But a discrete thing is considered to be one thing separate (or at least separable) from all others. If it is composed of parts and this entails that it is not a discrete thing then it cannot be a unity, surely. — Janus

There is nothing about "discrete thing", which denies that the discrete thing can be made of parts. It is a unity and a unity may have parts. That it is bounded makes it a discrete thing. It is when we look at the parts as discrete things in themselves, that we put in jeopardy the unity of the original thing. To say that the parts are discrete things requires that we assume another principle to account for unity of the original thing. So it is by this other principle, the mereological principle, that the parts make up a whole. The nature of the mereological principle is what monists and dualists disagree on.

If we deny the need for a mereological principle we end up with apokrisis' systems approach. As a whole, or as a part, are two different ways of looking at the same thing. Whether it is related to a larger thing or to smaller things, determines whether it is a part or whether it is a whole. This denies the need for a mereological principle to account for unity, but a unity is just an arbitrary designation relative to one's perspective.

The traditional terminology for ‘discrete things’ is ‘particulars’, in distinction from ‘universals’. I think in the classical understanding, ‘particulars’ are only considered to be real insofar as they are ‘instances’ of universals; so for example an individual is an instance of the species. In fact the sense in which individual things can be considered real is one of the basic factors behind the whole discussion. I think we’re inclined nowadays to assume that individual particulars are the paradigm of what is real; this pen, that chair. But Greek philosophy was inclined to doubt that mere things, perishable as they are, ought to be considered real in their own right. — Wayfarer

In Aristotelian logic, "substance" is given to the individual, the particular. Substance is at the bottom, as that which validates the universals, and therefore is the most well known, the most real. This is evident in his law of identity, which puts the foundation of the entire logical structure in the identity of the thing, the individual.

If you have a division defined in terms of opposing limits, then you also get the continuous spectrum of possibility that lies between. — apokrisis

The problem I have with this, which I am trying to explain, is that if you place the opposing limits, within the same category, as "the continuous spectrum" which is assumed to be within that category, then these limits are not real. They are arbitrary because they are derived from what is observed as the maximum and minimum of that category. They are not derived from what is actually limiting that category. Once you allow that there is something real which is actually limiting that category, then the thing which is doing the limiting is necessarily outside of the category. Therefore the limits cannot be of the same category as the thing limited. If they were part of the same category, they wouldn't have the capacity to limit it.

MU accepts unbroken as an antonym of continuous, but not as a synonym of undivided. — apokrisis

I don't know what you mean by "unbroken as an antonym of continuous". But in case you haven't noticed, definitions are usually composed of defining terms, not synonyms. Red is defined as a colour, but this does not mean that "red" and "a colour" are synonymous. So your reference to synonyms and antonyms, whatever you are trying to say here, is completely irrelevant and is in no way a representation of what I said.

Is a discrete entity continuous within itself? — Janus

I doubt that very much. And the reason that I doubt it is that we know things to be composed of parts, and we know the parts of one thing overlap with the parts of another. For instance, there is air within my body. And atoms, which are supposed to be things over lap each other as molecules. So it doesn't appear likely that a discrete thing is even continuous within itself. I think it is highly unlikely that a discrete thing is in any way continuous, and that is why we separate these two as mutually exclusive. Apokrisis likes to create ambiguity in well defined categorical differences, and this ambiguity allows the separation between the categories to be dissolved in support of a monist materialism.

Right, I may have told you before that I don't find Stanford to be very helpful in their philosophical principles. First, they are not at all rigorous in their philosophical definitions and descriptions. And, I disagree with the physicalist perspective from which they formulate their definitions and descriptions.

My dictionary defines continuous as "unbroken, uninterrupted". And an entity is a distinct thing, which implies necessarily, boundaries. Accordingly, an entity, a whole, is necessarily a discrete thing. So if continuity is opposed to discreteness, as suggested by your Stanford entry, it is impossible under the law of non-contradiction, that an entity, a whole, which is a discrete thing, is also a continuity.

After some very superficial study of philosophy and religion I had the feeling that faith was nothing more than A=belief without evidence. Position A is, from all angles, completely irrational and so, clearly, anti-philosophical. — TheMadFool

It is very questionable what exactly "belief without evidence" means, and whether it is truly irrational. We must consider what it means for a belief to be justified. A belief may be justified through logical process, so if "evidence" means justifying the belief by means of the senses, then many beliefs are justified without evidence. Further, if something is told to us by a person who is believed to be an authority on the subject, then many people would agree that belief in what the person says is justified. But isn't believing what a person says, simply because that person is thought to be an authority on that subject, nothing more than having faith in that person?

I really don't understand this comment. I could draw you a unit circle, show you tangents and whatever else you need if you really want me to graph out the basis of trigonometry. That the measurement system is arbitrary (360 degrees as opposed to 100 degrees in a circle) hardly impacts the validity or usefulness of the conclusions. And, even to the extent that mathematics is abstract, it hardly puts it in the same epistemological class as religion. — Hanover

Without the measurement system, there is no procedure. You cannot proceed without accepting on faith, these arbitrary assumptions, the numerals. You could draw me circles, and whatever shapes you like, showing me how they are related, but these are useless without the numerals.

The best I can decipher this argument is that you're saying that the world's a complex, confusing place, and there are things none of us understand in the physical world, so it's just as acceptable to posit religious truths as explanations. — Hanover

The argument is that faith underlies all we do. To reject something simply because it is faith based, is an unjustified rejection.

The reason "2" means 2 is because someone declared it a while ago. How's that mysterious? The reason we refer to transubstantiation as "transubstantiation" is for the same reason. That's not where the mystery lies. The mystery lies in how bread becomes the flesh of a guy who died thousands of years ago. — Hanover

You haven't quite stated the analogy properly here. We interpret "2" not as 2, but as having a meaning, "2" has a meaning. The meaning is roughly one individual is grouped with another individual, to make a unit, and this unit of distinct individuals is signified by one symbol, "2". That is how I interpret "2", maybe you don't interpret the meaning in exactly the same way as I do, but we do not interpret the meaning of "2" as 2 because that is circular and it doesn't give us any meaning at all. Further, the reason why "2" has such a meaning is not because someone declared it as such, but because this belief is upheld, and this is faith.

You interpret "transubstantiation" as "bread becomes the flesh of a guy who died thousands of years ago". As is the case with "2", the reason why "transubstantiation" means this is because the belief that this is what it means, is upheld, and this is faith. You say that it's a mystery as to how bread becomes the flesh of a guy who died a thousand years ago. I say that it is a mystery as to how one individual is grouped with another individual to make one unit. Why are they one unit under the symbol "2", which is what is declared in mathematical proceedings, and they are not two distinct units, as the meaning of "2" indicates? Now how is your mystery any more mysterious than my mystery?

We can try to ascertain whether they correspond with reality or we can ascertain that the convention exists. — Benkei

So I go to a number of different Catholic churches and observe that the items are referred to as body and blood of Christ, so I ascertain that this convention exists. You perform your tests, and insist that the items are stale bread and bad wine. Why should I accept your unclarified claim that what you say "corresponds with reality", over the convention of the church, which are very clear. Your claim of "corresponds with reality" is just a covert appeal to convention with your definitions of bread and wine being nothing but convention. I am very suspicious of such covert activity so I prefer the Church's position where the role of convention is fully exposed, and not concealed by a claim of "corresponds with reality"

No problem. It's a busy time of year. Cheers!

I don't see any reason why Thomists would say that. — Wayfarer

This was Samuel's point, which I didn't disagree with.

My view (and I think the Thomists') claims that individuals are true identities as the starting point; and from there, we find genera (genus in plural apparently), that individuals participate in. — Samuel Lacrampe

It is an Aristotelian principle, the law of identity, a thing is the same as itself. This hands identity to the thing itself, as a particular, such that the identity of a thing is not the description of the thing, the description employing universals, because identity is particular to the individual.

After all the Bible states that 'God is no respecter of persons'; and 'He who loses his life for My sake, will be saved'. Christians are 'saved' not because of their personalities, but in spite of them. Of course that is bound to be a contentious claim, but in any case, I think you far overestimate the importance of the notion of 'the individual' to ancient and medieval philosophy, where it was hardly a matter of consideration for them; that only comes about with much later democratic humanism. — Wayfarer

I don't quite see how your reference to the Bible is relevant to the issue of "true identity". It is argued strongly by Paul, in the New Testament, that in relation to resurrection, the eternal, immortality of the soul, it is the individual person whose existence persists. And if you think about it, these concepts loose their meaningfulness when removed from the individual.

The "individual" is of extreme importance to Aristotelian logic, as is evident from his law of identity discussed above. It forms the basis for the concept of "substance", and substance is the grounding of all logic. Here's the first line of Ch.5 of Aristotle's "The Categories":

Substance, in the truest and primary and most definite sense of the word, is that which is neither predicable of a subject nor present in a subject; for instance, the individual man or horse.

We don't need time to discuss change in space. So, my point is that change, per se, isn't adequate for a well developed notion of time. We need a specific type of change which I referred to as cyclical change. Without the cycle of day-night, year, atomic cycles etc. we wouldn't be able to use the concept of time at all. — TheMadFool

I think we do need time to discuss a change in space. A change in space requires movement, which requires time. Imagine points in space lined up like your number line, 1,2,3,4. Without time there is no change. In order for change to occur something has to move from 1 to 2, or otherwise, and this requires time.

Open a dictionary, try using language on an everyday basis. No faith involved. Although admittedly your language use is getting increasingly idiosyncratic. — Benkei

Correctness in language use is totally faith. The fact that I can remove myself from good faith and get idiosyncratic if I want, demonstrates the reality of this. You seem to already recognize this so I don't see why I need to tell you.

Algebra and trigonometry do in fact have concrete references, and I agree that it's a poor way to teach to simply itemize the steps the students are to perform without offering an understanding as to why those steps must be performed. — Hanover

If you think that the reasons for making the particular steps which are made, in these mathematical proceedings having concrete references, then I think you are hallucinating. The reasons why the steps are performed, are complex, often ambiguous, and in no way constitutes a concrete reference; just like the Church's reasons for performing their rites cannot constitute a concrete reference. In mathematics, the reasons for the steps of procedure being as they are, are extremely vague, and sometimes completely arbitrary. That the circle has 360 degrees for example, is completely arbitrary.

The problem I have with transubstantiation is not that the teacher has failed to provide the underlying concrete basis for it, but it's that the teacher has specifically told me that it's a mystery. — Hanover

That these symbols, 1,2,3, etc., are the symbols which are used, to signify what they do, is just as much of a mystery, or more, as the mystery of transubstantiation. But that does not incline anyone to loose faith in the use of these symbols. So I really don't believe that it is the simple fact that transubstantiation is a mystery which inclines you to have no faith in it. I think that there is something else about it that you do not like, so you refer to this "mystery" as a scapegoat, an excuse to reject it. It's as if I didn't like mathematics for some reason, so I turn to the mystery of why "2" is used, and why "3" is used, and why all the other symbols are used, instead of some other symbols, as an excuse to reject the proceedings of mathematics for being based in something "mysterious". The very act of having faith is the means for accepting that which is a mystery. To withhold faith from everything which is a mystery would produce the ultimate skeptic. You don't appear like the ultimate skeptic, so I think your withholding of faith is not really because it is a mystery.

The argument is a resort to humility, to argue I should just accept there are certain things beyond my comprehension, and instead of smugly rejecting them, I should take pause and recognize it is my limitations that keep me from understanding it. — Hanover

The argument is that your rejection is unjustified. If you are so smug in your rejection, that demonstrating this to you requires humility, then the blame for this humility is your smugness, not the argument.

Q1) When something is undivided, is it:

A) Divided?
B) Continuous? — apokrisis

A) is excluded by the law of non-contradiction. To answer with B) would require definitions. If you define "undivided" as continuous you are begging the question. Furthermore, if you define "undivided" in this way, you have a contradiction in your question. Your question refers to "something". Therefore defining "undivided" in this way would imply that there is something which is continuous. The definition of "thing" is such that it is a discrete entity, so it is contradictory to assume a thing which is continuous.

Q2) When quantifying an amount of water, do we ask:

A) How many water is there?
B) How much water is there?

Q3) When quantifying an amount of apples, do we ask:

A) How many apples are there?
B) How much apples are there?

Q4: When you have fallen into a pit of logical incoherence, do we:

A) Keep digging?
B) Cease to dig? — apokrisis

I don't see the relevance of the rest of these questions Whether it is common vernacular to ask "how much water" or "how many water" doesn't seem relevant. Your method of argumentation continues to be an appeal to ambiguity, as is consistent with your habit.

And so this conversation ends with a lame insult like most. — Hanover

I'm sorry, I meant to make an illustration by analogy, not to insult.

The shared core argument you're making is the same flawed argument that gets dragged out in Philosophy 101 classes — Hanover

The argument is an argument from probability, it is not an argument from necessity. These are two different types of arguments applied to different types of subject matter, just like inductive and deductive are two different types of logic, used for different purposes. That the argument is a different type from what you are used to, does not make it a flawed argument.

When I was in high school I may have considered the principles of algebra and trigonometry as flawed because I was having difficulty understanding them. The lack of a concrete referent troubled me, so I could not proceed to the level of abstraction required because I was unwilling to accept the articles on faith alone, I needed to understand through concrete reference. The teacher did not provide concrete reference, because the time for concrete reference was grade school and I was supposed to be far beyond that. I now recognize that my unwillingness to accept these principles on faith did not make those principles faulty, but it did make me a bad mathematician.

Faith is one of the methods which we employ in our approach to the unknown. When we apprehend someone as authoritative we may be inclined to accept on faith what is given to us by that authority. Another method of approach is probability. When the solution to the problem at hand cannot be known, we judge the likelihood of success in various solutions, and proceed on probability.

Plato demonstrated that virtue is associated with how we approach the unknown. Courage for instance is an approach to the danger within the unknown, which involves a judgement of risk, in today's term, "probability". To judge all forays into the unknown as risky, leaves one without courage, cowardice. And inversely, to judge all such forays as without risk leaves one as rash. The capacity to judge such probabilities (risk) correctly is courage, and courage is a virtue. So Aristotle described virtue as the mean between the extremes.

If an individual is unwilling to accept the articles of faith, this person still requires an approach to the unknown, in order to maintain one's status as virtuous. That approach is the approach of probability, likelihood. When you reject the approach of probability, as you did when you said these arguments of probability are flawed, this makes you a bad philosopher, just like my rejection of the articles of faith made me a bad mathematician.

After you named it "the body and blood of Christ" we can run every conceivable test on it and establish that it's still stale bread and bad wine. So my statement actually corresponds to reality and isn't something "unseen" as it is a claim about the world as-is. — Benkei

After you run all your test, you still have the issue of what qualifies as "stale bread" and "bad wine", your definitions. This is necessary in order to make your judgement as to whether the test results are according to the definitions. That these terms ought to be defined in the way that you define them is something "unseen".

It appears we have no hope of understanding one another. I asked you how your statement was relevant, if it is at all. What you said doesn't seem to be at all relevant. Do you believe that it is?

Relevance?

Glad you agree. Maybe we've got a starting point then. Do you agree also that the discrete and the continuous are inherently incommensurable?

And yet all still capable of further sub-division apparently. And how can there be further division if there is nothing further that counts as the undivided? — apokrisis

Each unit is discrete. That a unit is potential divided into other discrete units does not imply any continuity. It implies that the unit is composed of discrete units. Where do you pull the continuity from out of your hat?

The shared core argument you're making is the same flawed argument that gets dragged out in Philosophy 101 classes every semester as proof against moral relativism: There must be absolutes because every culture shares the same basic moral truths. — Hanover

One of the first principles taught to you in philosophy class, and you dismissed it, without reason, as "flawed". Some people just weren't meant to be philosophers.

That's why I got out of mathematics, I couldn't grasp what they were teaching in algebra, so I knew mathematics was not my calling.. You can't grasp what they teach in philosophy, yet for some reason you still want to be a philosopher.

So how do you divide up a foot into inches unless there is some underlying continuity to be divided? — apokrisis

The foot, as well as inches, are the measuring units, there is no underlying continuity. Divide the inch into halves, quarters, however you wish, they are still all discrete units. Numbers are discrete units of value , and no matter how you divide them they will always be such. Any assumption that there is an underlying continuity is simply false, because as much as you assume that they are infinitely divisible, they always exist as discrete units. But the thing which they are applied to, to be measured, may be assumed to be continuous.

One second we are talking about units of measurement, the next about actual substantial objects out there in the real world? — apokrisis

I have been trying to maintain the categorical distinction. You have been switching back and forth at will, because you denied the categorical distinction in the first place. You want the degrees of difference to be in the same category as the hot and cold. That;s your most fundamental ontological principle, deny the categorical separation of dualism, and replace it with terms of dichotomy. This moves things which are inherently incommensurable, into the same category so you can proceed under the illusion that they can be related through mathematics. You want to compare apples and oranges.

Now this is the consequence of your ambiguous principles, you can't even determine which of these categories we're referring to at any particular time, because you've already synthesized them in principle.

So are these discrete units bounded lumps of continuity or not? — apokrisis

Of course not, that would be contradictory to say that a continuity has bounded lumps. If it has bounded lumps, it is not a continuity. This is simply a matter of avoiding contradiction.

What dichotomy properly defines your notion of "unit" here. — apokrisis

That things are defined by dichotomies is where I strongly disagree with you. This is the point I am making. Things are defined by description. According to the description, we may place classify the thing. The class is a universal. A universal itself may be defined by a dichotomy hot/cold, big/small, etc.,, but the individual thing, is not defined by a dichotomy. The "unit", being an individual thing cannot be defined by a dichotomy, it can only be described.

So now you are saying that a unit is a continuity chopped into discrete pieces? — apokrisis

No, that's not what I'm saying at all. I said that a continuity is measured by discrete units. This is the point I am trying to make, that the measurement is made with something categorically different from the thing measured. You put them together in some ambiguous mess.

Yes, I think this is about right. There are differences between religions, but there certainly is a shared mystical core in all of them. — Agustino

The shared core is one of the things which validates religion as a real thing. It is a real property of human existence. Likewise, as much as we are all very different, as human beings there is a "shared core", and it is the shared core which validates the claim that there is a single species called human being.

when you measure a degree of continuity, what else do you measure that against except a corresponding degree of absence of discreteness? — apokrisis

A degree is a discrete unit. By measuring a continuity in degrees, you are applying discrete units to the continuity. That is exactly my point, to make sense of things within one category, they must be related to another category. Your way of relating things only within the category leaves us with nonsense.

A is continuous to the degree it isn’t .....

Go on. Try to fill in the blank with a word that doesn’t mean discrete. — apokrisis

That of course is a statement of nonsense, as is your habit, stating nonsense to defend a nonsense metaphysics. If A is continuous then it is not discrete. To insert the word "degree" here is simply to insert unnecessary ambiguity, which is nonsense. If a thing is hot, then it is not cold. To say that a thing is hot to the degree that its not cold, is to replace a clear logical principle with an ambiguous one, allowing contradiction that the thing be both hot and cold, qualifying this with the ambiguity of "by degree".

Instead, what we do in reality, is assign a temperature to the thing. The degree is the temperature. The temperature is meant to be objective and any temperature in itself, is neither hot nor cold. But the temperature scale is related to something completely independent, separate, with standards of judgement as to which levels are to be interpreted as hot, and which as cold. Depending on the application, what is hot by one standard might be cold by another, but the independent standard allows us to avoid the nonsense of "it is hot to the degree that it isn't cold".

meaningless is really just semantics. I defined faith earlier in this thread as "the evidence of things unseen". When I say "remove faith" we are removing any evidence submitted for things unseen such as souls, God, miracles and transubstantiation. — Benkei

What about the meaning of words, aren't they things unseen? Or do you claim to have seen the body and blood of Christ? If you've taken part in the Eucharist, you have evidence that the items are body and blood of Christ, because you've seen them, and seen that this is what they are called. If you think that the words refer to something else, or that the items should be called something else, you are going on faith in something unseen.

If attempting to decipher the nature of reality, I rely upon my senses and reason and you rely upon the five books of Moses, surely you can see that we don't just have different foundational anchors, but they are of a significantly different type altogether. My point being that I am relying upon some fairly basic means of acquiring information, whereas you are relying upon some old book, and I therefore can say that we are not using faith in the same way. — Hanover

I don't see that we use "faith" in a different way. I would think that you have as much faith in modern books, like the stuff taught to you in schools, as you have in your senses, just like me. So for instance, you probably believe that things are made of molecules and atoms, though you don't sense them. And you probably believe things about the universe which you don't sense, and about historical things which you weren't there to sense. But I have very little faith. That's why I scour the books for consistency, reserving my faith for things which have been demonstrated to be deserving of faith. And, I believe that it is reasonable to have more faith in ancient books than modern books because they have stood the test of time, by demonstrating their consistency.

The thing about faith is that it is the means by which knowledge is passed from one person to the next without immediately testing that knowledge. If the knowledge turns out to be faulty, this will eventually be exposed, it will be dropped, and will not stand the test of time, like the geocentric universe. In relation to the vast amount of knowledge that was produced thousands of years ago, only a very small part has remained, the rest has been dropped because it wasn't really worthy of our faith in the first place. In relation to the vast amount of knowledge which is produced in the modern environment, we have no way of knowing which aspects will persist, and which will be dropped. Therefore the probability is much higher that the knowledge from ancient times is more deserving of our faith. Compare fragile ideas which have been in existence for two thousand years, with fragile ideas that were created yesterday. The person who created the ideas yesterday insist that they will be around for a long time into the future. Which do you think are more deserving of your faith?

It's clear that there are all sorts of religions worldwide with tremendous diversity among them, many thousands of years of old and many with hundreds of thousands and even millions upon millions of followers. Surely they can't all be right, which would indicate their being right has little to do with their success. — Hanover

The different religions have fundamental principles which are very similar, God, communion, good behaviour, etc., especially if you allow for the different social conditions within which they exist. And if they have similar fundamental principles, then your claim "surely they can't all be right" is unjustified. Atheists like to pick at accidental differences and say "see they're all different, they can' t all be right". But look at all the different people out there in the world. Would you say "see they're all different, they can't all be human beings"?

Of course people have faith and they have religious experiences. Yet neither faith nor religious experiences have anything useful to say about reality. You just get a "says you" "no says you" discussion that never ever goes anywhere. So take out faith and religious experiences and we can start talking about the things we both at least agree on exist. — Benkei

But faith is reality, you just admitted so much. And the "says you", "no says you" attitude is reality too. So it's nonsense to say "let's just remove faith from reality, and make this attitude go away, and then we can have a real discussion". A reality without faith is not real, therefore we have to deal with this attitude, it's very real. You can't assume that having faith in non-faith will make faith go away.

Sorry Samuel, I missed this post so I'm delayed in response.

My view (and I think the Thomists') claims that individuals are true identities as the starting point; and from there, we find genera (genus in plural apparently), that individuals participate in. This view allows for both individual forms and universal forms. — Samuel Lacrampe

I agree, individuals are true identities. The question here though, is where do universals come from. Are they something pre-existing which we discover, or do we create them within our minds? We all want to say that they pre-exist, and we discover them, because this validates as "real", our knowledge. It makes for well-grounded epistemology. The problem is that we make mistakes, we find out later that our universals were not accurate, so we change them. Then our complete system of universals appears like something changing, evolving, such that the pre-existing universals are only ideals which we strive for, but never completely obtain , and the reality of them is hard to justify.

Unless I misunderstood, it sounds like you claim that the whole, the universe, is the one and only true identity as the starting point; and then from there, associate individual things as the divided parts of the whole, like body parts are to one body. Where does the individual form fit in, if individuals do not possess true identities? Also, is your view pantheism? — Samuel Lacrampe

So we take the whole "the universe", as an individual, one. And as an individual it has true identity as one particular. But as the whole, of everything, it is also a true universal. Now the universal is grounded with true identity, true independent existence, as a particular. When we proceed to validate universals as true and real, now, we must proceed from that "One" to position each universal in relation to the One. So we might proceed to differentiate animate from inanimate for example. If we start from a particular individual, like the individual man, and assign a species "man" to the individual, then assign a genus, "animal", etc., we are proceeding in the opposite direction, creating the universals as we go, for that particular purpose. And the universals created are not necessarily real unless they are properly related to the true universal, the One.

Exactly. A good point to stop talking then and move on. — Benkei

The problem is that faith is something very real, it is just as real as the food we eat, and we all partake. That someone can't handle the proposition that faith is real, and we all partake, so we as good philosophers ought to try to understand it, doesn't make faith go away, it just makes that person a lesser philosopher.

My account was rather more general than that. — apokrisis

Your account was one of constraints, and degrees of freedom, which implies necessarily an agent which is to some degree free and constrained. So your description of past and future is the perspective of an agent, and therefore subjective. It tells us how past and future appear to an agent, but we need to get beyond that, and produce a description of what the difference between past and future really is. And this requires relating it to material existence, things which are not active agents, but have passive existence, and may be acted upon.

The maths of limits works. My approach explains metaphysically how it could in fact work. It explains in what sense there are limits to approach even if these limits could never be reached. — apokrisis

Sure the math works, but it doesn't explain what the limits are. Nor can it determine what the limits are. The limits are imposed on the mathematics by the rules of application, the axioms.

If one extreme of a dichotomy is defined by its "distance" from the other, then it is both possible always to be measurably moving towards one limit - by measurably moving away from the other limit - while also never arriving at this other limit, as then that would result in the nonsensical claim of having left the other limit "completely behind". The other limit would have to have vanished. And what then could measure a distance from it? — apokrisis

The point is that the limits are always determined by referring to something outside the system which is being measured. So the limits, by the very fact that they limit, must be outside, and therefore completely distinct form the thing limited. If there is no such real limited, then the entire scale is arbitrary and meaningless.

In other words, there must be a categorical separation between the scale, and the things measured by the scale or else the measurement is meaningless. Measuring things by comparing them to themselves, is completely meaningless. So we set up a scale where the limits are the "absolutes", and the absolutes are produce by relating the things to be measured to something completely different from the things to be measured. The limits must always be in a different category from the thing being measured by that dichotomy or else the measurement is meaningless. What makes the measurement meaningful is its relationship to something outside the category of the things being measured.

The past is the constraints on future degrees of freedom. The future is the remaining free possibility that the past hasn't managed to constrain. Of course the definition is reciprocal. — apokrisis

As I said, you have no description of the qualitative difference between what has already been, and what will have being in the future. What you express is the description of an agent at the present, who has constraints relative to the past, and freedoms relative to the future. You have no description of what it means to be constrained or to be free.

Here's an example. Say we have hot and cold, as dichotomous terms which define each other, with degrees of difference assumed to be "between" them. By defining hot with not-cold, and cold with not-hot, and degrees of difference, we have no description of those qualiies, what it means to be hot, or what it means to be cold. So if you proceed in this direction now, to define what it means to be hot, and what it means to be cold, you'll see a fundamental difference between them, such that hot and cold are completely distinct ideals which cannot be related through the degrees of difference. Hot and cold are discrete, while the degrees of difference are continuous.

In all such instances there is an incommensurability between the discrete (hot and cold, constraint and freedom) and the continuous (degrees of difference). Incommensurability is beyond the capacity of mathematics. So we have an incommensurability between the continuous existence of the agent at the present, and the two discrete things, constraints of the past, and freedoms of the future. That incommensurability cannot be grasped with mathematics.

Was that much of nature really revealed by an Aristotelian level of physics? — apokrisis

You're missing the point. Nature, with all of its various patterns, reveals itself to us, with the passing of time, it is not something that we reveal through applications of physics or mathematics.

So there are clear rules for forming proper dichotomies. It's not a matter of "perspective". It is an exact mathematical relation. — apokrisis

I don't think so. A dichotomy is a mathematical relation only if you define it that way. But there are fundamental differences which cannot be expressed as mathematical relations, such as the dichotomy between future and past, the difference between what has been and what has not yet come to be.

Mathematics reveals nature's fundamental patterns. — apokrisis

The patterns of nature are revealed to us before we apply mathematics to them. They are there, revealed to us, naturally. We apprehend them through sight, hearing, and other senses, in all their beautiful splendor, before we apply mathematics. The passage of time reveals nature's fundamental patterns to us, we apply mathematics in an attempt to understand them.

This is an example of the bad thought habit I just highlighted - turning a "soft" contrary into a "hard" contradiction. It is the reductionism you always complain about.

So it is not a problem that knowledge is structured by it having two poles of being - ideas and impressions, concepts and percepts, rationality and empiricism. — apokrisis

That's only a matter of perspective. The other perspective claims that making categorically distinct things, like the sensible and the intelligible (the particular and the universal, material and immaterial), into two poles of one category, with degrees of separation, is the real mistake.

It is an important fact that the best mathematical models of psychology support the view that ideas and impressions are not hard contradictions - a dualism - but only a soft or relative state of dichotomisation. — apokrisis

It is this form of idealism, the desire to make all things mathematical, which drives this mistake. So of course the mathematics will support it.

Yet natural philosophy rejects actual dualism. And science supports its immanent understanding of nature. — apokrisis

Natural philosophy does not reject dualism, it is only interested in the one aspect, the natural. It is metaphysics like yours, which attempt to bring the two categories of dualism into the fold of "natural philosophy", which was never developed with this intent, which fall into error.

I was struck by the simile of the raft being makeshift - twigs and the like 'being bound together' - so that it doesn't present 'the vessel' as being something of fine manufacture, you might say. In a way it's quite self-deprecating. — Wayfarer

I think it is important to understand the raft as something we must make ourselves, each one of us. The Buddha does not give you the understanding, what is given to you is just the means. If you want to get to the other side of the river, build a raft.

I never liked this parable of the raft. Largely because of the ending of "leaving the raft behind" instead of sending it back down the stream so that others may find it and use it to cross the river. An opportunity lost. — Agustino

But this is just the nature of understanding, it is something which each one of us has to create ourselves. It is not something which we can take, ready-made from someone else. So the raft can't be passed on. It's like Plato's cave people, the philosopher may feel the duty to go back and show the way to the people in the cave, beyond the reflections toward the true reality, but unless they have the will to follow, in the first place, they will think that the philosopher is crazy. So without the desire to cross the river, the raft is useless. And once one has the desire, the need for a raft is not an obstacle.

There is an abundance of leaves and twigs. — Wayfarer

That's the point, but the raft still has to be made, and each one of us has to make our own, as we forge our own understanding.

The whole parable is a category error, he's basically saying - if you agree with me that my teaching can be like a cumbersome weight, then you should let it go once it's served its purpose. — Inter Alia

Look though, the teaching can be nothing more than giving the student direction. And when the student follows the direction and gets to where the teacher is, the teacher can no longer give the student direction. To go forward from this point, the student must find a new direction, which will necessarily be contrary to the direction which brought the student to that point. It is not like there is one direction for us all, and we mark off the points as if we proceed always in a straight line, always in the same direction, straight toward some distant end. We choose goals, proceed until we get there, then choose a new one. We cannot assume that the direction we proceed from a goal will be the same direction as proceeding to that goal.

The raft represent the teachings - the teachings may now be useless to you now that you are enlightened, but send them down the river, someone who isn't enlightened may find them, and they will be of use to him/her. — Agustino

But the raft cannot directly represent the teachings, because the raft is something that must be built by the student. So the teachings may direct the student on how to build the raft, once the student has developed the desire to follow the teacher, thus helping the student get to the other side, where the teacher is, but the teacher cannot produce the understanding for the student. So the raft is the understanding itself, and this must be built by the student. When the understanding is produced, the teachings are no longer needed. The student cannot pass along one's own understanding (the raft) to others, only the teachings.

I think, that by definition, accidentals cannot enter into the universal. If the accidentals are part of the description, then the description is a description of a particular, and not a universal. That is what separates the particular from the universal, the accidentals.

To those participating I'd suggest that they, before moving on to particulars, try to agree on a single definition if this thread is to have any chance of moving forward. — Benkei

Now that's a pointless suggestion. The reason why we cannot decide whether transubstantiation refers to something real, is because we cannot agree on what the word means. If we came to an agreement as to what the word means, the discussion would be over.

There is no arguing against faith as it isn't reasonable to begin with based as it is on unfalsifiable assumptions. It's why I never substantively participate in philosophy of religion to begin with (which I think is akin to beating a dead horse). There's selection bias going on on both sides as to defining transubstantiation. — Benkei

The problem here, is that what a word means, or refers to, any word, is a matter of faith. You are adverse to arguing faith, as you've stated here, so you say "let's just agree on a definition, and get on with the discussion". But if we remove "faith" from this discussion, there is nothing left to discuss.

Fame corrupts the mind. It's unavoidable, almost to the point of absolutism. Necessity is the mother of invention (sorry Frank et al), and fame removes necessity.

Is there a good reason to believe that a lion would resolve the basic questions of ontology assembling any differently then we do? Individuals, classes, attributes, relations, function terms, restrictions, rules, axioms, events... Which one would the lion miss? For that matter, which one a neutron star would miss? — Akanthinos

You would think that the lion would recognize the difference between night and day for example, and this might enter into the lion's categorization as something recognizable to us. However, if this difference is completely unimportant to the lion, then the lion probably would not talk about it nor even recognize it. So I would think that such categorization is based in what is important to us, and the ability to communicate is dependent on a commonality of values. Therefore language gets structured so as to encourage such commonality, enabling itself.

Just consider action and direction to be accidental properties of potentiality. — apokrisis

I don't see how action and direction could be other than universals, and therefore they cannot be accidentals. Each of these is a relative term, referring to relations between things. And relations are described in no way other than through the use of universals.

Accidentals are the properties of particulars. So action and direction cannot be accidentals because what these words refer to is relations between particulars, which are described by universals, they do not refer to properties of particulars.

You want to judge rules as correct or incorrect without reference to rules? — Banno

That's right, we look for substance, things like reality, truth, and soundness, when judging rules as correct and incorrect. The point being that rules must be grounded in something, or else they're meaningless. So if following rules is what is correct, rather than the proper grounding of rules being what is correct, then we might just follow the rules right into the abyss of meaninglessness. That's why StreetlightX says above, that we can follow rules without "making sense".

And the "prime problem" is that Aristotle was focused on how actuality creates potentiality, rather than the more truly foundational issue of how potentiality creates actuality. — apokrisis

The thing is, Aristotle demonstrated that actuality is necessarily prior to potentiality. Potentiality will not produce anything actual unless it is acted on. So this act which acts on potentiality to produce something actuality must be prior to potentiality. That's why Aristotle focused on how actuality creates potentiality, because the inverse, how potentiality creates actuality is an impossibility. Potentiality cannot create anything unless it is acted on.

However then - a further now metaphysically speculative slant, as it is not quite yet mainstream science - we could see all nature ruled by semiosis. Even a plasma may have this irreducible structure in some meaningful sense. And so we would be able to track a continuity of kind (to some degree) as we go from living organisms back across the epistemic modelling divide to regard the simple material world again.

The advantage of this pan-semiotic view is that it would properly ground the phenomenon of living being in the world. It would articulate both what is the ontic difference, and also what is the basic dynamical causal mechanism “all the way down”. — apokrisis

The problem with this pan-semiotic view is that it is completely unsupported by evidence, and is actually contrary to the evidence. The need to assume such a principle, that plasma employs semiosis, which is contrary to the evidence, points to bad metaphysics. Even metaphysics which requires the assumption of God is better metaphysics, because at least God is supported by the evidence rather than contrary to the evidence.

How would you address the problem then? My way of using words is right according to my rules, and Michael's way of using words is right according to those rules. The two ways are very contrary, so they can't "really" be both right. You could claim to know the right way, and that both mine and Michael's are wrong, or you could side with one or the other, but that still wouldn't make your way any more right than either of ours, even if it were two against one. Furthermore, we can't appeal to pragmatics because my rules are good for my purposes and yours are good for your purposes. How would we determine which purposes are the right purposes? If we all insist that we are using words in the correct way because we are following our rules, how do you propose that we might compromise and find agreement? And if we do not find agreement, won't our ability to communicate be jeopardized?

I've shown you a cardinal's take on the matter here. — Michael

This is what you said there:

The body and blood of Christ are present in the sacrament by reason of the promise of Christ and the power of the Holy Spirit, which are attached to the proper performance of the rite by a duly ordained minister. — Michael

See, the presence of Christ is dependent on "the proper performance of the rite".

You don't seem to understand the difference between those who claim that transubstantiation is literal and those who claim that it isn't. — Michael

That's right, I look at this whole question of whether or not it is "literal" as a red herring, and nothing more. "Literal" is a vague, ambiguous term which holds no force in comparison with the law of identity which allows for the direct association of a symbol to an object. Am I "literally" MU, or is that just a name I call myself? When we are discussing the identity of an object, the question of "is it literal?" is not even relevant

The issue is whether or not it is correct, or right, for the Church to name (identify) the items as they do. It makes no sense to ask whether the items are literally what they are called, because it is implied that there is a direct symbolic relation between the words and the items, such that if the relationship were anything other than direct, it would not be an instance of these items having this name.

Although the latter is just a case of naming items, the former is a case of describing what a thing is (and open to being wrong). We're supposed to be talking about the former. — Michael

That we're "supposed" to be talking about a description of what a thing is, is your false presupposition. Descriptions refer to properties, and that's where I corrected you when we first engaged. Now you keep wanting to slip back into descriptions of what the thing is, as if that is what we are "supposed" to be talking about. It is not, we are talking about identity, not description. Is it correct for the Church to identify these objects as body and blood of Christ? You want to turn to descriptions of the objects, and a description of what "body an blood of Christ" refers to, in order to address this question. But this is not what we're supposed to be talking about, and it is completely irrelevant because of that, we are supposed to be talking about substance. Clearly we're not supposed to be talking about descriptions and this is made clear by the word "transubstantiation".

Look at the quote above. This is what is claimed. There is "the proper performance of the rite". There is the promise by Christ to appear, which is carried out by the Holy Spirit. That is the description. If it is true, as you seem to be insisting, that there is no presence of Christ, then one or both of these conditions must not have been met. Either the rite was not properly performed, or the Holy Ghost did not fulfill the promise of Christ. There is nothing else to describe.

I don't think we're talking past each other. I think he's just wrong, and not making any sense. — Michael

Thinking that the other person is not making sense is exactly what "talking past each other" is.

He seems to want to say that if it doesn't literally happen then it happens by fiat, which is ridiculous. — Michael

If, "proper performance of the rite", means "fiat" to you, then it happens by fiat. What you do not seem to recognize is that assigning identity to an object is an act of fiat. The proper performance of the rite is the act of fiat which assigns identity to the objects.

Your claim seems to be that these words, which are assigned to the objects for the means of identification, have a meaning (some sort of "literal meaning") other than the meaning which is created by the direct association of identification. Your argument seems to be that this "literal meaning" is inconsistent with the meaning created by direct association. I can only assume that the objects named by direct association do not appear to you to fulfill the conditions of your "literal meaning", and that is the basis of your rejection. But the Church has dealt with this objection, it is not a matter of appearance here.

Else I might as well argue that because I refer to him as being "wrong" and me as being "right" then ipso facto he is wrong and I am right. It's a bastardization of Wittgenstein's "meaning is use", which he seems to be pushing. — Michael

This is exactly the problem with "meaning is use". I am wrong because you say I am, in reference with your rules of usage, and you are wrong because I say you are, according to my rules of usage, and that's the way it is. Right and wrong are relative to our rules of usage so we may both refuse to compromise because we are both right. What recourse do we have but to appeal to God?