice I make is not my choice?

It doesn't matter whether you are habituated to good action or bad action, both are still available to you. You have free will and your habits do not get in the way of you exercising that to choose to do good, or do bad. — Dan

I think you are in denial, refusing to recognize the reality of the situation. When a person is habituated in a specific way, that person naturally proceeds in the way of the habit any time that the circumstances warrant that activity. Your behaviour in this discussion provides a real example. Through your education you have been inclined to think in a specific way about freedom. This habituation of your thinking patterns closes your mind to what I am saying, so you continually deny that what I am saying is the truth.

Maybe it will help to understand if we characterize habits as neural patterns. Once initiated, the pattern is followed, restricting the possibility of choice in that thought. That habituated way of thinking is a restriction on the person's freedom to choose and to act.

If you studied Plato, Augustine, and Aquinas, instead of whatever philosophy you did study, you would understand that habits truly do get in the way of one's freedom to choose and do what is good. Directed by Socrates, Plato questioned the relation between virtue and knowledge. It was claimed at the time, that virtue is a form of knowledge. However, Socrates demonstrated that a person can know what is good, yet not do it. Augustine, delved much deeper into this subject, how it is possible that a person knows what is good, yet may consistently act in a contrary way. Aquinas developed the role of "habit" in restricting one's capacity to choose to do what one knows is good. In other words, the person has the knowledge of what they ought to do in the circumstances, yet does otherwise, because the person's freedom to choose to do what is good is compromised by the person's preexisting habits.

Whether that choice belongs to you is very much morally relevant, because that is the type of freedom that FC is trying to protect: that over those choices that belong to the person in question. — Dan

This statement appears to rely on an incoherent sense of "belong". You appear to be saying that when a person chooses to do something while under the influence of habit, the choice does not "belong" to the person. I assume that criminals will be using that defence in court. "I am not responsible for my criminal activities because those choices don't belong to me." Are you saying that a person is not responsible for one's habitual actions because the choices involved don't belong to the person, they come from the teacher? is that how you account for education? A person acquires ways of thinking from one's teachers, such that the ways of thinking involved don't actually belong to the person who acquires them?

unlike logic. — TonesInDeepFreeze

Confession is the road to redemption. Nice start!

No, a habit isn't a restriction of one's freedom. — Dan

So says you, but I say you do not understand freedom and the true nature of its restrictions.

No, the principle I'm claiming is that my car, being my property, is something that belongs to me and not something that you get to make choices over, morally speaking. — Dan

When you say "morally speaking" you imply that I ought not make that kind of choice. But oughts, moral principles, do not restrict one's freedom, they give us rules which serve as guidance in our decision making. The actual decisions are what restrict one's freedom.

Therefore I get to make choices concerning your property whenever I want, and I refer to moral guidance whenever I do. Nothing restricts my freedom to do this, even though some would say that I ought not covet any property of anyone else. However, it is the responsibility of each individual to follow the moral principles, and establish ways of curbing one's own inclinations toward making choices which one ought not make. The principal way of restricting one's own freedom of choice is by developing good habits. This is begun when we are very young, being trained by our caregivers, and it continues through schooling, and to some extent throughout our lives.

Whether or not to steal my car is not a choice that belongs to you, because it is [my car. — Dan

Whether the choice "belongs" to me or not, is irrelevant. The issue is whether I have the capacity to freely make that choice. And clearly I do. Therefore it is incorrect for you to say that I don't get to make a choice on this matter. If I didn't get to make a choice in this sort of matter, then every time I was inclined toward taking someone else's property, I would, and every time that I wasn't inclined to take someone else's property I wouldn't, because there would be no decision making going on, no choices, I would be acting on impulse. However, what is really the case, is that every time that I get inclined toward taking someone else's property I decide not to. Therefore I truly do make choices concerning whether or not to take someone else's property. Because I am morally responsible, I decide not to. But for you to say that I don't get to make choices in this matter is nothing but a falsity.

Freedom of choice vs freedom to act is not a distinction I am drawing. — Dan

I've noticed that. However, I think it is very important to make this distinction if you desire to understand freedom. Otherwise you'll believe that just because I am not free to actually steal your car, because you will kill me if I try, I am also not free to choose to steal your car, which the act of you killing me would demonstrate that I am free to make that choice. See, the very nature of "punishment" demonstrates that we are free to choose what we are not free to do. Therefore the distinction is a requirement if we want to understand freedom.

What "ontology of rules"? — Lionino

The ontological status of rules. If rules are real, then they have some form of existence. Ontology is the study of what there is, and the possibility of different forms of existence. An ontological study of rules will determine if there is such a thing as rules, and if so what type of existence they have.

Consider it is the same sort of issue as the ontological status of numbers, for comparison. We can ask, is there such a thing as rules, just like we can ask is there such a thing as numbers. If we answer yes, there is such a thing as rules, then we may proceed to ask questions like are they objective, and if the answer to this is yes, then we are in Platonism. If we answer no, rule are only subjective, then we are faced with a whole lot of problems as to how such a thing as a rule could actually exist.

For example:

https://ontology.buffalo.edu/smith/articles/Hart_Rawls_Searle.pdf

Because a threat to your freedom is being imposed in one case (you better not steal or else), and in the other case you are just acting in a not very considered way, which is your "right" (term isn't quite accurate, but useful in this context). — Dan

So, the law is a threat to restrict one's freedom, the habit is an actual restriction of one's freedom.

If you want to steal my car and prevent you doing that, that hasn't violated your freedom in a morally relevant way (depending on how I do the preventing) because stealing my car was not your choice to make. — Dan

What is the principle you are claiming here? People attempt to steal cars all the time. Clearly, to steal your car is a choice which can be made. Are you saying that since you believe that you have the capacity to prevent me from stealing your car, (dissuade, threaten, kill me, or whatever it takes), this means that I cannot choose to steal your car? I think that if you really believe that, you are delusional.

Obviously you are confusing potential (theoretical) restrictions to one's freedom of choice, with actual (practical) restrictions to one's freedom of choice. In practise, my freedom of choice is primarily restricted by the internal workings of my body, brain, and mind, through things that influence my thoughts and feelings. Your potential actions of persuasion and threats have a secondary position by being able to influence my thoughts in a secondary way, through my use of my senses. And if you act in a way of physical violence to prevent me from carrying out what I choose, then this is not a restriction on my freedom of choice, it is a restriction on my freedom to act. In this case, my freedom of choice allows that I can choose to do what is physically impossible to do. That is actually a common situation in the case of mistaken actions.

I believe I mentioned this distinction between the freedom to choose and the freedom to act, earlier, briefly. If someone chooses to do what is physically impossible for that person to do, and this is evident to the person, this is an indication of irrationality, being unreasonable. So if it is the case that you have made it clear to me, that if I move to steal your car, you will physically prevent me from doing this with an act of violence, then I would be irrational to continue with that act. However, in some cases of demonstrating a point, one might rationally choose what is known to be physically impossible, to bring attention to one's conditions, as an instance of protest or something like that.

Laws are a restriction of freedom because they come with a threat against said freedom attached. — Dan

The point though, is that the way that laws work is through social conformity and habit. It doesn't make sense to say that laws are a restriction, but the means by which the laws work to constrain us are not restrictions. Do you see what I mean? The law says I better not steal, and it's a restriction on my freedom because it threatens me with jail time. So I decide that I better not steal, and I create habits which always incline me away from that idea of taking the thing, if such an idea ever starts to come into my mind.

Why do you think that the law qualifies as a restriction on my freedom, yet the ideas and habits which the law helps to form in my mind, and which is what actually causes me to behave in a restricted way, are not restrictions on my freedom? The "real" restrictions are the ideas and thinking patterns within my mind, in the realm of ideas and mental activity. The external law just provides incentive for me to create those restrictions within my mind. This is what Plato showed in The Republic, the realm of ideas is more immediate to use, and so it is where the real causal power is. Today we understand this as "ideology", an the effect which ideology has on the actions of human beings.

Perhaps I can clarify with an example. Let's say I choose to chop off my leg. This prevents me from doing a bunch of stuff with it in the future, but this is not problematic. So long as I am choosing to remove/destroy the thing, then I am choosing to give up those things and therefore my freedom over them. — Dan

I follow your example well, but I think that what you need to consider is the effects of training, ideology, and even what we used to call brainwashing. Human beings are mostly not leaders, but follows, staying safe in the midst of the herd. As such they are very gullible. When we see all the many institutions which direct people in a good way, like educational institutions, and legal institutions, we overlook how all these things are really robbing people of their freedom, because the institutions are set up to do this for "the good". But people who do not get drawn in, and persuaded by that ideology, might become wayward, and they may be directed in many different ways.

The point being that when a person makes a bad choice, you say that was their freedom to make that bad choice, and now they must live with the consequences of having made that bad choice. But this does not get to the real issue, which is why the person made the bad choice. Something misled them. The "why", why did they make that choice, I classified under "ideology", their ideology misled them. Now freedom and the goal of protecting that underlying principle which provides for freedom becomes very problematic because the lazy mind likes to follow the herd and is therefore gullible to be misled by ideology. So the underlying inclination is to neglect that principle of freedom which you wish to protect, follow the herd, and be led or misled accordingly.

Suppose I am raising my children, and I homeschool them, and do everything I can to promote free thinking and a very open mind. This I do to protect their freedom of choice from the ideologies of "the system", as i am in disagreement with that ideology.. Unless I feed them some other ideologies about "good behaviour", and instill an acceptable ideology within their minds, they may develop a hole there, which amounts to a lack of direction. Then they would be exceptionally gullible, and could be preyed upon by others with bad intentions.

What i am saying is that there's a risk going to far in protecting the principle of freedom. We want a person to develop a good strong capacity to reason, and make one's own choices from an open mind, but at the same time we want that person to be directed so as the choices are within a specific range of "good" choices. And to determine "good choices" we look to something like consequentialism.

I think we might apply Aristotle's doctrine of the mean. The principle of freedom which you want to protect is at one end of the scale, one extreme. To protect this implies allowing the person to be free from ideologies which may be harmful, to have an open mind and not to be influenced by prejudice. At the other extreme is the ideological "good" of consequentialism. We see that there is a need to have a person trained to be naturally inclined toward what is considered as good. Virtue, lies somewhere between these two extremes as the mean between them.

Right, but mastering circumstances towards what end? Presumably we want to take control of circumstances to direct them towards some end we find good, else why bother trying to shape them at all? — Count Timothy von Icarus

I think it's like I said. Once we learn how to master the circumstances, then we might be able to understand why this is good.

And it seems to me that survival can be superceded as an end—that we can recognize higher ends (e.g. Socrates, St. Paul, Boethius, Origen, etc.) — Count Timothy von Icarus

I don't think that these are examples of people recognizing higher ends rather than that they recognize that there is higher ends. I do not deny that there is higher ends, I just think that we need to address the issues which are present to us now, fulfil the immediate ends. It's a matter of taking things one step at a time. We know that we need to climb the ladder. We cannot see the top, and we have no idea where the ladder leads. However, we can always see the next step and we can work to get to the top of it. After that, we'll be able to see the next step.

People doing the wrong thing due to akrasia, or weakness of will, is not a case of their freedom being restricted, but rather them failing to do the right thing, and I think this is what you are describing here when you talk about habits. — Dan

Mental constraints are just as much a restriction to one's freedom as physical constraints are. Mental constraints of habit are how social conformity works, and how laws, and rules and training in general, work to restrict one's freedom. It is a very real restriction, because understanding our environment is what prevents us from choosing to do what is physically impossible, also it helps us to avoid mistakes, and all sorts of unnecessary risks.

You might think that there is a clearly delineated separation between physical constraints and mental constraints, but that is not the case. When we start to consider the material body of the human being, and how the physical constraints of the human body influence mental constraints, we see that the two are intertwined, just like feelings and thoughts are, and one is not easily separable from the other.

The assertion that we can know causes and effects in one but not the other seems unsupported. — Dan

The opposite assertion seems unsupported as well, only supported by some preliminary theory you have presented. Let's compromise then, and agree that we can have some degree of understanding of cause/effect relations in both, the external world observed through sensation, and the internal world observed with the mind. I think you'll agree that the issue is the causal relation between the two, not the causal relations of one or the other.

Suppose "free" means that there is not a direct cause/effect relation from the external to the internal. If there was such a direct relation, all of our thoughts would be directly caused by our sensations of the external, consequently our decisions and actions as well would be, and we'd have no free will. So, we assume that there is no direct relation of causal necessity, this supports "free will". Also it serves as the foundation for "freedom" which you say ought to be protected.

To be able to protect it, don't we need to be able to understand it a bit? Would you agree that we need to assume a source of activity within, which is not caused by external activity, as the base, the foundation, which makes "freedom" possible, and therefore that which needs to be protected?

Also, I fundamentally disagree that not choosing increases ones freedom, so all of this discussion about whether or not we can see the consequences of not choosing and instead engaging in contemplation (which does seem to be implied by what you are saying), is really just debating an ancillary claim you made. — Dan

I now believe I understand why you disagree with the principle that choosing restricts one's freedom. You do not believe that states of mind, or mental activities in general, can be constraints or restrictions on one's freedom. Consider for example, that choosing X restricts my freedom to choose not-X, not in an absolute way though, until I carry out actions associated with X, because I could still change my mind. But once I choose X, the likelihood of me choosing not-X is greatly reduced, because I will no longer consider not-X as a possibility.

Do you agree that free will requires an internal source of activity, without external causation as proposed above? If you do, then you'll see that there must also be internal restrictions to this internally sourced activity, or else it would have no direction, and be random in its effects. But it does have direction, and this is due to the restrictions imposed by mental activities like thoughts, decisions, and states of mind. As described above, the restrictions are not absolute, and do not make the contrary action impossible, they just guide the actions in a favourable direction. This is the way laws work, they do not make the illegal activity impossible, they just serve to guide activity in a favourable direction. But just because they do not make the restricted activity impossible, this does not mean that they are not restrictions on freedom nonetheless.

I would maintain though that a vision of freedom where maintaining one's freedom requires a flight from all definiteness is contradictory, for the reasons I have stated. Here, the exercise of freedom itself makes one less free. — Count Timothy von Icarus

I don't see that your "reasons" were well thought out. You assumed an absolute freedom, which is clearly not what I was talking about.

Being determined by circumstance seems like a definite limit on freedom however. — Count Timothy von Icarus

Circumstances are not "definite" though, as things are constantly changing. That's the issue, we live in a world of constant change, where many things are by nature indefinite.

But if our ends are not determined rationally, but rather as a coping response to circumstance, then it seems to me they are less than fully free. — Count Timothy von Icarus

How are these two different? Coping with circumstance may be the end which guides the rational mind.

It seems like "survival" is functioning as the overarching end here. But sometimes it seems like some ends trump survival, e.g. Socrates' acceptance of death. If we are always oriented towards survival rather than what we think is truly best, that will be a constraint on freedom of action. We could consider here the case where Socrates succumbs to cowardice and flees even though he knew he ought not do so. Here, he is not free to do what he thinks is best, but is rather ruled over by circumstance and fear. — Count Timothy von Icarus

What one thinks is "truly best" is subjective, meaning that one's "good" actions are dependent on the opinion of the subject. Coping with circumstances is objective, making one's "good" actions dependent on the activities of the object.

If an agent is "oriented towards no specific end," but rather the ends are "determined by circumstance," then how is it not circumstance in the driver's seat? No doubt, we have to deal with the circumstances we face, but freedom would seem to come from mastering them to the extent possible. — Count Timothy von Icarus

I don't see why you think that this puts circumstances in the driver's seat. When you drive a car, and you avoid obstacles which come up in front of you, the objects are not in the driver's seat.

But you're right, freedom comes from mastering the circumstances, that's exactly the point. So if freedom is the highest value, then mastering circumstances is the means. And, if we get to the point where the circumstances are completely mastered, not just "to the extent possible", then we can set another goal, produced from this new perspective.

I think Plato has a very good argument for why reason has to guide free action. We can't very well be fully free if we don't understand why we are acting or why it is good to do so. But the "rule of the rational part of the soul," would seem to require determinant aims. — Count Timothy von Icarus

I think that using reason to deal with circumstances is a very good example of using reason to guide free action.

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. — Wikipedia: Formulism (Philosophy of Mathematics)

However you frame it, rules are an essential aspect of formalism. So the ontology of rules needs to be addressed if we want to determine whether formalism can actually avoid Platonism, or whether it is as I say, just a deeper form of Platonism.

Any determinancy in thought or action becomes a constraint on freedom. — Count Timothy von Icarus

Right, this is truth, determinacy is a constraint on freedom. Why try to deny it?

the "freest we could possibly be," turns out to be a state where choice is impossible since any determinant choice is a fall from absolute freedom as pure potency. — Count Timothy von Icarus

Nothing I said makes choice impossible. It's just a matter of recognizing as fact, that to choose is to intentionally limit your own freedom. What's wrong with that? Our freedom is significantly limited by the circumstances in which we live, so there is never the issue of "absolute freedom" anyway. Where do you get that idea from? However, it is the case, that not choosing is a way to sustain one's maximum freedom.

Yet "the inability to choose anything," is the exact opposite of what is meant by "freedom." — Count Timothy von Icarus

You are misrepresenting what I said. It is not "the inability to choose anything", it is a case of willfully not choosing anything. The ability to choose remains, therefore choice is not impossible as you claim, it's simply a matter of none of the possible choices appearing to warrant being chosen at the present time. As a result of not choosing, one maintains the freedom to choose, and perhaps as time passes, one choice may appear to warrant choosing, or another possibility, which hadn't been apprehended earlier may enter the mind. The latter is the obvious benefit of not choosing. One's freedom with respect to that specific choice is maintained, and at a later time a better option may appear, and the person is still free to choose that, having not already chosen something else.

If freedom is defined without any reference to the Good, then there is no determinant end to which the "perfectly rational and self-determining agent," should tend. — Count Timothy von Icarus

Right, this is the exact nature of "freedom", there is no specific end toward which the agent "ought" to be inclined. This allows the agent maximum capacity to act according to the circumstances, not being constrained by any sense of "ought". What's wrong with that? That is what survival requires, the maximum capacity to act according to the circumstances. So if survival is important to the agent, then freedom from "the Good" is justified.

Then it seems that our perfectly self-determining agent must, in the end, be determined by what is wholly arbitrary. Their judgements of "what is truly best," do not flow from reason, but from "nowhere at all." — Count Timothy von Icarus

You seem to be forgetting about the natural constraints of the circumstances within which one lives. The existence of such is obvious. The agent's judgements are not arbitrary, nor do they flow from "nowhere at all", they are produced in accordance with the agent's understanding of one's circumstances. Furthermore, since no two sets of circumstances are the same, the agent must have maximum possible freedom of choice to be able to best deal with any possible set of circumstances.

A society organized around "maximizing freedom," will be a society oriented towards arbitrariness when freedom is conceptualized as mere "freedom from constraint/determinancy." — Count Timothy von Icarus

Like I just explained, it is not a matter of arbitrariness, because the circumstances we find ourselves in are not arbitrary. The circumstances are however, to a large degree, unpredictable and often dangerous. This necessitates that the agent must have maximum freedom of choice to be able to best deal with whatever comes one's way. Your conclusion of "arbitrariness" is completely unfounded because you completely ignore the natural constraints of circumstances.

I meant that acting out of habit is not, in itself, restricting freedom. — Dan

Acting out of habit clearly does restrict one's freedom. The habit forms an inclination which prevents the person from choosing to do otherwise, in a way contrary to what the habit inclines, therefore restricting the person's freedom of choice to do otherwise. That is why habits are so difficult to break. The person's freedom to choose an activity other than the habitual activity is greatly restricted due to the force of the habit. Notice that the habit is described as an acting force of influence. It doesn't make the contrary choice impossible, but it still acts as a restriction.

To your second point, and using the same example, murdering someone as a habit would violate my victim's freedom, but it wouldn't violate mine. In this hypothetical, could have not done that and should have not done that. — Dan

I don't quite understand "murdering someone as a habit", unless you are saying that the person is in the habit of murdering people. If so, I agree that the person could have not done the murder. But that is not the issue. The issue is that to have not done a murder, the person would first have to break the habit. And breaking the habit requires the will power, and forcing oneself not to choose (as I explained earlier) what one is inclined toward choosing. So the person is free to not murder, but to exercise that freedom, the person, being influenced by habit, first needs the will power to abstain, and not to choose to murder. This restraint from choosing is what enables the person's freedom not to murder, because the person is already inclined to choose to murder. So the person's freedom to not murder is only actualized by the person's will not to choose, because if the person allowed oneself to choose the choice would be to murder, by the force of the habit.

Claiming that I am merely deceiving myself about my own mental states, or their order, if it conflicts with your claim that I can't observe cause and effect relationships in my mind seems like the classic, unfalsifiable refrain of the psychological egoistic when faced with altruism. It seems like if a specific memory (or for that matter a specific experience) reliably and repeatably evokes specific emotional states in me, then it would be reasonable to say one caused the other.

A mutual feedback relation appears to be a cause and effect relation, at least regarding the persistence of the thing, if not it's initial inception. — Dan

None of this justifies your claim that one might have a clear determination of which is cause and which is effect.

Also, regarding not knowing the likely consequences of an action, are you assuming expected value consequentialism? Because it seems that actual value consequentialism doesn't need to know the "likely" consequences of an action to evaluate it, only the actual consequences that followed from an action. That's not really relevant to the main point though, and either one would have issues if you really couldn't evaluate the consequences of actions if they involve mental states. Luckily, that appears to not be the case. — Dan

By deferring to "the actual consequences that followed from an action, you are further demonstrating the reliance on observation and inductive reasoning.

I'm still waiting for you to show a reliable way to demonstrate the likely consequences of mental activity. An angry person for example might yell, or get violent, or turn and walk away. How could you know which is most probable?

Whether someone has a bad habit is not morally relevant. — Dan

You have a completely different understanding of "morally relevant" from what I have. A habit inclines one to act in a specific way, and if that way is morally bad, or morally good, then the habit is morally relevant.

This is also the case when engaging in an activity. If I choose to go read a book, I don't become less free in a morally relevant way than before I decided to do so, because I am still able to understand and make those choices that belong to me to the same degree as before. It is not freedom of all kinds that is being protected here, it is specifically the ability of persons to understand and make their own choices. — Dan

Switch out "go read a book" with an activity which is considered to be morally bad. When a person acts on impulse, and the impulse is related to habit, then the person's freedom is very clearly restricted. The person's ability to understand is restricted due to the force of habit. If that person decides to engage in an activity which is morally bad, due to the influence of a "bad habit", then that person's ability to choose what is good is affected in a morally relevant way.

You don't need to know the likely consequences of actions in order to evaluate actions by their consequences. — Dan

This seems contradictory. You can evaluate consequences without knowing them?

To use an example that would be morally relevant to any kind of hedonistic utilitarianism: If I remember something funny, I experience happiness. In fact, given that almost all consequentialist measures of value appear to evaluate effects that occur within the mind of people. — Dan

Sure, you can provide all sorts of examples like these, but they are simply manufactured, and do not actually justify the claim as to your ability to make such cause/effect judgements. You say, remembering something funny causes you to experience happiness, by ignoring the possibility that being happy may be what causes you to remember something funny. So your claim is merely self-deception, by framing things in a way which supports what you happen to believe.

Second, it is you who is claiming that contemplation increases freedom, not me, which suggests to me that you have at least some basis for thinking that there is a cause and effect relationship between the one and the other, which you now appear to be claiming is impossible to know. — Dan

This is a misrepresentation. I did not say that contemplation increases freedom, I said that the freedom derived from not choosing enables contemplation. The two are entwined in a mutual feedback relation. We might represent not choosing as the cause of deliberation, or vise versa, it really doesn't matter. And, that is why it escapes the consequentialist conceptual structure, cause/effect is not relevant. So, just like in your example,( happiness/remembering something funny), whichever is the cause, and which is the effect needs to be taken as irrelevant, because it cannot be decisively determined. Because of this consequentialism is inapplicable.

If freedom is conceived of as a pure power/potency, then even good habits are deleterious to freedom since they still constrain possibilities of action. — Count Timothy von Icarus

That's right, if "freedom" is assigned the highest value, then no habit can be good, as it detracts from freedom.

But the virtues were generally thought to perfect freedom precisely because they allow one to act in accordance with what they think is "truly best," not because they allow someone to act "in any way at all." This would amount to mere arbitrariness, which is sort of the inverse of freedom. — Count Timothy von Icarus

What you are showing is that perhaps freedom ought not be the measure of value. This can be approached from another direction as well. Living beings such as humans have a natural tendency to be active, so acting is a natural good. From this perspective, doing something is better than doing nothing. And, "doing something" means that your freedom is restricted by the inclination to do something, what we call "good". So "good" is an action. And doing nothing, deliberating and contemplating, is a means toward determining the good action.

I'm not sure I follow this Metaphysician Undercover. You mean to say that when I act according to my free choice, I am actually less free than when I am figuring out what I want to do? — NotAristotle

Yes, that's exactly what I am saying. You are constrained by the situation you are in. If you are not presently doing anything than you have more freedom to choose than if you are engaged in an activity which is effectively restricting you already.

I did mention though, it is better to consider this freedom being protected rather than promoted. So long as the person is able to understand and make their own choices, then there is nothing that, as it were, "needs doing". Whether the person has constrained their own choices in some fashion is (in most cases) morally irrelevant. — Dan

I don't understand this difference, between protecting and promoting freedom. Bad habits are morally relevant, and habits guide our decisions when we do not take the time to deliberate. To protect one's freedom of choice requires that the person resists the formation of habits in one's thinking. To be inclined this way, i.e. to resist habitual thinking, requires that freedom be promoted, because choosing not to choose is an intentional skill requiring will power to develop, and the desire for freedom is the required intention. This is where consequentialism really fails us. It does not properly provide for the value of will power.

Also, consequentialism refers to a broad range of theories (or, if you prefer, the feature common to a broad range of theories) that share the common feature that they evaluate actions by reference to their consequences. That doesn't necessarily require observation, certainly not external observation. — Dan

To evaluate actions by reference to their consequences requires observations of actions to know the likely consequences. It is a matter of having general principles which provide predictive capacity. The principles are produced from inductive reasoning derived from observations exactly like empirical sciences. Consequentialism is an attempt to characterize moral philosophy as an empirical science.

Also, it does seem as though you could, at least in some cases, observe contemplation — Dan

This is more relevant, but no less problematic. Since these thoughts are internal, cause and effect relations cannot be properly justified. Justification requires demonstration. Wittgenstein approached this with the private language example, and decided it's better just to make judgements according to observable externalities, rather than consider internal aspects.

As psychologists know, within this internal 'realm' there is an interplay of thoughts and feelings. We can, in principle, associate thoughts with the conscious mind, as somewhat controllable, and feelings with the subconscious, having a source in sensations, and uncontrollable. However, it is quite obvious to anyone who has observed their own contemplation, that thoughts have an extension into the subconscious, and feelings extend into the conscious. And, the interplay between them is more rapid than the conscious mind observing can apprehend. This leaves determinations of cause and effect as impossible. All this indicates that consequentialism, which bases judgements on a cause/effect relation has no real merit in the internal 'realm'.

I explored this question somewhat in my Grundlagenkrise thread, specially in my chat with Banno, but there was no interest in the topic died after 3 days — folks prefer to go around circles about ethics instead and keep it shallow. The ontology of rules are ultimately derived from logic, be it first-order or second-order — and logical terms can be taken as primitives defined from their truth tables — and the usage of undefined terms, such as "line", "+", or, in the case of ZF, membership ∈. — Lionino

If logic is following rules, as formalists seem to think, then to say that rules are derived from logic is circular. That's the issue with formalism to avoid the vicious circle, rules must exist as Platonic Forms. So formalism really cannot avoid Platonism, because the only ontologically coherent formalism is Platonism.

I don't think you are using "freedom" in quite the same way. — Dan

I took the meaning of "freedom" directly from your article. Check it out:

For freedom consequentialism, the measure of value is, unsurprisingly, freedom. However, since “freedom” can mean a lot of different things, I should explain what I mean by it here.
When I use the word “freedom” in this context, I mean the ability of free, rational agents to understand and make the choices that belong to them. — Freedom consequentialism primer

As I said, not choosing, rather than choosing, provides the most freedom, because every choice made restricts one's freedom with respect to that choice already made. And, since the measure of value is freedom, as you say, then the highest value is to not choose, because this provides the most freedom. And, not choosing is what enables deliberation and contemplation. This is consistent with Aristotelian virtue, which places contemplation as the highest activity.

Also, consequentialism does not require the perspective of an observer, nor is it really connected with such a perspective. — Dan

Consequentialism definitely does require the observational perspective. It is a system which derives principles for moral action, from observations of similarly classed actions, and the effects of these actions, just like empirical science. It is an observation based theory, inductive principles concerning the utility of different types of acts, are produced, to guide in decision making.

Instead, most consequentialists claim that overall utility is the criterion or standard of what is morally right or morally ought to be done. Their theories are intended to spell out the necessary and sufficient conditions for an act to be morally right, regardless of whether the agent can tell in advance whether those conditions are met. Just as the laws of physics govern golf ball flight, but golfers need not calculate physical forces while planning shots; so overall utility can determine which decisions are morally right, even if agents need not calculate utilities while making decisions. If the principle of utility is used as a criterion of the right rather than as a decision procedure, then classical utilitarianism does not require that anyone know the total consequences of anything before making a decision. — SEP: Consequentialism

Since not choosing cannot be empirically observed and the activities derived from not choosing, contemplation and deliberation, cannot be observed as the effects of not choosing, the value of not choosing cannot be considered by consequentialism because it has no observable utility. However, it actually provides the highest value when value is measured by freedom. Therefore value measured by freedom, and value measured by consequentialist principles are two incompatible value structures. In other words, a person has the highest level of freedom to act, when not currently acting. So not acting receives the highest value when freedom measures value. Consequentialism only judges the value of actions, and therefore cannot value inaction, nor can it properly value freedom.

Hi Dan,
I believe there's a very simple answer to this problem. Because you contextualize "value" in relation to freedom, freedom must be your highest value. And the choice which gives one the most freedom is the decision not to choose. This is because each judgement which a person makes acts as an intentional restriction on one's capacity to choose, by having already chosen in relation to that judgement. This choice, not to choose is what enables deliberation, and Aristotle's highest virtue, contemplation.

Consequentialism however, is a judgement of one's actions from the perspective of an observer, and the observer cannot see one's contemplations or deliberations as actions. This excludes the action which has the highest value in relation to freedom, from the possibility of even being considered as having any virtue in the consequentialist's value structure.

Therefore the "freedom" perspective and the "consequentialist" perspective of moral virtue are inherently incompatible. The freedom perspective has as its highest act, something which is not even an act, from the consequentialist perspective, because it is an act with no observable effect. Deliberation, or contemplation, is an act without a decision or choice, therefore without the manifestations of moral consequences, yet it provides one with the highest degree of freedom. However, as Aristotle indicated, contemplation must be considered to be "an act" with causal capacity, because of its temporal nature, and the effect which it has on one's choices. Therefore it must be given the highest position, denying the truth of the incompatible consequentialism.

OMG, the cat grabbed my hand. I meant to say "nothing to be ashamed of".

A premature ejaculate, nothing to be ash

Back to the question of formalism... How does a formalist typically account for the ontology of rules? What kind of existence do rules have? Consider the rule of how to spell "judgement" for example, how does that rule exist?

Is judgement with the extra 'e' a Britishism? — fishfry

I don't know, but there are lots of US/Brit differences, the common one being the "o/ou", which most are familiar with. I'm Canadian so I'm stuck in between, getting it from both sides. For us, the 'proper' way is the Brit way, which my spellcheck hates. I have the keyboard option for Canadian English, but it seems to default to US. There are some interesting nuances, such as the practice/practise difference. We would use "practise" as a verb, an activity, but if a professional like a doctor, or lawyer, sets up a practice, we have the other form as a noun. It's not a very useful distinction, and difficult to figure out when you're writing, so screw it! What's the point in such formalities?

I believe efficient cause refers to the source of motion, the moving thing which acts as a force to cause change. The ngnb could be portrayed as efficient cause, because it would be activity, simply causing change without any view toward good or bad. That's the way we see activity today, and efficient causation, in physics for example. Activity must be directed toward good or bad, by a conscious choice of free will. But Plato doesn't represent it this way in that passage. Plato says that the ngnb must be moved toward a good. Once he does this, he is bound to say that it must then already be bad in that respect.

So the neutrality of the efficient cause is denied by Plato, saying that the thing which becomes from the activity of cause is always better than the prior state. And that is why you say he "conflates" efficient and final cause, he really annihilates the idea of efficient cause in that discussion, to say all causes must be fundamentally final causes, acting for the sake of something.

But this denies the reality of what we would call misfortune. This is when acts which appear to be ngnb have a bad effect. We cannot say the act is for the sake of some good, like Plato does, because it appears to be all bad. And when we see the activity as leading from a better state to a worse state, we cannot apprehend the source of the act as for the "sake" of something, because nobody intentionally moves toward something apprehended as bad.

Furthermore, this certainty can be leveraged to great effect in the building of structures, the estimation of value, and so on and so forth. — Wayfarer

The fact that it has leveragability in the material world, means that there is something more to it than "it just is". It is useful.

So maybe, in some sense, the demand that mathematics itself be explained is a bit like the child’s question. Mathematics, after all, is the source of a considerable number of explanations, not something that itself needs explaining. — Wayfarer

The explanation needs to take a different tact, one which addresses the usefulness which we observe. That's why Peirce was led into pragmaticism. Notice in my exchange with @Tarskian above, I was quickly led to ask what makes one theory "better" than another. Tarskian claimed the "perfect" model of an abstraction is one which is identical with the abstraction which it models. However, this is clearly incorrect if we consider what actually works in practise. In practise, what makes one specific model of an abstraction better than another is some principle of usefulness, and this is not at all a principle of similarity. That is reflected in the fact that the symbol often has no similarity to the thing symbolize ("2" in my example, is not similar to the idea of two).

I see it all as final cause. Where does efficient cause fit in?

5 is an attribute of the fingers on your hand, would you grant me at least that? — fishfry

No, I'd say "it has five fingers" is an attribute of your hand. An easy way to think of attributes, is as what something has, a property. So ask yourself, do the fingers on your hand have 5. It doesn't make any sense to say that your fingers have the number 5 as an attribute. Number is a value, and values are proper to the subject, not the object. 5 is not an attribute in the way you propose it's a value.

I think of fingers as a physical instantiation of the concept of 5. But if you disagree, then we must be using the word differently. I'm ok with that. How about representation, in the same sense that the first cave man to kill five mastodons and make five marks in the ground to keep track. — fishfry

Using what word differently, instantiation, or 5? As I said before, I don't believe that numbers have any physical instantiations. Numbers are values and values do not have physical instantiations. So I don't understand what you're asking.

This is manifestly false. Not a matter of opinion or interpretation or language. Flat out false. — fishfry

OK, so we have a difference of opinion, and you are extremely convinced that you know the truth, and my opinion is false. This indicates to me that unless you can prove to me the truth of your opinion, then discussion is pointless. Maybe you can explain it to me. Imagine a person with no understanding of number, a young child just learning to speak for example. You believe that this person can stare at one's own fingers and abstract the concept 5, without any explanation. Please explain how this would be done.

On the contrary, it is exactly through the experience of looking at one's hand that one at first does apprehend the number 5; and only later, by analogy and induction, all the other natural numbers. — fishfry

Come on fishfry, say something reasonable. This is ridiculous. You are asserting that the number 5 is the first number that a person learns.

Oh no. 5 is learned by bijection with the fingers, not with counting. Counting is a higher function. Bijection is more primitive or intuitive. If you've seen a mother cat missing a kitten from her litter, she is not going "One, two, three ..." She's comprehending the total number instinctively and knowing when she's one short. — fishfry

Now it's time for me to say that I think you are wrong. I never learned bijection with my fingers, I learned how to count. We learned how to count to ten. Then we were given examples of the quantities which each name signified, but that was only after we learned how to count. Learning how to count was first because that's how we memorized the names, and their order. Once the names were memorized we could learn the quantity signified by the name. We did not learn bijection, that's a much more complex skill then simply memorizing the order of some words. All simple arithmetic was a matter of memorizing. Did you not use flash cards?

Cats don't do bijections, nor do young children learning about numbers. The mother cat knows each kitten intimately, and knows when one is missing because she misses it. She does not count them in any way.

There is a modern trend of misspelling judgment, and I can't let it go by. No middle 'e' in judgment. — fishfry

Sorry, the devil made me do it. For some reason, out of all the words that have multiple spellings British/American mainly, people on this forum complain about judgement/judgment. Why is this worthy of a correction? You didn't correct me when I spelled color colour.

If 2 + 2 is 5, then I am the Pope.

That is a true statement that does not correspond with reality. — fishfry

That's nonsense. There is nothing to relate "2+2=5" to you being the pope. So this conditional is clearly false, not true as you claim. If 2+2 is 5, how could that make you the Pope, there's no logical connection to support your claim of truth.

Statements assumed true in a fictional context so as to work out the consequences. — fishfry

Uh huh, fictional statements which are assumed to be true. That's contradiction. Do you mean a counterfactual? Obviously they are not assumed to be true. You and I seem to have a completely different idea as to what constitutes truth, so I think we'd better leave that alone.

An instance of literally false? — fishfry

"Literally false" was your terminology. Why pretend not to understand it?

"They're meta-false, as I understand you. They're not literally false. If the powerset axiom is false, you get set theory without powersets. You don't get some kind of philosophical contradiction. You are equivocating levels."

This discussion has degenerated. Let's evacuate.

The notion of group may indeed be an abstraction, a way of perceiving things, but there are still five people, which are physically there. — Tarskian

Then the matter at issue is what constitutes a distinct individual, in order that we say that there is five of them. And this is a product of the way that we sense things. We sense things as having a separation from their environment, as distinct objects, particulars.

Fewer differences. — Tarskian

But the simulation is completely different. By the conditions of your example, it is digital, a numerical representation. How are numbers similar to the world which is represented? The number "2" is in no way similar to two separate objects.

A perfect map of an abstract world is the abstract world itself. Perfect means "isomorphic" in this case. — Tarskian

This still does not make sense to me, it gives no real meaning to "perfect" You are saying that what was first described as two, the abstract world and its simulation, are really just one, because the simulation is "perfect". But then there really is no simulation, just the one "perfect" abstraction. So all you are saying is that to be an abstraction is to be perfect. So all abstractions are perfect, ideal, as being one and the same as themselves.

Hence, an isomorphic mapping of a structure is equivalent to the structure itself: — Tarskian

Now you're using "equivalent to the structure", and before you said the perfect map "is" the structure it maps. This is saying two different things. When we say it "is" that, we allow no difference, but to say it is "equivalent" allows for a world of difference. In my example above, "2" is completely different from the two things it represents, but it is equivalent.

Two abstraction are not truly identical. They are identical up to isomorphism. — Tarskian

You already said, "the perfect map of an abstract world is the abstract world itself". If it "is" the thing then it is truly identical. But now you take that back and claim they are not truly identical. If they are not truly identical then we need to account for the difference between them. You say they are "isomorphic" and that implies that they have the same form. So how could the abstraction and the model of the abstraction have the very same form, yet be different? A difference is always a difference of form. And since they are both abstractions there is no "matter" here to account for the proposed difference. Therefore we end up with contradiction. They are not truly identical so there must be a difference between them. The difference must be a difference of form. Therefore they cannot be isomorphic.

For example, the symbols "5" and "five" are identical up to simple translation (which is in this case an isomorphism). Two maps can also be isomorphic. In that case, they are "essentially" identical. — Tarskian

This is where the problem is, "essentially identical" is an oxymoron. "Identical" means the same, but you degrade "identical" to say "essentially identical", such that it can no longer mean "the same" any more, because "essentially identical really means different. All you are really saying is that it is the same but different, which is contradictory.

Abstraction are never truly unique. — Tarskian

I totally agree, but the problem comes when we try to say that an abstraction, which is never truly unique, has an identity, just like a thing which is unique does. That is the case when you say "A perfect map of an abstract world is the abstract world itself". You have given identity, uniqueness, to the abstract world, to allow that there is a "perfect" map of it. Only if the abstraction is truly unique could there be a perfect map of it. If it is not truly unique, as you admit here, then the map could equally be a map of a number of different abstractions. This would mean that it is ambiguous, and less than perfect, by that fact.

Formalists take rules for granted. That's Platonism.

For example, if there are five people in a group, this situation is structurally similar to a set with five numbers. It does not mean that a person would be a number. — Tarskian

It's structurally similar because what constitutes "a group" is artificial, just like what constitutes "a set" is artificial. So you are just comparing two human compositions, the conception of a group and the conception of a set..

You could conceivably make a digital simulation of the entire universe and run it on a computer. This simulation of the universe would consist of just numbers. What you would see on the screen will be an exact replica of what you would see in the physical world. It would still not mean that this collection of numbers would be the universe itself. — Tarskian

If it's not the same as the universe, but a replica, then there is no limit to the difference which there may be between the two. I could show you a piece of paper and say that it's a replica of the universe. How would your proposed computer simulation provide a "better" replica of the universe? That's the thing about maps, they only show what the map maker decides ought to be shown.

A map of the world can help us understand the world. The map will, however, never be the world itself. — Tarskian

Then there's something more to reality than maps and the world which is mapped. There must also be something which makes one map "better" than another. This cannot be shown by the map nor is it a part of the world which is mapped.

Now, if it is about an abstract world, then the perfect map of such abstract world is indeed the abstract world itself. There is no difference between a perfect simulation of an abstract world and the abstract world itself. — Tarskian

This makes no sense. what would make an abstract world the perfect abstract world? Do you see what I mean? If there is no difference between the perfect simulation and the abstract world which is simulated, then they are one and the same thing. So now we have an abstract world which you claim is |a perfect simulation". What makes it perfect? It's just an abstract world like any other.

Then I would say that they misunderstand the foundations of the principles they believe in.

That is not true for every formalist. If you want to know why, look it up. — Lionino

I believe it is required to validate any formalist approach. If you think otherwise maybe you could explain.

In modern lingo, arithmetical theory, i.e. the theory of the natural numbers (PA), and the unknown theory of the physical universe exhibit important model-theoretical similarities.

For example, the arithmetical universe is part of a multiverse. I am convinced that the physical universe is also part of a multiverse.

The metaphysics of the physical universe is in my opinion nothing else than its model theory.

Model theory pushes you into a very Platonic mode of looking at things. In my opinion, it is not even possible to understand model theory without Platonically interpreting what it says. — Tarskian

If we don't differentiate between objects sensed and ideas grasped by the intellect. then there is nothing to prevent us from believing that the universe is composed of numbers. This is known as Pythagorean idealism, and often called Platonism. But Plato, along with Socrates, was very skeptical of this type of idealism, revealing its weaknesses. Aristotle, following Plato is often claimed to have decisively refuted Pythagorean idealism. He developed the concept of matter as a principle of separation between human ideas and the independent universe.

To reify is to 'make into a thing'. Numbers don't exist as objects, except for in the metaphorical sense of 'objects of thought'. — Wayfarer

The problem which I have encountered in this forum, is that there is an attempt by many, to represent numbers, and other mathematical objects like sets, as things which are subject to the law of identity. The law of identity states what it means to have an identity as a thing, and it is known to be applicable to material objects. By representing mathematical objects as subject to the law of identity, which applies to things, mathematical objects and material objects are implied to be of the same type, each having the identity of "a thing".

The result of this is that there are significant conceptual structures, set theory, and mathematical logic in general, which are based on the assumption that there is no difference between 'objects' of thought' and material objects. This leads to absurd ontologies like model-dependent realism.

It is my opinion that this conflating of the two is the reason why quantum observations are so difficult to understand, and quantum theory interpretations are many and varied. Within quantum theory there are no principles which would allow for a distinction between the material object and the 'object of thought' so that the two are combined in a confused model of wave/particle dualism.

I don’t think anyone should be forced to register for anything. — NOS4A2

Birth certificate? Driver's license? Social security? Taxation? What are you anarchist?

That doesn't make sense automatically because formalism is a program for foundations, platonism is an ontological claim. And idk what post of MU it is. — Lionino

Ontological assumptions are what foundations are made of, and Platonism provides the assumptions required for formalism, the idea of pure form.

Meaningless word games. The fingers on your hand are a physical instantiation of the number 5. Positive integers have the property that the smaller among them may be physically instantiated. 12 as in a dozen eggs, 9 as in the planets unless an astronomical bureaucracy demotes Pluto. That's one for the philosophers, don't you agree? The number of planets turns out to be a matter of politics, not math or astrophysics. — fishfry

I don't see what this all has to do with your claim that a concept like a number, 5, could have a physical instantiation . Fingers are fingers, and are therefore physical instantiations of fingers, not of numbers, not matter how many of them you have. Wittgenstein took up this issue in the Philosophical Investigations, showing why there is a lot more involved with learning a language than simple ostensive definition. Abstraction is very complex, and with complex concepts like number, an explanation of what it is about the thing which is being shown, which is being referred to with the word, is a requirement.

A person cannot simply look at the fingers on a hand and apprehend the concept 5. An explanation about quantity, or counting is required. The concept 5 is learned from the explanation, not from the ostensive hand, therefore the hand is not a physical instantiation of the number.

Judged by who? Politicians? Academic administrators? Philosophers? How about by their fellow mathematicians? That's the standard of what counts as math. — fishfry

It can be judged by anyone. The issue though, is that many, like yourself refuse to make such a judgement. You say that there is no truth or falsity to mathematical axioms, they are simply tools which cannot be judged for truth. Since mathematicians tend to think this way, they are not well suited for judging truth or falsity of their axioms. But I've shown how axioms can be judged for truth. If an axiom defines a word or symbol in a way which is inconsistent with the way that the symbol is used, then it is a false axiom.

So for example, if a mathematical axiom defines "=" as meaning "the same as", yet in applied mathematics the mathematicians use "=" to mean "has the same value as", then the axiom makes a false definition. This axiom will be misleading to any "pure mathematician" who uses it to produce a further conceptual structure with that axiom at the base, just like if anyone else working in speculative theories in other fields of science starts from a false premise. False propositions are fascinating, sometimes leading to theories which are extremely useful, because they are designed for the purpose at hand.

They're meta-false, as I understand you. They're not literally false. If the powerset axiom is false, you get set theory without powersets. You don't get some kind of philosophical contradiction. You are equivocating levels. — fishfry

Sorry, I don't understand what you mean by "meta-false". I am talking about "literally false". False to me, means not corresponding with reality. For example, if someone says that in the use of mathematics, "=" indicates "the same as", but in reality, when mathematicians use equations, "=" means "has the same value as", then the person who said that "=" indicates "the same as" has spoken a falsity. Do you agree that this would be an instance of "literally false"?

A model, not a description. Is that better? — fishfry

That doesn't help. Numbers form discrete units, and discrete units cannot model an idealized continuum. There is an inconsistency between these two, demonstrated by those philosophers who argue that no matter how many non-dimensional points you put together, you'll never get a line. The real numbers mark non-dimensional points, the continuum is a line. The two are incompatible.

So you can bet that Trump is going to use this attempt as a weapon against Biden, — Wayfarer

That's foregone, the moment the shot rang out:

Biden incited them to shoot Trump. Isn’t that how it works?

“We’re done talking about the debate, it’s time to put Trump in a bullseye."

- Joe Biden — NOS4A2

a mathematician is an explorer trying to find a path extending knowledge in a particular direction or discovering new directions. — jgill

I would say that this is a type of problem solving, wouldn't you? The problem being worked on is not necessarily a practical issue. Philosophy is like this too, as well as speculative theorizing, there is a wide range to the types of problems. Sometimes, problems are being worked on without any obvious practical implications.

I see an out. In this para you have stated your aim about the real numbers and the number 5. I don't think I have any interest in this topic. I know it's important and meaningful to you, but it isn't to me. Perhaps I'm to dim to grasp all these philosophical subtleties such as you raise. If so, so be it.

But secondly, and I'd be remiss if I didn't add, that I have formally studied the real numbers and the number 5. That doesn't make me right and you wrong, by any means. What it does mean is that I'm not likely to ever defer to your opinions about the real numbers or the number 5. — fishfry

Well, "the real numbers", and "5" being an instance of a real number, was your example. I agree that by some accepted principles of mathematics, the axioms of set theory, etc., 5 is an instance of a real number. This I believe to be the influence of Platonism which assumes that a number is an object. I disagree with this, and think that a number is a concept, and conceptions are quite different from objects. The way that one concept relates to another for example is completely different from the way that one object relates to another.

You might think that it doesn't matter whether a number is an object or not. You might think that within the confines of the logical system of "the real numbers", a number can be whatever the mathematician who states the axiom wants it to be. My argument is that numbers are used billions of times a day by human beings, and according to that usage there is some truth and falsity about what a number is. Therefore when an axiom makes a statement about what a number is, and it's not consistent with how numbers are actually used, the axiom can be judged as false.

When it suits my argument. I'm a formalist as well at times. — fishfry

Like I explained earlier, formulism is just a specific type of Platonism. It takes Platonist principles much deeper in an attempt to realize the ideal within the work of human beings, while other Platonists allow the ideal to be separate from human beings.

Mathematical philosophies are tools, nothing more. Conceptual tools, frameworks for thinking about the development and structure of math. They aren't "true" or "false," they're just models, if you will. — fishfry

Do you not look at mathematics, and mathematicians as real human beings, carrying out activities in the real world? If so, then don't you think that there is such a thing as true and false propositions about what those mathematicians are doing? If you follow, and agree so far, then why wouldn't you also agree that mathematical philosophies, as tools, or models, ought to be judged for truth and falsity? If a mathematical philosophy provides false propositions about what mathematicians are doing, offering this philosophy as a tool for understanding the structure and development of math, it is likely to mislead.

Problem solvers and theory builders. The theory builders don't solve problems at all. They create conceptual frameworks in which others can solve problems. — fishfry

As I explained to jgill above, theory building is a form of problem solving, it just involves a different type of problem. There are many different types of problems which can be categorized in different ways.

LOL. 1 + 1 and 2 are each representations of the same set in ZF, with "1" and "2" interpreted as defined symbols in the inductive set given by the axiom of infinity; and likewise "+" is formally defined. — fishfry

Yes, this is the problem, axioms of set theory are false, in the way described above.

BUT! Are you telling me that you don't believe in the physical instantiation of the natural number 5? Just look at the fingers on your hand. I rest my case. — fishfry

I said that 5 is not an instance of a real number. Also, I would say that the fingers on my hand are not an instance of the number 5, they are an instance of a quantity of five. You see, this is the problem of mixing up the ideal with the physical. "The natural number 5" is an ideal, a type of Platonic object called "a number". There is no physical instantiation of numbers, they are by definition ideal. So we need to refer to the use of "5" to see its meaning, and then we can find a physical representation for its meaning. In the context of usage of the natural numbers my understanding is that 5 represents a specific quantity, and the fingers on my hand provide an example of this specific quantity.

If we say that the numeral 5 represents a number, which goes by that name, 5, we have no meaning indicated to assist us in finding a physical example of the number five. All we have is that there is a type of thing called a number, and one of them is named 5. In order for numbers such as 5 to be used in practise, we need to provide something more, otherwise we're stuck with the interaction problem of idealism, these ideal things have no bearing on the real world. But if we give the number 5 further meaning, such as "a specific quantity", to allow it to be useful in the world, then the ideal, the number 5 becomes redundant, and completely useless. Why not just say that the numeral "5" means a specific quantity, and be done with it. Well I'll tell you why not. The numeral "5" is assumed to represent a number, 5, which is an abstract, Platonic object, for another purpose. The other purpose is mathematical philosophy, building structures and frameworks to be used as tools for understanding the development of math. However, as explained above, rather than assisting understanding, it misleads.

Why me? — fishfry

You are free to abandon me anytime you want.

If I'm understanding you, I agree. I don't think the mathematical real numbers refer to anything in the world at all. They describe the idealized continuum, something that we have no evidence can exist. — fishfry

If you truly believe this, then how would you validate your claim that the number 5 is an instance of a real number. Do you see that when you talk about "a real number", and "the real numbers", you validate the claim that "the real numbers" refers to a collection of individual objects? And that is contrary to what you say here. And do you see that in set theory, "numbers" also must refer to individual things, and this is contrary to being a description of "the idealized continuum".