I agree. That takes it to the realm of the meaning of words: reality. — jgill

Right. I was recommended a book by Fooloso4 - again, a very difficult read - but I found this snippet which exactly described my original intuition as to what the Ancients were seeking through mathematical knowledge:

Neoplatonic mathematics is governed by a fundamental distiction which is indeed inherent in Greek science in general, but is here most strongly formulated. According to this distinction, one branch of mathematics participates in the contemplation of that which is in no way subject to change, or to becoming and passing away. This branch contemplates that which is always such as it is and which alone is capable of being known: for that which is known in the act of knowing, being a communicable and teachable possession, must be something that is once and for all fixed. — Jacob Klein, Greek Mathematical Thought and the Origin of Algebra

Bertrand Russell remarks, in the History of Western Philosophy, in his chapter on Pythagoras, that it is this combination of mathematics and mysticism which distinguishes the Western philosophical tradition from the Asiatic. It is also, one could argue, why the 'scientific revolution' occured in the West (contentious claims, I know.)

This kind of insight goes back to the Platonist distinction between the 'unreliable' testimony of sense, and the (supposedly) apodictic certainty of rational or mathematical reason. Of course there's been a lot of water under the bridge since, but I still feel there's an element of truth which has been largely forgotten. That's the thread I've been following.

Nice commentary. Thanks. :cool:

I disagree with him entirely-

The problem, though, is that this world is essentially full of junk. The vast majority of it is simply useless, and of no interest to anyone whatsoever. — Streetlight

There is no junk, there is only mathematical truth. An example is chess: Chess is a concept built on a few simple ideas and rules. Once these ideas exist chess exists, potentially, in its entirety. But this entirety contains good chess and 'bad' chess. All possible games of chess from genius to silliness. They exist because chess as a concept exists. If math exists all math exists potentially. Is there a difference between an actual Platonic realm (containing good math) and a potential Platonic realm (containing 'junk')?

the idea of natural numbers (1, 2, 3...). Rovelli basically asks: why does anyone think natural numbers are natural at all? We certainly find it useful to count solidly individuated items, but he notes that what what actually counts as 'an object' is a very slippery affair: "How many clouds are there in the sky? How many mountains in the Alps? How many coves along the coast of England?". — Streetlight

Very woolly thinking here. Numbers exist as an abstraction, there is no need to have 2 or 3 actual things to have numbers:
/ = 1
// = 2
/// = 3 etc.
If all mathematics exists then it is natural for our experience to awaken (induction) particular aspects of mathematics. eg. If there are sheep their multiplicity might awaken numbers in our intuition. If we lived without a need for numbers their existence might not have been awakened by our experience. But numbers would exist anyhow.

As for the Platonic realm - does it mean that the number 3 exists in some concrete reality or does it mean that in the depths of mathematical reality there is a potential for '3' to exist - depending on what events bring it into existence? That is, is there a mathematical potential, above our specific forms of math, that makes these forms of math possible? If we say mathematics 'exists' we have to be very clear on what we mean by 'exist'.

The concept of chess can exist without a single game of chess being played in 'real' terms. In this situation, does chess exist if it exists as a concept but no games are ever played? What is the difference between a game of chess that is played and one that is merely possible, because the concept of chess exists? I think the Platonic realm does exist in the sense that it makes all kinds of math possible but not necessarily realized. I don't think he is getting very far by making a distinction between math that we have become aware of and math that might have been if the world had been different.

Maybe the Platonic realm is God's Mind, which contains all possible forms of math in the way the rules of chess makes all chess games possible.

If math exists all math exists potentially — EnPassant

I think the Platonic realm does exist in the sense that it makes all kinds of math possible but not necessarily realized — EnPassant

This is an excellent point. Once a concept is defined within an existing framework of mathematics, in a sense all that logically flows from it is potential, awakened by diligent investigations and discovery. The question remains, When a new concept seems to appear out of nowhere, is that creation or discovery?

(I speak from personal experience, not philosophical conjecture)

As for the Platonic realm - does it mean that the number 3 exists in some concrete reality or does it mean that in the depths of mathematical reality there is a potential for '3' to exist - depending on what events bring it into existence? That is, is there a mathematical potential, above our specific forms of math, that makes these forms of math possible? If we say mathematics 'exists' we have to be very clear on what we mean by 'exist'. — EnPassant

:100: :clap: Well said. The way I put it is that numbers are real, but they're not existent in the sense that phenomenal objects are existent, but mainstream thought can't accomodate this distinction because there is no conceptual category for intelligible objects, in the Platonic sense.

Once a concept is defined within an existing framework of mathematics, in a sense all that logically flows from it is potential, awakened by diligent investigations and discovery. — jgill

The way I put it is that numbers are real, but they're not existent in the sense that phenomenal objects are existent, — Wayfarer

Yes, mathematical potential exists because our forms of mathematics exists - linear equations, set theory etc. So the question is, where is this potential? Is it merely inside our skulls or does it exist independently of the human brain? Is it universal?

The way I put it is that numbers are real, but they're not existent in the sense that phenomenal objects are existent, but mainstream thought can't accomodate this distinction because there is no conceptual category for intelligible objects, in the Platonic sense. — Wayfarer

You may have answered this earlier in the discussion, but my obvious question is: what do you mean by real? If you take a Kantian view of the matter, mathematical objects are universal, necessary, and objective. All good so far. But at the same time, this objectivity for Kant is possible only via the subject of experience, by means of the faculties of understanding and intuition. Rather than full-on objectivity, this might be closer to intersubjectivity, in that it's only objective within the realm of human subjects.

Doesn't this almost look more like mathematical psychologism than platonism? The latter would demand that mathematical objects are entirely independent of human minds, and Kant is not quite able to say that, no matter how much he'd like to.

So, do we bite the platonic bullet and assert that Kant underestimated the realness of mathematical objects, or do we retreat to the Kantian middle-ground?

You may have answered this earlier in the discussion, but my obvious question is: what do you mean by real? If you take a Kantian view of the matter, mathematical objects are universal, necessary, and objective. — Jamal

Excellent question. And the fact that this causes us to ask 'what we mean by "real"' is central to the whole matter. As you say, Kant is usually said to adhere to conceptualism, which is a kind of middle ground regarding universals. But my objection is that the rules of logic and arithmetic are the same for all who think. The paradoxical quality which this implies is that whilst they are independent of any particular mind, they can only be grasped by the mind. So they're mind-independent, in the sense of being independent of any particular mind, but only perceptible by reason. I think that's suggestive of the not-often-discussed philosophical attitude of objective idealism.

So again that raises the whole question of the nature of their reality. The usual response is

So the question is, where is this potential? Is it merely inside our skulls or does it exist independently of the human brain? Is it universal? — EnPassant

...because we're accustomed to thinking of what is real as being 'out there somewhere'. But notice that underlying this question is the implicit division of self-and-world - the sense that what is 'in here' (the activities of the mind) and what is 'out there' (the objective domain) are exhaustive of what is real. That is the implicit metaphysic of modern individualism.

Note 'Augustine on Intelligible Objects':

1. Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way; it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. Augustine concludes from these observations that intelligible objects cannot be part of reason's own nature or be produced by reason out of itself. They must exist independently of individual human minds.

2. Intelligible objects must be incorporeal because they are eternal and immutable. By contrast, all corporeal objects, which we perceive by means of the bodily senses, are contingent and mutable. Moreover, certain intelligible objects - for example, the indivisible mathematical unit - clearly cannot be found in the corporeal world (since all bodies are extended, and hence divisible.) These intelligible objects cannot therefore be perceived by means of the senses; they must be incorporeal and perceptible by reason alone. — The Cambridge Companion to Augustine

This is of course strongly and adamantly rejected by Rovelli and empiricist philosophers generally. Oil and water, because of its obviously theistic heritage and implications (after all, Augustine is said to be the 'third most senior Christian' behind only the Apostle Paul.)

So where I'm coming to is that number (etc) are real as 'structures within reason'. They're concepts, but not as the product of the mind. They are real as the constituents of reason, what Frege described as the 'laws of thought' (see Frege on Knowing the Third Realm, Tyler Burge.) They're how the mind orders and organises its experience in the world, but they're not themselves part of experience (transcendental in the Kantian sense.) Hence, real, but not corporeal. Which is why it is incompatible with naturalism and empiricism.

So the question is, where is this potential? — EnPassant

And the fact that this causes us to ask 'what we mean by "real"' is central to the whole matter. — Wayfarer

We might combine these two questions, to ask what does it mean to say that potential is real. The best way to look at this, in my opinion, is in respect to the nature of time. The reality of "potential" can be found to inhere within the way that time passes at the present. In relation to the future, there is real possibility as to what will come to be. This real possibility constitutes the reality of potential.

From the perspective of the living breathing human being, there is real possibility (therefore real potential) with respect to future acts. This real possibility is what gives human beings their power of choice, and their power to create. Mathematics is a great tool in exercising this power, therefore the reality of mathematics, in our understanding of it, is related directly to human potential.

But this opens the question of how human potential is related to real potential. We, from our human perspective, comprehend real possibility to inhere within the passing of time. The passing of time provides us with real possibility in future acts. However, it appears to us, that this real possibility requires the human mind to manifest its realness. How this could be the case is extremely difficult to grasp. How could it be that physical existence appears to progress in a completely determined manner of causation, yet somehow the human mind grasps real possibility to inhere within this determined world?

This is to say that the physicist will model the passing of time in the physical world as deterministic, and maybe even some would claim that this is a real representation of the world, yet this model excludes the reality of possibility. Then the philosopher will step in and say wait, human potential demonstrates real possibility. Now we get a sort of compromised understanding. The compromise is to say that there is real possibility, real potential within the world, but that real potential only exists as a property of the human mind, as ideas and conceptions within the human mind.

Any rigorous analysis of this compromised understanding will demonstrate that it is faulty. If the human being has real capacity to change things in the world, the potential for change must inhere within the world itself, in order that the world itself may be changed. And if the capacity to change things in the world is only a property of the human mind, it is an illusion, a falsity. The one perspective is that of free will. The other perspective is that of determinism. The compromised understanding is compatibilism.

:up: I quite agree. This is the core of an article I’ve frequently referred to that argues that there is a category of ‘res potentia’:

At its root, the new idea holds that the common conception of “reality” is too limited. By expanding the definition of reality, the quantum’s mysteries disappear. In particular, “real” should not be restricted to “actual” objects or events in spacetime. Reality ought also be assigned to certain possibilities, or “potential” realities, that have not yet become “actual.” These potential realities do not exist in spacetime, but nevertheless are “ontological” — that is, real components of existence.

This new ontological picture requires that we expand our concept of ‘what is real’ to include an extraspatiotemporal domain of quantum possibility,” write Ruth Kastner, Stuart Kauffman and Michael Epperson.

Considering potential things to be real is not exactly a new idea, as it was a central aspect of the philosophy of Aristotle, 24 centuries ago. An acorn has the potential to become a tree; a tree has the potential to become a wooden table. Even applying this idea to quantum physics isn’t new. Werner Heisenberg, the quantum pioneer famous for his uncertainty principle, considered his quantum math to describe potential outcomes of measurements of which one would become the actual result. The quantum concept of a “probability wave,” describing the likelihood of different possible outcomes of a measurement, was a quantitative version of Aristotle’s potential, Heisenberg wrote in his well-known 1958 book Physics and Philosophy. “It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.”

I think it’s the ‘realm of possibility’ and that it is a real realm, in a way analogous to ‘the realm of intelligible objects’.

I think it’s the ‘realm of possibility’ and that it is a real realm, in a way analogous to ‘the realm of intelligible objects’. — Wayfarer

I agree, and I see a problem with the determinist attitude. Describing activity in the physical world in terms of efficient causation has been a very useful and practical venture. The problem is that this descriptive format has limitations which the determinist ignores or denies. We find that within human beings there is an active mind, working with immaterial ideas, to have real causal affect in the physical world. Causation from the mind, with its immaterial ideas is described in terms of final cause (goals purpose and intent), choosing from possibilities, which is completely distinct from efficient causation.

So there is a very real need to recognize the limitations of "efficient causation" as an explanation of the activities in the physical world. And we need to accept the reality of the immaterial "final cause" as having real efficacy in the material world.

I agree, and I see a problem with the determinist attitude. Describing activity in the physical world in terms of efficient causation has been a very useful and practical venture. The problem is that this descriptive format has limitations which the determinist ignores or denies. We find that within human beings there is an active mind, working with immaterial ideas, to have real causal affect in the physical world. Causation from the mind, with its immaterial ideas is described in terms of final cause (goals purpose and intent), choosing from possibilities, which is completely distinct from efficient causation.

So there is a very real need to recognize the limitations of "efficient causation" as an explanation of the activities in the physical world. And we need to accept the reality of the immaterial "final cause" as having real efficacy in the material world. — Metaphysician Undercover

According to one of the two main accounts of causality, namely the perspectival "interventionist" interpretation, a causal model is a set of conditional propositions whose inferences are conditioned upon variables that are considered to have implicative relevance but which are external to the model, such as the hypothetical actions of an agent. These models, whose use is now widespread in industry and the sciences, are thus naturally "compatibilist" in conditioning all models inferences upon hypothetical or possible values of external variables that are considered to be chosen freely. So I presume you are criticising earlier historical conceptions of causality such as Bertrand Russells', which assumed a causal model to be a complete description of a system's actual dynamics (thus making cause and effect redundant notions).

What I don't follow is the relevance of a "final cause", unless it is surreptitiously being used to refer to an initial cause, i.e. a bog standard cause. For example, if I am working to build a shed in the back garden, what is the "final cause" of the shed here? Obviously my thoughts, goals and motivation throughout the project cannot be considered a literally "final" cause, which speculation notwithstanding, leaves the resulting actual shed as the only remaining contender for the final cause. Are you insinuating that the resulting shed caused me to build it? (which incidentally isn't likely to look anything like my imagined shed due to my terrible practical skills)

We might combine these two questions, to ask what does it mean to say that potential is real. — Metaphysician Undercover

I think chess is a good analogy. Once the concept of chess exists all possible chess games are given potential. Once a chess game is played (even in one's mind) that chess game becomes real.

According to one of the two main accounts of causality, namely the perspectival "interventionist" interpretation, a causal model is a set of conditional propositions whose inferences are conditioned upon variables that are considered to have implicative relevance but which are external to the model, such as the hypothetical actions of an agent — sime

Very illuminating, thank you. Also has relevance in quantum physics, I would think.

What I don't follow is the relevance of a "final cause", — sime

I'll let MU answer for himself, but I had thought the Aristotelian 'final cause' was 'the reason why x exists'. For instance, the final cause of a match is fire, as that is the reason why matches are made. That's also a good example, because the efficient cause of the fire is the match, which says something about the possible relationship of 'efficient' and 'final' causes.

Once a chess game is played (even in one's mind) that chess game becomes real. — EnPassant

I'm a follower of an excellent chess channel on Youtube, hosted by an ebullient Serb, Agadmator. He makes a point of saying, in every game, the point at which 'this position has never previously been reached before, from here on. it's a totally new game'. Usually happens around moves 8 -11. I guess databases must be used to identify that, but it serves once again to remind one of the infinite number of possible combinations of moves in Chess.

I think chess is a good analogy. Once the concept of chess exists all possible chess games are given potential. Once a chess game is played (even in one's mind) that chess game becomes real. — EnPassant

I think 'chess is the possibility-space (i.e. actuality) of all chess games and players are the potential realizers of all chess games' is clearer.

According to one of the two main accounts of causality, namely the perspectival "interventionist" interpretation, a causal model is a set of conditional propositions whose inferences are conditioned upon variables that are considered to have implicative relevance but which are external to the model, such as the hypothetical actions of an agent. These models, whose use is now widespread in industry and the sciences, are thus naturally "compatibilist" in conditioning all models inferences upon hypothetical or possible values of external variables that are considered to be chosen freely. So I presume you are criticising earlier historical conceptions of causality such as Bertrand Russells', which assumed a causal model to be a complete description of a system's actual dynamics (thus making cause and effect redundant notions). — sime

Look at it this way. The "variable" in the model described is a freely chosen act. But from the perspective of the agent, the chosen act is not a variable. It is known by the agent, chosen, and in that way determined. So to model the chosen act as a variable does not provide a good description of what a chosen act really is.

What I don't follow is the relevance of a "final cause", unless it is surreptitiously being used to refer to an initial cause, i.e. a bog standard cause. For example, if I am working to build a shed in the back garden, what is the "final cause" of the shed here? Obviously my thoughts, goals and motivation throughout the project cannot be considered a literally "final" cause, which speculation notwithstanding, leaves the resulting actual shed as the only remaining contender for the final cause. Are you insinuating that the resulting shed caused me to build it? (which incidentally isn't likely to look anything like my imagined shed due to my terrible practical skills) — sime

"Final cause" is the intent, the purpose. So it is exactly the case that your thoughts, goals, and motivation are literally the final cause of the shed. Whatever reason you had, whatever purpose you had in your mind, this is the reason why the shed was built. Therefore these ideas, as intent, are the cause of your actions, and by extension the cause of existence of the shed. This is the basis of the concept of "intent" in law, the decision to bring about consequences.

That is why "variable" does not serve as an adequate representation. The fact that you wanted a shed, and this motivated you to go out and built a shed, is the cause of the shed. And you could further specify the particular purpose you had in mind for the shed when you built it. The intent, purpose in mind, or "final cause", is not a "variable" in the coming into existence of the shed, it is the cause of existence of the shed

.

"Final cause" is the intent, the purpose — Metaphysician Undercover

:up: I think the whole idea of final causation was a casuality of the Scientific Revolution and the rejection of scholastic/Aristotelian ideas of causality. Note however Aristotle's Revenge by Edward Feser

I'm a follower of an excellent chess channel on Youtube, hosted by an ebullient Serb, Agadmator. — Wayfarer

Yes, I have looked at some of his videos. V. good.

I think the whole idea of final causation was a casuality of the Scientific Revolution and the rejection of scholastic/Aristotelian ideas of causality. Note however Aristotle's Revenge by Edward Feser — Wayfarer

I think that's right, that "Revolution" came along with the rejection of Aristotelian philosophy. It started when Galileo and others demonstrated faults in his physics. Then there was no need to teach his physics, and this attitude progressed through his other topics, and eventually even his logic was removed from the standard curriculum.

As a part of his physics, "final cause" was an early casualty. It was completely removed from the field of physics, as irrelevant. The social sciences, such as law, replaced "final cause" with "intention". Now, "intention" retains the status of "final cause", as causal. But in as much as intention is seen as causal in law, this is far removed from physics, so the relationship between these two types of causes, efficient cause and intention, is not very well upheld in any discipline.

Because of this, we have no accurate representation of intention as a cause in the physical world, physics using "efficient cause". There is intention in law, where it is implied that intention is a cause, and there is efficient cause in physics, where it is presumed that there are no other forms of causation. As a result, intention is commonly comprehended as a form of efficient causation. Then there is no understanding of "final cause" at all, in any scientific discipline.

You can see this from sime's reply. The idea that thoughts and goals caused the existence of the shed is off-handedly rejected, because it is inconsistent with the understanding of "cause", as efficient cause. After this off-handed rejection, sime is left with the incoherent proposition 'the shed caused me to build it', as a representation of final cause.

"Final cause" is the intent, the purpose. So it is exactly the case that your thoughts, goals, and motivation are literally the final cause of the shed. Whatever reason you had, whatever purpose you had in your mind, this is the reason why the shed was built. Therefore these ideas, as intent, are the cause of your actions, and by extension the cause of existence of the shed. This is the basis of the concept of "intent" in law, the decision to bring about consequences.

That is why "variable" does not serve as an adequate representation. The fact that you wanted a shed, and this motivated you to go out and built a shed, is the cause of the shed. And you could further specify the particular purpose you had in mind for the shed when you built it. The intent, purpose in mind, or "final cause", is not a "variable" in the coming into existence of the shed, it is the cause of existence of the shed — Metaphysician Undercover

I understand Aristotle's definition of a 'final cause', but it makes no sense to me to muddle such "final causes" with the "causes" meant by the modern scientific definition of "causes" that refer to experimental inventions that go on to produce measurable effects. Especially considering the fact that 'Final Causes' are reducible to iterative evolutionary or adaptive feedback loops between an agent or population and their environment that are understandable in the bog-standard "initial cause" sense.

'Final causes' might be reasons with cognitive significance but imo reasons and causes are best kept apart, for they don't obey the same logic.

I understand Aristotle's definition of a 'final cause', but it makes no sense to me to muddle such "final causes" with the "causes" meant by the modern scientific definition of "causes" that refer to experimental inventions that go on to produce measurable effects. — sime

You don't seem to understand causation sime. There is no scientific definition of cause. Cause is a philosophical concept.

You don't seem to understand causation sime. There is no scientific definition of cause. Cause is a philosophical concept. — Metaphysician Undercover

I think that's misleading and somewhat inaccurate. It is true that causation didn't undergo strict formalisation until the twenty first century, economists being among the earlier pioneers of causal modelling in the twentieth century, and that causation is still undergoing formalization in tandem with the brother concepts of probability and temporal logic. Nevertheless, there has been a rapidly converging consensus in both the scientific community and industry in recent decades to the formal identification of causes with particular variables of a probability model, that if intervened upon by the actions of an experimenter, are expected to produce observable changes in the correlations among variables that lie "downstream" of the intervention. See Judea Pearl for an authoritative account.

Causal models merely express the concept that doing something leads to observations that otherwise wouldn't occur. Unlike Russell's conception, the modern meaning of causality is counterfactual. Causal models essentially define causes as being 'initial' with respect to the causal orders they define or describe, making "final causes" an oxymoron in the sense of the causal order.

Nevertheless, causal models have nothing to say regarding the order and linearity of time itself unless their variables are given additional temporal parameterization. All that they demand is that causes are considered to be controllable preconditions of their effects, not that causes are necessarily temporally prior to their effects in some absolute sense, which might well be considered a matter of perspective.

...and that causation is still undergoing formalization... — sime

If this is true, it's proof that there is no formalized definition of "cause".

And, since there are two distinct principal types of causation, efficient and final, there will never be an acceptable formalization of causation until the relationship between the two is represented properly. Formalization of one principal type of causation while excluding the other principal type of causation does not give a true formalization.

Causal models merely express the concept that doing something leads to observations that otherwise wouldn't occur. — sime

This is exactly why a formalization is impossible, and causation will always be philosophical rather than scientific. This provides no basis toward understanding the cause of "doing something". So, a person does something and this causes something which otherwise wouldn't occur. If we want to know whether the thing which otherwise wouldn't have occurred is intentional, or accidental, we need a much better principle than this. And if you claim that this is irrelevant to "causation", all that matters is whether the thing otherwise wouldn't occur, you fail to properly represent "final cause" in your formalization, and you provide no principles for excluding accidents from our actions. However, it's quite obvious that the effort to exclude accidents is very important.

Causal models essentially define causes as being 'initial' with respect to the causal orders they define or describe, making "final causes" an oxymoron in the sense of the causal order. — sime

The use of "final" in "final cause" seems to be misleading you. "Final" is used in the sense of "the end", and "end" is used in the sense of "the goal" or "objective". The terms "end", and "final" are used when referring to the goal or objective because the intentional cause is what puts an end to a chain of efficient causes when looking backward in time. So if D caused E, and C caused D, B caused C, and A caused B, we can put an end to that causal chain by determining the intentional act which caused A. It is called "the end", or "final" cause because it puts an end to the causal chain, finality.

Take a chain of dominoes for example. We look at the last fallen domino and see that the one falling prior to it caused it to fall. Then the one prior to that one caused it to fall. When we continue to follow this chain of causation, we find the intentional act which started the process, and say that this is "the final cause", because it puts an end to that causal chain. The terminology is derived from our habit of ordering things from the present, and looking backward in time, so that the causes nearest to us at present appear first, and the furthest are last.

Nevertheless, causal models have nothing to say regarding the order and linearity of time itself unless their variables are given additional temporal parameterization. All that they demand is that causes are considered to be controllable preconditions of their effects, not that causes are necessarily temporally prior to their effects in some absolute sense, which might well be considered a matter of perspective. — sime

This I do not understand at all. The fact that accidents are still considered to be caused, demonstrates that causes are not necessarily "considered to be controllable preconditions". Furthermore, I've never heard of a causal model which allows for a cause to be after its effect. You simply create ambiguity here by saying "in some absolute sense" because the principle of relativity of simultaneity allows that from the perspective of different frames of reference, the temporal order of two events may be reversed.

The fact that you say the cause is a "precondition" of the effect, implies a temporal order in itself. So to say that causes are not necessarily temporally prior to their effects is blatant contradiction whether or not you qualify this with "in some absolute sense".

If this is true, it's proof that there is no formalized definition of "cause".

And, since there are two distinct principal types of causation, efficient and final, there will never be an acceptable formalization of causation until the relationship between the two is represented properly. Formalization of one principal type of causation while excluding the other principal type of causation does not give a true formalization. — Metaphysician Undercover

But "Final causes" are representable in terms of bog standard causation without invoking teleological purposes, as demonstrated by reinforcement-learning algorithms that train a robot to implement "goal seeking" behaviour via iterative exploration and feedback . In this case, one might say that the "final cause" of the trained agent's behaviour is the trained evaluation function in the agent's brain that maps representations of possible world states to their estimated desirability. In other words, the final cause refers not to the actual goal-state in the real world that observers might colloquially say the learning agent "strives towards", but to the agent's behavioural policy and reward function that drive the agents behaviour in a mechanistic forward-chain of causation from an initial cause in a manner that is teleologically blind.

The agent's actions are not being "pulled" by the goal in any literal sense, so I am at a loss as to the incentive for mixing up purposes which refer to behaviour that converges towards a goal state, and causation which makes no reference to goal states.

This is exactly why a formalization is impossible, and causation will always be philosophical rather than scientific. This provides no basis toward understanding the cause of "doing something". So, a person does something and this causes something which otherwise wouldn't occur. If we want to know whether the thing which otherwise wouldn't have occurred is intentional, or accidental, we need a much better principle than this. And if you claim that this is irrelevant to "causation", all that matters is whether the thing otherwise wouldn't occur, you fail to properly represent "final cause" in your formalization, and you provide no principles for excluding accidents from our actions. However, it's quite obvious that the effort to exclude accidents is very important. — Metaphysician Undercover

If you accept the distinction between purposes and causes, then there is no case for the concept of causation to answer to regarding the distinction between intentions and accidents. For that's purely a matter of teleology and not causation.

The use of "final" in "final cause" seems to be misleading you. "Final" is used in the sense of "the end", and "end" is used in the sense of "the goal" or "objective". The terms "end", and "final" are used when referring to the goal or objective because the intentional cause is what puts an end to a chain of efficient causes when looking backward in time. So if D caused E, and C caused D, B caused C, and A caused B, we can put an end to that causal chain by determining the intentional act which caused A. It is called "the end", or "final" cause because it puts an end to the causal chain, finality. — Metaphysician Undercover

A is at the beginning :) Either a "final cause" is used to refer to a bog-standard initial cause that implies none of the teleological controversy commonly associated with aristotolean "final causes", else "final cause" refers to a teleological concept such as a purpose that is defined in relation to a goal state that is external to an agent's brain and that plays no causal role in the agent's behaviour, despite the fact the agent's behaviour converges towards the goal state.

Take a chain of dominoes for example. We look at the last fallen domino and see that the one falling prior to it caused it to fall. Then the one prior to that one caused it to fall. When we continue to follow this chain of causation, we find the intentional act which started the process, and say that this is "the final cause", because it puts an end to that causal chain. The terminology is derived from our habit of ordering things from the present, and looking backward in time, so that the causes nearest to us at present appear first, and the furthest are last. — Metaphysician Undercover

I suspect you are deviating from the commonly accepted notion of "final cause". The whole point of the "finality" in "final cause" is to imply that teleological concepts are necessary for explaining the effects of causation, which isn't the case in the dominoes example; teleology is explainable in terms of purposeless causation, as AI programmers demonstrate. But causation isn't explainable in terms of teleology. To mix up the concepts leads to confusion.

This I do not understand at all. The fact that accidents are still considered to be caused, demonstrates that causes are not necessarily "considered to be controllable preconditions". Furthermore, I've never heard of a causal model which allows for a cause to be after its effect. You simply create ambiguity here by saying "in some absolute sense" because the principle of relativity of simultaneity allows that from the perspective of different frames of reference, the temporal order of two events may be reversed. — Metaphysician Undercover

Which demonstrates the point i was trying to make, that what we call the "temporal order" has to be distinguished from the "causal order". That A causes B but not vice versa, doesn't necessitate that A occurs before B in every frame of reference. Also recall the time-symmetry of microphysical laws, models of backward causation etc.

But "Final causes" are representable in terms of bog standard causation without invoking teleological purposes, as demonstrated by reinforcement-learning algorithms that train a robot to implement "goal seeking" behaviour via iterative exploration and feedback . In this case, one might say that the "final cause" of the trained agent's behaviour is the trained evaluation function in the agent's brain that maps representations of possible world states to their estimated desirability. In other words, the final cause refers not to the actual goal-state in the real world that observers might colloquially say the learning agent "strives towards", but to the agent's behavioural policy and reward function that drive the agents behaviour in a mechanistic forward-chain of causation from an initial cause in a manner that is teleologically blind. — sime

As I explained already, this does not give a true representation of "final cause" because it provides no real basis for a distinction between consequences which are intended, and consequences which are accidental. In other words, if final cause was truly determinable from an agent's behaviour, all accidental acts by the agent would necessarily be intentional acts.

If you accept the distinction between purposes and causes, then there is no case for the concept of causation to answer to regarding the distinction between intentions and accidents. For that's purely a matter of teleology and not causation. — sime

Exactly, and that's why the model fails. Final cause is teleological purpose, by definition. You give me a model without purpose and teleology therefore your model models something other than final cause.

A is at the beginning :) Either a "final cause" is used to refer to a bog-standard initial cause that implies none of the teleological controversy commonly associated with aristotolean "final causes", else "final cause" refers to a teleological concept such as a purpose that is defined in relation to a goal state that is external to an agent's brain and that plays no causal role in the agent's behaviour, despite the fact the agent's behaviour converges towards the goal state. — sime

Why do you think that "purpose" ought to be defined in "a goal state that is external to an agent's brain"? Obviously, the goal which motivates (causes) one to act is within the agent's mind, and nowhere else. Furthermore, the truth and reality of acting toward goals is that such actions are not always successful. So the external state which is brought into being (caused) by the agent's actions is not necessarily consistent with the goal which motivated the action. Therefore the only true representation of the motivating factors (causes), must be to represent what is in the agent's mind.

I suspect you are deviating from the commonly accepted notion of "final cause". The whole point of the "finality" in "final cause" is to imply that teleological concepts are necessary for explaining the effects of causation, which isn't the case in the dominoes example; teleology is explainable in terms of purposeless causation, as AI programmers demonstrate. But causation isn't explainable in terms of teleology. To mix up the concepts leads to confusion. — sime

You "suspect" something, but according to what I've stated above, you are obviously quite wrong in your suspicious mind. "Final cause" was proposed as a means toward understanding the purpose behind intentional actions, as the cause of these acts. It's obviously not intended as a means toward understanding the effects, because the effects are plainly observable and do not require teleology.

Take Aristotle's example. Why is the man walking? To be healthy. The action is walking, the cause is the man's desire to be healthy. Whether or not the man actually is healthy or becomes healthy from walking doesn't even enter the scenario. We see him walking, we ask for the cause of him walking, and it is his idea (goal), to be healthy, which is the cause. We cannot judge teleology from the effects because often the person's ideas and beliefs are incorrect. Therefore the effects do not properly reflect the cause in a logical way. The man might become ill from walking, and we would never know that the cause of him walking was to be healthy, unless he told someone this.

Which demonstrates the point i was trying to make, that what we call the "temporal order" has to be distinguished from the "causal order". That A causes B but not vice versa, doesn't necessitate that A occurs before B in every frame of reference. Also recall the time-symmetry of microphysical laws, models of backward causation etc. — sime

Since temporal order is what defines causation, separating the two only renders causation as unintelligible.

As I explained already, this does not give a true representation of "final cause" because it provides no real basis for a distinction between consequences which are intended, and consequences which are accidental. In other words, if final cause was truly determinable from an agent's behaviour, all accidental acts by the agent would necessarily be intentional acts. — Metaphysician Undercover

Firstly, what makes you think that there is an objective matter of fact as to whether an effect was intended or accidental? Secondly, if there are such facts, then what do those facts consist of?

If we narrowly interpret the meaning of an "intention" as referring only to the agent's internal state, , then intentions as such cannot be teleological, for the agent's actions are explainable without final causes.

So in order for intentions to be considered teleological, one must consider both what is going on inside the agent as well as the environmental effects that the agent's behaviour produces, - effects which play no causal role in the agent's history of decision-making. Yet this understanding of 'intentionality' as a type of relationship between the agent's behaviour and the environmental biproducts of his actions, in turn implies that the agent is fallible with regards to knowing what his intentions are. For who now gets to decide what the agent truly intended?

Note that the problem of "Inverse Reinforcement Learning" is the problem of inferring an agent's overall goals from a history of the agent's behaviour, including the environmental consequences it's actions. It is a chicken-and-egg paradox; In order for observers to estimate an agent's overall goals given a history of it's behaviour, they must assume that the effects of the agent's actions were in accordance with it's intentions, that is to say, they must assume that the agent is an expert who understands his environment. But how can it be known whether the agent is an expert? Only by assuming what the agent's goals are :)

This implies that teleological concepts are either semantically or epistemically under-determined.

Since temporal order is what defines causation, separating the two only renders causation as unintelligible. — Metaphysician Undercover

Yes, if taken in the very hard sense of "separation". I'm referring to the fact that different observers from different perspectives, each of whom controls different variables, might have conflicting views as to what was the cause/intervention and what was the effect in a given situation.

Suppose Alice believes that if she presses button A, then a distant observer Bob will press Button B, otherwise Bob won't press button B. No other information is assumed.

Her causal belief might be represented by A => B.

Logically, this is equivalent to asserting NOT B => NOT A.

Therefore, in the event that Alice decides not to press the button, i.e. that event NOT A occurs, shouldn't Alice be open to the possibility that her decision not to press A was the effect of Bob deciding on NOT B 'before' Alice made her decision?

Posited examples of backward causation look a bit like teleology, but are categorically different. ,

Just saw this, but have to say excellent post. Clear and interesting.

Would be nice to have decent mathematical skills to delve into this topic with more detail, but, I suppose basic arithmetic already offers plenty of food for thought.

If we narrowly interpret the meaning of an "intention" as referring only to the agent's internal state, then intentions as such cannot be teleological, for the agent's actions are explainable without final causes. — sime

Have a glance at the wikipedia entry on the word teleonomy. It is a neologism coined in 1958 by a biologist to accomodate the awkward fact that virtually everything in biology is goal-directed, while trying to differentiate it from the Aristotelian 'teleology', a boo-word for modern science.

Furthermore, there's been an increasing recognition of the significance of telos and teleology in biology, with Aristotelian ideas being re-considered. An idle search of Aristotle and DNA will return some interesting papers on that subject.

Thanks! I was terrible at school maths, much to my later regret in life, but the point is philosophical rather than arithmetical - as jgill says, many maths educators are not the least interested in the philosophical question.

as jgill says, many maths educators are not the least interested in the philosophical question. — Wayfarer

I must admit that in my old age one philosophical issue does interest me: where does the set of potentials created by a "new" concept or discovery reside? And what triggers actualization in the arena of mathematical knowledge? My mathematical interests have always been in infinite compositions, and I see a structure therein that might model this process. :cool:

Wasn't trying to single you out - It was just some remarks you made earlier in the thread . (Did I mention Charles Pinter to you before? You can find his website here https://charlespinter.com/ . He has many publications in mathematics and has recently published what I consider an excellent book, not strictly speaking on philosophy, but with many interesting philosophical implications, Mind and the Cosmic Order.)