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".

Your view of intentionality strips out the essence of intention and swaps it for causality; which of no use when we analyze the intentions of someone. — Bob Ross

I strongly disagree with this. Our most reliable access to a person's intention is through observations of the actions which that person causes. This is because often if we ask a person what their goals were when they acted they do not answer honestly, they might just make something up. Furthermore, the issue I described already is that the person often does not even accurately know one's own intentions when actions are carried out. This is the case with habit. This boosts the inclination to make things up. Therefore the most accurate way to analyze the intentions of someone is through the actions which they cause.

The intention is wrapped up, inextricably, with the action; and what is caused is an effect. — Bob Ross

Exactly, what is caused is an effect, the effect of the person's intention. The effects of a person's intention are observable and analyzable. Because of this we can produce a reliable science of intention. On the other hand, if we ask a person what one's goals were, we generally do not acquire reliable information.

What is intentional is what is related to the intention; and the intention is the end which is being aimed at. — Bob Ross

That is your preferred definition of "intention" because it is most consistent with the convention which associates intention with purpose. What I am saying is that if we define "intention" as the cause of one's actions instead, this provides us with a more scientific approach toward understanding purpose, aims, and goals. This is because, as I described in the last post, a person's actions are often not consistent with the person's goals. There are many reasons for this inconsistency, the force of habit, the force of mental illness, and the common example of faulty reasoning. In many cases, the person's determination of the means to the desired end, is faulty.

Because of these factors, which produce inconsistency or incoherency between one's actions and one's goals, and the fact that for moral/legal purposes the person's acts must be considered "intentional" even when the acts are not conducive to the desired end, we need to associate "intention" with the act rather than with the end which is aimed for. This indicates that "intention" ought to be associated with the act rather than the goal.

You can’t implicate someone as intentionally doing something they entirely did not foresee happening just because it resulted from an act of intention towards something else. — Bob Ross

Of course you can. For example, if someone thinks that burning the front lawn is a good way to cleanup the yard, and lights it on fire, then lighting the fire is intentional, regardless of whether the yard actually gets cleaned up, or if the whole neighbourhood gets burned. What is significant is that the fire started from an intentional act. What the person's actual goal was when lighting the fire is insignificant. And even if the fire is started by carelessly throwing away a cigarette, that is an intentional act, so the person is responsible for the damage caused by the fire.

I don’t understand what you mean by a “conscious act” which is not intentional (in the traditional sense of intentionality); and this seems to be the crux of your argument. If I consciously decide to do X, then I intentionally did X—even if X is the end I am trying to actualize. — Bob Ross

You don't understand because you restrict "intention" to the end on your understanding. Take my previous example of tossing a burning cigarette. Suppose the person just does it by habit, having no goal in mind when the action takes place. The person does not consciously develop the goal of tossing the butt, just does it. That is what I mean by a conscious act which is not intentional (in your sense). I believe there are many such haphazard, whimsical type acts, which the average person does every day, which cannot be said to be goal-directed. You might try to say that the act itself is the goal, but it cannot be truly expressed the way you say, "X is the goal", because there is no goal, just the urge to act in a specific way. So anytime the answer to "why did you do that", is "I felt like it", this is an example. It's very common in the way that people converse (speaking being a conscious act), many times we speak without thinking, no deliberation at all. And after speaking, in these situations, I cannot say that it was my goal to say what I said, it just came to my mind in the circumstances. Young children are also more prone toward acting this way, before they learn to control themselves.

Of course not. If I take your position seriously, then it would be; because your view attaches the intentionality of an act to all causality related effects. — Bob Ross

Yes, that is what I am arguing. We ought to associate intentionality with the act itself, which is the means, rather than with the end. Intention is a cause, and what is caused is action. Within the mind, there is a process of reason which links the end to the means, and the decision is made that a particular act is required to bring about a specific end. So the relation between the means and the end is a product of the mind, and this may be mistaken.

The convention (as derived from Aristotle) is to associate "intention" with the end. But when we analyze the nature of "an intentional act", we see that intention causes an act, which is understood to be the means to an end, and intention does not necessarily cause the end (as the case of mistakes). Therefore, we can establish a direct relation between intention, (as cause), and the means, but we cannot establish a direct relation between intention and the end. So despite the convention, which is to associate intention with the end, we'd have a more true representation if we associated intention with the means, instead.

Before we dive into this, I need you to define what you mean by “intention”; because you are using it in very unwieldy ways here. — Bob Ross

I am using "intentional" to signify something which is cause by an act of intention. "Intention" refers to that part of a being which causes activity, which is commonly represented as the free will. This is slightly different from the convention, which associates "intention" with the aim, or purpose of a freely willed act. I am using it in this way, in an attempt to demonstrate that we can produce a better representation of the nature of intention, if we associate it with activities rather than the common convention which is to associate it with a thing intended.

I referred briefly to human responsibility for one's acts and one's mistakes, because the fields which deal with these acts, morality and law, are more advanced in this subject. They recognize "intentional acts". Intentional acts are supposed to be acts which are guided by an aim, or purpose, directed toward an end, but since it's often difficult for an observer to identify the goal, we often do not require that in designating an act as "intentional" in the fields of morality and law. Plato would call the intended goal "the good" toward which the act is directed, and Aristotle termed it as "that for the sake of". This is the goal of the intentional act. Intentional acts then, are understood as directed toward those goods which appear to the mind of the being.

However, this perspective runs into a problem exposed by Plato, and later discussed more extensively by Augustine. This is the question of how a man can know what is good, yet act otherwise. Quite often, the human mind apprehends a good, but does not act accordingly. This creates the issue of what exactly does direct the conscious actions which are not consistent with the apprehended good. The common explanation is that the actions are directed toward some other good. But such an "other good" is often not identifiable, and this is very evident in the case of habitual actions. So when we associate "intention" with "the good", end, or goal, we have a whole category of actions from conscious agents which cannot be classed as "intentional". These are actions of habit, and apparently random acts, which cannot be associated with any goal or end.

That is the reason why I propose that we could obtain a better understanding of the acts of conscious agents if we associate intention directly with the act, rather than with the aim of the act.

The point is that what one knows is relevant to what one is aiming at. — Bob Ross

Yes, knowledge and the aim are closely related. Reason, of some sort, tends to determine the aim, and even the goals of confused or "irrational" people are determined through some sort of faulty knowledge. The problem though is that many acts carried out are not consistent with any reasoned goal. This was the argument Plato brought against the sophists who claim to teach virtue, insisting that virtue is a type of knowledge. There is a definite separation between virtue and knowledge because virtue requires control over those habitual acts which are carried out without guidance from a reasoned aim, knowledge.

Was is intentional is not solely about the causation that occurs from a given act: it is more fundamentally about what the person is aiming at. — Bob Ross

This is what I am disputing. You get that idea because the convention is to associate intention with the aim. But what I am saying is that this convention is based in a faulty description of intentional acts. When we stipulate, that to be intentional, it is required that the act is associated with an end, then we leave a whole lot of actions of the conscious agent which cannot be categorized. They are not caused by determinist causes, nor are they directed toward an identified goal. So, I propose that we bring these acts into the category of "intentional", and this requires that we change the meaning of "intentional" to include acts which are not directed toward a specific goal.

I just think you're working yourself up over nothing. I'm losing interest. Can you write less? This is tedious, I find nothing of interest here. — fishfry

If you desire to avoid the long posts, I think, by the end of my reply here, that I have isolated the primary point of disagreement between us. It is exposed in how you and I each relate to what is referred to by "the real numbers", and what is referred to with "5" in the context of "the real numbers". And further, how this relates to the extension/intension distinction.

Therefore, I think you might just read through my post and reply to the aspects which are related to this issue. However, the issue of what mathematics is, how you and I would each describe "what mathematicians do", might also be important and relevant.

Pure math is math done without any eye towards contemporary applications. That's a decent enough working definition. Mathematicians know the difference. — fishfry

The issue though, is that even supposedly "pure" mathematicians work toward resolving problems, and problems always have a real world source or else they are really not problems, but more like amusements. A mathematician working in pure abstractions works with abstractions already produced, and may not even know how real world problems have shaped the already exist abstract structure. Even if we attempt to step aside from existing conceptions, and 'start from scratch' as philosophers often do, we are guided by our intuitions which have been shaped and formed by life in the world. And intuition comes from the subconscious into the mind, so we cannot get our minds beneath it, to free ourselves from that real world base. And since it is from the subconscious, we have no idea of how the real world effects it.

Mathematics is whatever mathematicians do in their professional capacity. — fishfry

I agree, but the description of what mathematicians do, is very difficult to get an agreement on. It's not a circular definition, but a proposal of how to produce a definition. So to actually provide the definition of mathematics, we need that description. It will be very difficult for you and I to agree on such description. You will probably place as the primary defining feature, (the essential aspect), of what mathematicians do, as working with abstractions. I will say, that description is problematic because then we need some understanding of what an abstraction is, and what it means to "work" with this type of thing. This almost certainly will lead to Platonism because we've already assumed as a premise, the existence of things called "abstractions".

Therefore I look at what mathematicians are doing as "solving problems". That's what they do, and there is a specific type of problem which they deal with. You are most likely not going to like this proposal for a description of what mathematicians are doing, because it eliminates the distinction between "pure" mathematics and "applied" mathematics. In the way described above, there is no such thing as "pure" mathematics. However, my starting point has the advantage of applying equally to all mathematicians, by applying the initial assumption of pragmaticism. Instead of saying "mathematicians are working with abstractions", we say "mathematicians are working with symbols (language), to solve problems. This way we avoid the messy ontological problem of "abstractions" It is only when we start sorting out the different types of problems which mathematicians work on, do we get the divisions within mathematics.

This is a standard complaint. If math follows from axioms, then all the theorems are tautologies hence no new information is added once we write down the theorems. But that's like saying the sculptor should save himself the trouble and just leave the statue in the block of clay. Or that once elements exist, chemists are doing trivial work in combining them. It's a specious and disingenuous argument. — fishfry

This is not the point at all, and you are not paying respect to the difference between the two distinct fields, mathematics, and mathematical logic, so your analogy is not well formed. If the field of mathematics is represented by the sculptor, then the field of mathematical logic is represented by the critic. Whenever the critic mistakenly represents what the sculptor is doing, then the critic is wrong. When mathematical logic represents mathematicians as using = to symbolize identity, the logic is wrong.

We agreed long ago that 1 + 1 and 2 are not the same string; and many people have explained the difference between the intensional and extensional meanings of a string. Morning star and evening star and all that. — fishfry

Fishfry, wake up! Was it getting late there or something? There is no physical object involved! There is no star! I think we've been through this before. The intensional/extensional distinction is completely irrelevant in this case because everything referred to is meaning (intensional). There is nothing extensional, no objects referred to by "1+1", or "2". That is the heart of the sophistic ruse. This intensional/extensional rhetoric falsely persuades mathematicians. It wrongly misleads them due to their tendency to be Platonist, and to think of mathematical abstractions as objects. As soon as meaning is replaced by objects, then "extensional" is validated, the sophist has succeeded in misleading you, and down the misguided route you go. In reality, there is only meaning referred to by "1+1", and by "2", everything here is intensional, and there is nothing extensional.

This is why I was very steadfast on the previous issue, to explain that "5" is not "an instance of a real number". It is that type of nomenclature, that type of understanding, which leads one into allowing that there is a place for extensional definitions in mathematics. Really, "5" in that example is just a part of that conception called "the real numbers". It receives it's meaning as part of that conception. there are no extensional objects referred to by "the real numbers", and "5" is just an intensional aspect of that conception. When you apprehend "the real numbers" as referring to a collection of things, instead of as referring to a conception, then you understand "5" as referring to an instance of a real number, instead of understanding it as a specific part of that conception. Then you may be misled into the "extensionality" of real numbers, instead of understanding "the real numbers" as completely intensional.

What math teacher hurt your feelings, man? Was it Mrs. Screechy in third grade? I had Mrs. Screechy for trig, and she all but wrecked me. It's over half a century later and I can still hear her screechy voice. I hated that woman, still do. When I'm in charge, I'm sending all the math teachers to Gitmo first thing. — fishfry

Again, you are not distinguishing between "mathematics", and the "mathematical logic" which the head sophist preaches. One is the artist, the other the critic. My beef is not with mathematics (the art), it is with mathematical logic (the critic). I see mathematical logic as sophistry intended to deceive. And I will explain the reason why i say there is an intent to deceive.

Mathematics has a long history of exposing us to problems which we just cannot seem to solve. These are issues such as Zeno's paradoxes, and other apparent paradoxes discussed at TPF, which generally amount to problems with the conception of infinity, the continuity of space and time, etc.. What mathematical logic does, is create the illusion that such problems have been solved. So, the intent to deceive is inherent within the conceptual structure, which makes these problems solvable. It deceives mathematicians into thinking that they have solved various problems, by allowing them to work within a structure which makes them solvable. The problem though is that the basic axioms (extensionality for example) are blatantly wrong, and designed specifically so as to make a bunch of problems solvable, regardless of the fact that incorrect axioms are required to make the problems solvable.

Whatevs. I can't follow you. And I've already noted that the difference between pure and applied math is often a century or two, or a millennium or two. — fishfry

Future application is not the issue here. The issue is that mathematicians work toward problem solving, by the very nature of what mathematics is. The problems are preexistent. Therefore mathematics by its very nature is fundamentally "applied". If you remove problem solving from the essence of mathematics, then it would be random fictions. But mathematics is not random fictions, the mathematicians always follow at least some principles of "number", already produced.

Now what do I mean by "essentially the same?" Well now we're into structuralism and category theory. Sameness in math is a deep subject. I'll take your point on that. — fishfry

What I think, is that there is really no such things as sameness in math, and this is better described as a misleading subject. Mathematics actual deals with difference, and ways of making difference intelligible through number. Similarity is not sameness, but difference which can be quantified. To me, "essential the same" just means similar, which is different.

Even so, 5 is one of the real numbers. What do you call it if not an instance? What WOULD be an instance of a real number? — fishfry

This appears to be the substance of our difference, or disagreement. If you do not like long posts, we could just focus on this specific issue. The issue is whether "the real numbers" refers to a conceptual structure, or whether it refers to a group of things, numbers. I believe the former, and the fact that "numbers" is plural is just a relic of ancient tradition. From my perspective, "5", in the context of "a real number" is just a specific part of that conception. Then the relations are purely intensional, and there is nothing extensional here. If however, you apprehend "the real numbers" as referring to a group of things called "numbers", then "5" refers to one of those things, and there is the premises required for extensionality.

Explicity stated in any textbook in mathematical logic. — TonesInDeepFreeze

This is exactly the problem. Notice you refer to "any textbook in mathematical logic", rather than any textbook in mathematics. If you look at a textbook in mathematics, you'll find "=" defined in the way of my reference, "equals"... "indicates two values are the same". So there is a discrepancy between what "=" means in mathematics, and what "=" means in mathematical logic. And, since mathematical logic is supposed to provide a representation of the logic used in mathematics, we can conclude that mathematical logic has a false premise. The proposition of mathematical logic, which states that "=" indicates identity, or that it means "is" or "is the same as" in mathematics, is a false premise. This is a false representation of how "=" is used in mathematics. As I explained in other threads, if "=" indicated "is the same as", then an equation would be absolutely useless, because the left side would say the exact same thing as the right side. (Incidentally, this is what many philosophers have been known to say about the law of identity, it is a useless tautology). In ontology though we see the law of identity as a useful tool against sophistry like yours.

You agree with me about pure math. — fishfry

I agreed with you about "pure math", for the sake of discussion, so that we could obtain some understanding of each other. But I will tell you now, as came up one other time when we had this discussion, I do not agree that there is such a thing as "pure math" by your understanding of this term. So I agree that if there was such a thing as pure math, that's what it would be like. However, I think your idea of "pure math" is just a Platonist/formalist fantasy, which is a misrepresentation of what mathematics is. In reality, all math is corrupted by pragmatics to some degree, and none reaches the goal of "pure math". You criticize me to say, it's not a goal, it's what pure math is, but I say that's false, it is a goal, an ideal, which cannot be obtained. Therefore "pure math" as you understand it, is not real, it's an ideal.

I think the issue being exposed here is a difference of opinion as to what mathematics is. Since this is a question of "what something is", the type of existence it has, I think it is an ontological issue. Would you agree with this assessment? For example, the head sophist refers to "mathematical logic", and I find this defined in Wikipedia as the study of the formal logic within mathematics. So we have a distinction here between the use of mathematics (applied mathematics), and the study of the logic used by mathematicians (mathematical logic). "Mathematical logic" would be a sort of representation, or description, of the logic used in mathematics. What you call "pure mathematics", I believe would be something distinct from both, applied math and mathematical logic, as the creative process whereby mathematical principles are developed. But I think that this process is not really "pure", it's always tainted by pragmatics and therefore empirical principles.

The issue I have with the head sophist is with the way that mathematical logic represents the use of the = symbol as an identity symbol. In applied mathematics, it is impossible that "=" is an identity symbol because if both sides of an equation represented the exact same thing, the equation would be absolutely useless. This I've explained in a number of different threads. In reality, as any mathematics textbook will show, "=" means "has the same value as". Therefore we can conclude that any mathematical logic which represents "=" as an identity symbol is simply using a false proposition. When a "textbook in mathematical logic" states that "=" is an identity symbol, this can be taken as the false premise of mathematical logic.

You have conceded my point regarding math. I have no other point. — fishfry

I have conceded the point regarding what you call "pure math". However, I am now qualifying this concession to say that "pure math" is just an unreal ideal. There is no such thing as pure math. It's a term which people like to use in an attempt to validate their ideals. In reality though, such ideals are fiction, so all that I have really conceded, is that within the fictitious conception which you call "pure math", this is the way things are. Of course, I'm not going to argue about the way things are in your work of fiction, but I will argue about the way that your fiction bears on the real world.

Tens of thousands of professional pure mathematicians would disagree. — fishfry

Sure, there are thousands of people who might call themselves "pure mathematicians". In reality though, these people are not engaged in "pure mathematics", as I believe you understand this to mean. As I said above, all mathematics is tainted by pragmatics (applications), and there is no such thing as "pure" mathematics.

This is very evident in our discussion of the meaning of "=". In what you call "pure mathematics", we might say that "=" signifies "is the same as". This would remove the basic fact that what mathematicians work with are values. To make the mathematics "pure" we must remove this content, what the mathematicians work with, values. We remove the inherent nature of the thing represented by the symbols (i.e. that the symbols represent values) to allow simply that the symbols represent things without any inherent nature, no inherent content. Then we might claim the left side of the equation represents the exact same thing as the right. However, this type of equation would be totally useless. We could do nothing with an equation, solve no problems.

Furthermore, there would be a disconnect, an inconsistency between the mathematicians practising "applied" math, who use "=" to represent "is the same value as", and those "pure" mathematicians creating mathematical principles which were inconsistent with the applied mathematics. Since the supposed "pure mathematicians" actually produce principles which are compatible with, and are actually used in applied mathematics, we can conclude that the supposed "pure" mathematics is not really pure, and the principles they are using and developing do not really treat "=" as meaning "is the same as". That's just a misrepresentation, supported by the misrepresentation that these people are doing "pure" mathematics.

Any two set theorists will give {0, 1, 2, 3, 4} as the definition of 5. That's due to John von Neumann, who invented game theory, worked on quantum physics, worked on the theory of the hydrogen bomb, and did fundamental work in set theory. Now there was a guy who blended the applied with the pure. — fishfry

I can't say I understand everything you wrote following this, but it mostly makes sense to me. I'll have to work on these ideas of "mod 4", and "cyclical group".

Can you give an example? I might have not followed you. — fishfry

What I mean, is that if you recognize that two things are different from each other, then that difference has already made a difference to you (in the subconscious for example) by the very fact that you are recognizing them as different. So for example, if you see two chairs across the room, and they appear to be identical, yet you see them as distinct, then the difference between them must have already made a difference to you, by the fact that you see them as distinct. So to say that the difference between them is a difference which doesn't make a difference must be a falsity from the outset. We might even say that they are identical in every way except that they are in different locations, but this very difference is the difference which makes them two distinct chairs instead of one and the same chair.

A type of number. No, don't agree. Real numbers and complex numbers and quaternions are types of numbers. The real number 5 is an instance of a real number hence an instance of a number. It must be so, mustn't it? — fishfry

I knew you wouldn't agree, but i wouldn't agree that the real number 5 is an instance of a real number. The problem I think has to do with the statement "a real number". "The real numbers" is a conceptual construct in itself. This conception dictates the the meaning of "a real number". So in reality any supposed instance of "a real number" is just a logical conclusion drawn from the dictates of "the real numbers". In other words its not a distinct or individuated thing, which would be required for "an instance", it's just a specific part of "the real numbers". Can we agree that the real number 5 is a specific real number?

= Equal sign ... equals ... Indicates two values
are the same -(-5) = 5
2z2 + 4z - 6 = 0

https://www.techtarget.com/searchdatacenter/definition/Mathematical-Symbols

it is explicitly stated that '=' is interpreted as 'is' in mathematics. — TonesInDeepFreeze

Explicitly stated by you, the head sophist

Mathematics adheres to the law of identity, since in mathematics, for any x, x=x, which is to say, for any x, x is x. — TonesInDeepFreeze

Sorry Tones, but "for any x, x=x" does not say "for any x, x is x", unless "=" is defined as "is". And, in mathematics it is very clear that "=" is not defined as "is".

Not necessarily. If the side effect is not easily foreseen, then we typically don't consider it intentional; or we might say that it was intentional insofar as the person was aware that there was a chance of it happening and accepting those odds. However, in the case that it is foreseeable or was foreseen (with high probability)(all else being equal), then I completely agree it was intentional: it as indirectly intended, which entails it was not accidental.

You can't say some accidents are intentional: that's like saying some orange squares are not orange. — Bob Ross

I'm talking about things totally unforeseen. I agree that we do not commonly call them "intentional", but in the sense that they are the direct effect of the intentional act, just like the desired end is the direct effect of the intentional end, there is fundamentally no essential difference between them. That is why we are just as responsible for our mistakes as we are for our correct actions. Do you agree that you are responsible for your mistakes, as they are the results of your intentional acts?

The hammer hitting your thumb was not intentional whatsoever prima facie in your example. The act of swinging the hammer, intending to bring about the end of hitting the nail into something, was intentional. — Bob Ross

I don't agree with this. The first premise is that the act of swinging the hammer was intentional. Do you agree? You claim that the effect of the act can be separated from its cause, to say that the cause was intentional but the effect was not intentional. The point being that when things are set in motion by an act of intention, and we allow that more than just the immediate act itself is intentional, that an effect is also intentional, then we need consistency, and say that all the effects are intentional.

What we are talking about is misjudgment, mistake. The fact that a person misjudges the effects of one's actions does not make the effects any less intentional. It just means that the person made a mistake in judgement. A mistake in judgement does not remove intentionality from the act, nor does it remove intentionality from the effects of the act.

Now, let's say you foresaw that the hammer might hit your thumb and new this with 20% probability and still decided to carry it out: we would say that you intentionally swung the hammer knowing it may result in an accident, but we would NOT say that you intentionally caused that accident. Now, let's say you foresaw with a 99% probability that you were going to cause the accident instead of what you really intend, then we might say you intended it because of the probabilistic certainty that you had of bringing it about. It depends though, because we might say you are just stupid and didn't realize that it doesn't make sense to carry it out with that high of a probability; or we might say you are unwise (unprudent) for doing it anyways out of (presumably) passion or desire to hit the nail. — Bob Ross

This does not make any sense to me. A judgement as to the probability of success of one's intentional acts, is not useful toward determining whether the effect of that act is intentional or not. Suppose I flip a coin, and the probability is 50/50. No matter what the outcome is, that outcome was intended, because I flipped the coin for the purpose of having an outcome, and the particular outcome which occurs is irrelevant to that intent. Likewise, when I make any intentional act, the goal is that the act will have an effect. It's true that I desire a specific outcome, like when I bet on the coin toss, but the fact that one outcome is more desirable than others, does not make that outcome more intentional than the others. Does it make any sense to say that when I bet on heads, if it lands heads, that was intended, and if it lands tails that was not intended?

My main point is just that accidents, by definition, cannot be intentional. That's categorically incoherent to posit. — Bob Ross

I do not agree with this. I think that we simply misuse "intentional" to say that the desired outcome is intentional, and the undesirable outcomes are not intentional. Each effect is essentially the same, of the same type or category, the effect of an intentional act. It is inconsistent, and therefore incoherent, to say that one effect of the intentional act is intentional, and another effect is not intentional.

Now explain this to me ONCE AND FOR ALL. Are we talking about pure math and set theory? Or are we talking about the physical world of time, space, energy, quantum fields, and bowling balls falling towards earth? — fishfry

I don't understand you. I gave you an example of how equivocation of "same" has a considerable effect. Of course it has no effect in "pure mathematics", because by definition "pure" mathematics maintains its purity, and the purity of its definitions. Pure mathematics is not applied, and therefore has no effect in relation to the physical world where "same" means something else.. We live in the physical world, our cares and concerns involve the world we live in, it is impossible that anything in the fantasy world of "pure mathematics" could actually concern us. This is known as the interaction problem of idealism. However, in reality we apply mathematics and this is where the concerns are.

You seem to misunderstand the issue completely. You appear to understand that there is a difference between the use of "same" by mathematicians (synonymous with equal), and the use of "same" in the law of identity (not synonymous with equal). You said that this difference has no bearing on anything you know or care about. The things included in the category of what you know and care about, are not limited to principles of pure mathematics, because you live and act in the physical world. The law of identity applies to things in the physical world which we live and act in.

So, to make myself clear, I do not claim that there is a problem with using "same" as synonymous with equal, within the conceptual structures of mathematics. The problem is in the application of mathematics, as inevitably it is applied, and this use of "same" is brought into the world of physical activity, and taken to be consistent with the use of "same" when referring to physical objects. That is where the problem occurs. Sophjists such as Tones enhance and deepen the problem by arguing that the use of "same" in mathematics(synonymous with equal) is consistent with the use of "same" in the law of identity (not synonymous with equal).

You can not have it both ways. — fishfry

This is exactly the issue, the reality of the situation is that we do have it both ways. There are two very distinct ways for understanding "same". You can dictate "you cannot have it both ways" all you want, but that's not consistent with reality, where we have both ways of using the term. If you think that we ought to reduce this to one, (insisting "we cannot have it both ways"), the two cannot be combined, or reduced to one, because they are fundamentally incompatible (despite what the head sophist claims). This means that we have to choose one or the other. If we choose the one from pure mathematics, then we have nothing left to understand the identity of a physical object in its temporal extension. If we choose the one from the law of identity, then we simply understand "equal" as distinct from "same", and the problem is solved. Obviously the latter makes the most sense, and doing this would support your imperative dictate: "You can not have it both ways."

No. You don't understand how math works, and you continually demostrate that. — fishfry

It is very clearly you are the one who does not understand how math "works". Math only works when it is applied. "Pure mathematics" does nothing, it does not "work", as math only works in application. You are only fooling yourself, with this idea that pure mathematics is completely removed from the physical world, the world of content, and it "works" within its own formal structures. That is the folly of formalism which I explained earlier. To avoid the interaction problem of Platonist idealism, the formalist claims that mathematics "works" in its own realm of existence. But the claim of "works" is sophistic deception, and the formalist really digs deeper into Platonism, hiding behind the smoke and mirrors of the sophistry hidden behind this word "works". That is when the term "mathemagician" is called for.

You finally said something interesting. Is the 5 in your mind the same as the 5 in my mind? I think so, but I might be hard pressed to rigorously argue the point. — fishfry

I believe, the concept of "five" in my mind is completely different from, though similar to, the concept of "five" in your mind. There is a number of ways to demonstrate the truth of this. The first is to get two different people to define the term, and see if they use the exact same expression. Another way is to look at what "five" means in different numbering systems, natural, rational, real, etc.. Another is from the discussions of mathematical principles in general. There is always difference in interpretation of such principles. You and I have significant differences, You and Tones have less significant differences.

Nevertheless, the differences exist and are very real. There is a principle which I've seen argued, and this is to say that this type of difference is a difference which does not make a difference. Aristotle called these differences accidentals, what is nonessential. The problem with that expression though, "difference which does not make a difference", is that to notice something as a difference, it is implied that it has already made a difference. So this argument is really nothing other than veiled contradiction.

Anyway, this is the issue with identity, in a nutshell. When we ignore differences which we designate as not making a difference, and say that two instances are "the same" on that basis, we really violate the meaning of "same". The meaning of "same" is violated because we know that we are noticing differences, yet dismissing them as not making a difference, in order to incorrectly say "same". Therefore we know ourselves to be dishonest with ourselves when we say that the two instances are the same, by ignoring differences which are judged as not making a difference. So when you say that you think the 5 in my mind is the same as the 5 in your mind, I think that this is an instance of dishonesty, you really know that there are differences, and if pressed to argue such a claim, you'd end up in contradiction, dismissing the obvious differences as not making a difference.

Is an apple an instance of fruit? Apples don't have a peelable yellow skin. 'Splain me this point. By this logic, nothing could ever be a specific instance of anything, since specific things always differ in some particulars from other things in the same class. — fishfry

Right, particulars are instances, specifics are not. The concept "red" is not an instance of colour, it is a specific type of colour. A particular red thing is an instance of red, and an instance of colour, exemplifying both. The concept "apple" is not an instance of fruit, it is a specific type of fruit. A particular apple is an instance of both. The concept "5" is not an instance of number, it is a specific type of number. A group of five particular things is an instance of both.

When I arrive home in the evening, it makes quite a big difference to me if I return to the same residence or just one that's "equal" to it in value. — fishfry

Hey fishfry, do you not remember what you said to me? You said " I don't make a distinction between "same as" and "is equal to." In math they're the same. If you have different meanings for them, it does not bear on anything I know or care about." Now you've totally changed your position to say "it makes quite a big difference to me", if the taxi driver took you to a house which had an equal fare as yours, but was not the same house.

I think it would be more accurate to say "The apparent unintelligibility is due to a thing's matter or potential." — Ludwig V

I don't quite get what you mean here. Let's say there's something about reality which appears to be unintelligible. If we assign a name to that aspect, aren't we saying that there is actually something there which is unintelligible, and we've named it. This is to take a step further than simply that it appears as unintelligible.

I don't think that's quite right. It is true that if the lamp is on, it has the potential to be off, and if the lamp is off, it has the potential to be on. But that's not the same as having the potential to be neither off nor on. — Ludwig V

The point is that potential defies the laws of logic. That's why modal logic gets so complex, it's an attempt to bring that which defies the laws of logic into a logical structure.

The point I made, derived from Aristotle, is that whenever the lamp switches from on to off, or vise versa, there is necessarily a period of time during which it is changing (becoming). In other words, it is impossible that the switch from one to the other is instantaneous, and this is proven logically. In this 'mean time', the lamp is neither on nor off, and this defies the law of excluded middle. Dialethists would hold that it is both on and off, defying the law of noncontradiction.

Aristotle uses the concept of "potential" to explain his choice for defying the law of excluded middle rather than defying the law of noncontradiction. For him, the concept of "potential" is required to explain how something changes form having x property (being on), to not having x property (being off). "Potential" is a requirement of such a change, the thing cannot change without having the potential for change. However, this is a temporal concept, and the conclusion is that actualization requires a duration of time. So there is always a period of time between having x property (being on), and not having x property (being off).

What the lamp problem does not take into account, is that period of time between being on and off, during which it is changing. Assuming that the amount of time required to change from on to off, and vise versa, remains constant, then as the amount of time that the lamp is on and off for, gets smaller and smaller, the proportion of the time which it is neither, gets larger and larger. So at the beginning, when the time on and off are relatively long periods, the time of neither seems completely insignificant. But as the off/on actualization rapidly increases, the time of being on and off soon becomes insignificant in comparison to the time of being neither. The time of neither approaches all the time

A lamp, by definition, is something that is on or off, but not neither and not both. There are things that are neither off nor on, but they are not lamps and the point about them is that "off" and "on" are not defined for them. Tables, Trees, Rainbows etc. — Ludwig V

You only say this, because the time of change in which the lamp is neither on nor off is so short and insignificant that it appears to be nil. Aristotle demonstrated logically that it cannot be nil. So when we say things like "lamps are a type of thing which must be on or off, and cannot be neither", this is a statement about how things appear to be, and this facilitates much of our talk about such things. But when we get down to the way that things actually are, the way that logic tells us they must be, we can see that this way of allowing appearances to guide our speaking is actually misleading.

I don't think that's quite right. The LEM does not apply, or cannot be applied in the same way to possibilities and probabilities. "may" does not usually exclude "may not". On the contrary, it is essential to the meaning that both are (normally) possible - but not both at the same time. — Ludwig V

I don't understand this. If a thing neither has nor has not the specified property, the excluded middle principle is violated (unless it's an inapplicable category). Potential itself neither is nor is not, and that's why we say it refers to what may or may not be. So "may or may not be" refers to the property we judge as in potential, and this says it neither is nor is not attributable to the thing.