Mind-independent empirical nature for Husserl is this relative product of constitution, a mere hypothesis. — Joshs

By investing the objective domain with a mind-independent status, as if it exists independently of any mind, we absolutize it. — Wayfarer

The attempt to conceive the universe of true being as something lying outside the universe of possible consciousness, possible knowledge, possible evidence, the two being related to one another merely externally by a rigid law, is nonsensical ~ Husserl.

That could have come directly from the lecture by Swami Sarvapriyananda in the other thread, 'The Indisputable Self'.

Hello, I come from the topic that talks about quantum physics and consciousness. I find what is said in the OP very interesting. My position is the following:

I would say that an impossibility of perception is not an impossibility of the perceived object. Think, for example, of a triangle. Think about the Pythagorean theorem which tells us something about a type of triangles. Now let's think about two people who have knowledge about that theorem and both people accept its universal truth. If the perspective adds something extra, this something extra cannot be the same for the two different perceptions and perspectives that each person has. And here comes the question: what does perspective add in each case? Does it add anything that would affect the theorem in its objective sense, to be different in each case?

Well, in both cases it doesn't add anything that we can say is a property of this type of triangle. With this example we can deduce that the objective properties of things, the being of things, is not reducible to subjective experience, whether understood as perspective. A judgment, therefore, if it hopes to be true, must exceed the order of perception and perspective.

Now let's think about two people who have knowledge about that theorem and both people accept its universal truth. If the perspective adds something extra, this something extra cannot be the same for the two different perceptions and perspectives that each person has. And here comes the question: what does perspective add in each case? Does it add anything that would affect the theorem in its objective sense, to be different in each case? — JuanZu

Interesting question. But is the Pythagorean theorem subject to perspectives? In other words, how would an individual perspective or opinion be relevant to the Pythagorean theorem?

But there are many other kinds of matters where perspective might be relevant. Consider complex historical questions for example. There might be levels of complexity which a particular individual is familiar with and which result in their ability to arrive at a superior analysis of the subject.

we can deduce that the objective properties of things, the being of things, is not reducible to subjective experience — JuanZu

I don't think I've claimed in the OP that the objective properties of things are reducible to subjective experience. What I'm claiming is that experience even of apparently mind-independent things has an irreducibly subjective ground.

As for the 'being' of things, it is an open question as to what kinds of entities are beings. I take it that organisms are beings in a way that inanimate things are not, although that is a different topic to this thread.

Well, in both cases it doesn't add anything that we can say is a property of this type of triangle. With this example we can deduce that the objective properties of things, the being of things, is not reducible to subjective experience, whether understood as perspective. A judgment, therefore, if it hopes to be true, must exceed the order of perception and perspective. — JuanZu

The Pythagorean theorem makes the two perpendicular lines of a square as in commensurable. This is known as the fact that the square root of two is irrational. Because of this irrationality we cannot conceive of "this type of triangle" as a real object, with real "objective properties". There is inherent within this supposed object, "this type of triangle", a fundamental irrationality.

You seem to have a restricted concept of a “real object.” It is also not clear to me how you deny that the Pythagorean theorem tells us anything about right triangles. "Something about X" means that we are pointing out a property of X. In this case, an equality between the parts that constitute the object called "Right Triangle".

But there are many other kinds of matters where perspective might be relevant. Consider complex historical questions for example. There might be levels of complexity which a particular individual is familiar with and which result in their ability to arrive at a superior analysis of the subject — Wayfarer

But doesn't the historian present himself in a clearly theoretical attitude? I mean, the historian tries to affirm something about some historical moment. Is it not a fortiori an intention of truthfulness? The historian carries out a judgment, which jumps squarely into the field of transcendental validation with a claim of superiority over other views and perspectives. He aspires to universality and the neutralization of his perspective as opinion (doxa) and finally establish an impersonal statement about a state of things.

You seem to have a restricted concept of a “real object.” It is also not clear to me how you deny that the Pythagorean theorem tells us anything about right triangles. — JuanZu

I did not deny that the Pythagorean theorem tells us anything about right angle triangles. What I clearly said is that it demonstrates to us is that this type of triangle is not a real object. If you do not agree with the reasons I gave for this conclusion, then you could have simply said so.

"Something about X" means that we are pointing out a property of X. In this case, an equality between the parts that constitute the object called "Right Triangle". — JuanZu

The problem is that there is no such equality between the parts, hence the irrational ratio between the two legs. This irrational ratio is known as the square root of two. If the proposition states that the two legs are equal then the straight distance between the two defined points, known as the hypotenuse, is an indefinite distance, unmeasurable. It is said to be irrational. This indicates that in actuality there is an incommensurability between the two legs which are assumed to be equal, such that they cannot actually be equal. The proposition that they are equal, forces the logical conclusion that the hypotenuse is indefinite, irrational, therefore the proposition that they could be equal must be rejected as illogical.

The problem is that there is no such equality between the parts, hence the irrational ratio between the two legs. This irrational ratio is known as the square root of two. If the proposition states that the two legs are equal then the straight distance between the two defined points, known as the hypotenuse, is an indefinite distance, unmeasurable. It is said to be irrational. This indicates that in actuality there is an incommensurability between the two legs which are assumed to be equal, such that they cannot actually be equal. The proposition that they are equal, forces the logical conclusion that the hypotenuse is indefinite, irrational, therefore the proposition that they could be equal must be rejected as illogical. — Metaphysician Undercover

But isn't that just for the case where the length of each leg is 1?

On the other hand, I would like to know what you mean by "Real Object."

But isn't that just for the case where the length of each leg is 1? — JuanZu

That is the proposed equality. When the two legs are proposed as equal, the problem of incommensurability arises. Therefore I propose that we ought to conclude that they cannot actually be equal.

On the other hand, I would like to know what you mean by "Real Object." — JuanZu

Let's say that a real object is something which has a description which is logically consistent. If a logical problem in the description of the object, such as contradiction, is evident, then the described object cannot be a real object. So the logical problem with the right angled object is the incommensurability of the two sides, as explained above. This logical inconsistency indicates that the object described cannot be a real object.

We find a very similar problem with "the circle". The square and the circle are two very distinct ways of representing two dimensional "objects", two straight lines at an angle, or a curved line. Both have a very similar logical problem. There is also another similar problem which arises from the distinction between a one dimensional line, and a zero dimensional point. What I propose is that what we ought to conclude is that the "dimensional" representation of objects is logically flawed, and therefore does not accurately represent "real objects".

Now I understand. In that case the equality would be rather an approximation between the value of the sum of the square of the legs and the value of the hypotenuse that connects them. As an asymptotic approximation, if it is valid to say so. This value of the square root of the sum of the squares of the legs would be closer –closer than anything– to X, with X being an irrational number.

On the other hand, you call a real object one that is logically consistent. I, however, regarding the case, would speak of a qualitative incompatibility in the objective nature of the right triangle as an object. Adding the term "Real" or "not real" would not make much sense once we consider it this way.

This value of the square root of the sum of the squares of the legs would be closer –closer than anything– to X, with X being an irrational number. — JuanZu

In my opinion you have this inverted. The value of the square root of the sum of the legs is something indeterminate, a number which cannot be expressed. We might signify this with X, but X then signifies a value which is impossible to determine, and therefore impossible to express numerically. That's probably why pi is called "pi" rather than expressed as a number. It cannot be expressed as a number. The irrational number is our attempt to express this value, which is close to what is signified by X, but not X.

On the other hand, you call a real object one that is logically consistent. I, however, regarding the case, would speak of a qualitative incompatibility in the objective nature of the right triangle as an object. Adding the term "Real" or "not real" would not make much sense once we consider it this way. — JuanZu

It was not a matter of adding the word "real", it was a matter of describing what makes an object real what constitutes "realness", or "objectiveness". The issue was how do we get from stated properties, to the conclusion that the thing with those properties has real, objective existence. My proposal was that to be a real object the stated properties must be logically consistent. So the "qualitative incompatibility" you speak of would exclude the "objective nature" of the triangle, leaving it as something other than a real object.

Expressible... It is expressible. But in an anexact and generalized way. It is not a value that confuses or leads to ambiguity [If I want to determinate the value of the hypotenuse given the value of two legs, I obtain an specific value and not a random one every time ]. It is not just any value and can be located on the real line. In Cartesian terms it is "clear and distinct." This X, however, is objective, since it is properly deduced from the relationship between two parts of a right triangle.

In my opinion the term "Real" has no place in the discussion because a thing like that, a thing like a triangle simply "gives itself" and presents itself to us as an object of study, without being able to be reduced to a psychological act. To say that there is an incommensurability in its being does not add to or take away anything from the fact that it is presented and given to our knowledge and has effects on it. That is why it is objective, since an internal relationship can be established, whether one of incommensurability, which tells us what a triangle like this – is.

Recall that Euler's postulates weren't given in relation to a system of numbers; he took lines and points to be primitive concepts. Relative to his informal axiomatisation, the length of a hypotenuse is "real" in the sense that it is a constructible number, meaning that it can be drawn using the practical method of 'straightedge and compass', which is algebraically expressible in terms of a finite number of mathematical field operations.

When it is disputed that a hypotenuse has a "real length", it is when geometric postulates are used to interpret Euclidean space in relation to a fixed Vector-space basis. The irrational points of a Euclidean space aren't extensionally interpretable unless the basis of the underlying vector-space is rotated so as to transform those irrational points to rational values, which also leads to previously rational-valued points to become irrational. So the problem of incommensurability is really about the fact that it isn't possible to represent all points finitely at the same time, which implies that Euclidean Space cannot serve as a constructive logical foundation for geometry.

The obvious alternative is to follow Alfred North Whitehead in 1919-1920, and abandon classical Euclidean topology for a 'point-free topology' that refers only to extensionally interpretable "blobs", namely open-sets that have a definite non-zero volume, whose intersections approximate pointedness . Then it might be possible to extensionally interpret all such "blobs" in relation to a fixed basis of topological description in a more constructive fashion, meaning that extensional ambiguity is handled directly on the logical level of syntax, as opposed to on the semantic level of theory interpretation.

In my opinion the term "Real" has no place in the discussion because a thing like that, a thing like a triangle simply "gives itself" and presents itself to us as an object of study, without being able to be reduced to a psychological act. — JuanZu

This is what i disagree with. I think that any instance of the conception of a triangle actually does reduce to a purely psychological act. If you assume that it "presents itself" to us, you need to ask how it does this. Then you see that it is a matter of learning, the concept must be learned, and learning is a psychological act.

So, you might ask where did it first come from. There cannot be an infinite regress in time, of human beings teaching each other the concept, it must have come from somewhere in the first place. This is easily understood as a matter of creative genius. As is evident in all axioms of mathematics, they are clearly thought up by human beings, created by them. With modern math, we see a clear history of who created what, the history is very well documented. In ancient conceptions such as the right angle, the documentation is not there, but there is no reason to think that the process was any different in principle.

To say that there is an incommensurability in its being does not add to or take away anything from the fact that it is presented and given to our knowledge and has effects on it. That is why it is objective, since an internal relationship can be established, whether one of incommensurability, which tells us what a triangle like this – is. — JuanZu

This claim of "objective" is unjustified. That the triangle is "presented and given to our knowledge" is supported only by the evidence of learning. And inter-subjectivity does not objectify. Furthermore, there obviously cannot be an infinite regress of learning. This is why Plato investigated the theory of recollection in The Meno. But this theory has its own problems, which Aristotle expounded on. Aristotle's solution was that the geometrical constructions only exist potentially, prior to being actualized by the mind of the geometer. But something which exists only potentially cannot be an "object", and potential cannot be said to be "objective".

This is what i disagree with. I think that any instance of the conception of a triangle actually does reduce to a purely psychological act. If you assume that it "presents itself" to us, you need to ask how it does this. Then you see that it is a matter of learning, the concept must be learned, and learning is a psychological act. — Metaphysician Undercover

Well, you can't. Since we are talking about an internal relationship that is deduced from elements of an object that differs in its identity from the mind. That is, in order to reduce it to a psychological act you would have to express the internal relationship in terms of a relationship of psychic elements. For example, if we assume that the psyche is nothing more than synaptic processes between neurons, your claim would have to be represented in the form: "this synapse is the relationship of equality between two elements, and it is also an incommensurability." Which is obviously doomed to failure.

It is for this reason that you cannot reduce knowledge to a creation of human genius, even if it has no other origin than humanity. Because knowledge is something like the relationship with something objective. In no case can it justify the objectivity of knowledge based on the particular psychological movements of, in this case, Pythagoras. You may say, “but logic is the condition of objectivity” Well, what you say about geometry (its reduction to psychological acts) you say a fortiori about logic.

What I say about geometry I say a fortiori about knowledge and knowledge as language. For example, you and I possess the meaning of a right triangle (or the identity principle of logic); If the meaning is nothing more than psychological acts... how can you say that it is the same meaning in each case if they are two different psychic phenomena? The particularity of each case denies its universal formulation, and is not able to justify why it is the same meaning and is repeated in different minds, different languages, different cultures, etc.

The obvious alternative is to follow Alfred North Whitehead in 1919-1920, and abandon classical Euclidean topology for a 'point-free topology' that refers only to extensionally interpretable "blobs", namely open-sets that have a definite non-zero volume, whose intersections approximate pointedness . Then it might be possible to extensionally interpret all such "blobs" in relation to a fixed basis of topological description in a more constructive fashion, meaning that extensional ambiguity is handled directly on the logical level of syntax, as opposed to on the semantic level of theory interpretation. — sime

Very interesting post, although I don't have enough mathematics background to follow all of the details. Could you provide a link to a 'Blobs for Dummies' article?

Since we are talking about an internal relationship that is deduced from elements of an object that differs in its identity from the mind. That is, in order to reduce it to a psychological act you would have to express the internal relationship in terms of a relationship of psychic elements. — JuanZu

Husserl analyzed the origin of geometry in terms of a historical genesis, imaging the proto-geometer as someone who needed to strive toward more and more abstractive forms out of practical needs.

"In the life of practical needs certain particularizations of shape stood out and that a technical praxis always aimed at the production of particular preferred shapes and the improvement of them according to certain directions of gradualness. First to be singled out from the thing-shapes are surfaces—more or less "smooth," more or less perfect surfaces; edges, more or less rough or fairly "even"; in other words, more or less pure lines, angles, more or less perfect points; then, again, among the lines, for example, straight lines are especially preferred, and among the surfaces the even surfaces; for example, for practical purposes boards limited by even surfaces, straight lines, and points are preferred, whereas totally or partially curved surfaces are undesirable for many kinds of practical interests. Thus the production of even surfaces and their perfection (polishing) always plays its role in praxis. So also in cases where just distribution is intended. Here the rough estimate of magnitudes is transformed into the measurement of magnitudes by counting the equal parts."

“Out of the praxis of perfecting, of freely pressing toward the horizons of conceivable perfecting "again and again/' limit-shapes emerge toward which the particular series of perfectings tend, as. toward invariant and never attainable poles. If we are interested in these ideal shapes and are consistently engaged in determining them and in constructing new ones out of those already determined, we are "geometers." In place of real praxis—that of action or that of considering empirical possibilities having to do with actual and really [i.e., physically] possible empirical bodies—we now have an ideal praxis of "pure thinking" which remains exclusively within the realm of pure limit-shapes. Through a method of idealization and construction which historically has long since been worked out and can be practiced intersubjectively in a community, these limit-shapes have become acquired tools that can be used habitually and can always be applied to something new—an infinite and yet self-enclosed world of ideal objects as a field for study.

Like all cultural acquisitions which arise out of human accomplishment, they remain objectively knowable and available without requiring that the formulation of their meaning be repeatedly and explicitly renewed. . It is understandable how, as a consequence of the awakened striving for "philosophical" knowledge, knowledge which determines the "true," the objective being of the world, the empirical art of measuring and its empirically, practically objectivizing function, through a change from the practical to the theoretical interest, was idealized and thus turned into the purely geometrical way of thinking. The art of measuring thus becomes the trail-blazer for the ultimately universal geometry and its "world" of pure limit-shapes.

What makes geometric idealities identically transmissible form person to person and culture to culture is their rootedness in the construction of numeration, in which we abstract away everything meaningful about a collection of objects except their identity as an empty unit, for the purposes of iterating the ‘same thing different time’. This empty enumeration at the heart of geometric idealities makes the latter ideal rather than real.

I have always found especially interesting that step to the limit that characterizes Husserl in the discovery of essences. Said step to the limit consists of showing how when crossing it the thing stops being what it is to be something else. For example, Husserl tells us about how, taking the limit of predicates, we cannot conceive a color without extension. Something like this would happen with geometric essences. Isn't the limit something that is imposed on us from the things themselves? (I.E. imagine a perfect triangle-square) We cannot impose that limit on ourselves at will, it is shown as something foreign to our will.

Must confess I totally agree, that is true, a very Kantian categorical expression that predicted such limit.

Well, you can't. Since we are talking about an internal relationship that is deduced from elements of an object that differs in its identity from the mind. That is, in order to reduce it to a psychological act you would have to express the internal relationship in terms of a relationship of psychic elements. For example, if we assume that the psyche is nothing more than synaptic processes between neurons, your claim would have to be represented in the form: "this synapse is the relationship of equality between two elements, and it is also an incommensurability." Which is obviously doomed to failure. — JuanZu

I do not reduce the psyche to synaptic processes, so I do not see how this reply is relevant at all. You have in no way addressed the points I made.

It is for this reason that you cannot reduce knowledge to a creation of human genius, even if it has no other origin than humanity. Because knowledge is something like the relationship with something objective. In no case can it justify the objectivity of knowledge based on the particular psychological movements of, in this case, Pythagoras. You may say, “but logic is the condition of objectivity” Well, what you say about geometry (its reduction to psychological acts) you say a fortiori about logic. — JuanZu

Furthermore, as I indicated, you have in no way justified your claim of objectivity in knowledge. And now you simply repeat your unjustified assertion that knowledge is "objective", and use this unsound premise to support your insistence that knowledge cannot be an artificial creation.

If the meaning is nothing more than psychological acts... how can you say that it is the same meaning in each case if they are two different psychic phenomena? — JuanZu

I do not claim that you and I ever associate the very same meaning with the same words. In fact, I think the evidence that different people associate different meaning with the same words is overwhelming, and ought not even need to be discussed. Simply hand two people the same sentence, or the same word, and ask them to write a very inclusive statement as to what it means to them, and compare the reports. You will see that even with very simple concepts like "circle", "square", or "triangle", they will produce a variance. The only time the reports will be the same is if the two people have memorized the same definition. But then they would just write a different interpretation of that same definition anyway. Two people referring to the same definition is the result of learning, which I addressed in the last post, and you seem to have completely ignored for some reason.

The particularity of each case denies its universal formulation, and is not able to justify why it is the same meaning and is repeated in different minds, different languages, different cultures, etc. — JuanZu

The point is that this idea, that "it is the same meaning and is repeated in different minds" is simply false. Each mind relates to the same words in ways exclusive, and unique to that mind. We might say that it is "essentially the same", but we cannot ignore the accidentals which actually make it not the same.

I do not reduce the psyche to synaptic processes, so I do not see how this reply is relevant at all. You have in no way addressed the points I made. — Metaphysician Undercover

Maybe you think it's not relevant because you're not understanding it very well. For example, if you don't talk about neuronal synapses, you can talk instead about cognitive processes, or psychological acts. So what I have said about neural processes a fortiori is said of any theory that attempts to reduce (reductionism) one field to another.

Furthermore, as I indicated, you have in no way justified your claim of objectivity in knowledge. And now you simply repeat your unjustified assertion that knowledge is "objective", and use this unsound premise to support your insistence that knowledge cannot be an artificial creation. — Metaphysician Undercover

I did. As I have exposed an internal relationship between the elements of a closed field, in this case geometry. And not only that but also its ideality has been exposed (repetition in different cultures, different subjects, different psychological acts, etc. Or can u say that geometry theorems are different through different cultures? ). Then we have a field where an infinity, so to speak, of internal relations that is established from some constitutive elements. Just as we could compose the field of quantum physics from elementary particles.

Now, you will say "but geometry does not represent anything and is something created." Quantum physics is also something created, logic is too. But of course the fact that it is something created does not prevent it from being something objective (even if we follow ur argument no one can say that a computer or a sintetic chemical element is non-objective just because it's artificial) . Physics has its means of objective validation in technological operation and mathematic consistency (a field bigger of terms, relations, operations, etc) , while geometry has its validation in the internal relationships that are discovered through iterative operations) and demonstrated accurately in most cases.

Ur argument, if I understand correctly, is based on a sense of objectivity as representation wich grounds it. That is, as the correspondence between the theory and a referent wich is provided by the sensory system. But if we abandon that idea of ​​objectivity as representation we also abandon what you say about geometry as something non-objective. And let me tell you: We have to abandon your sense of objectivity as a representation or as a necessary link between theory and an empirical reference that must correspond to. In the case of geometry it can be said that it is its own reference, and to the extent that we discover its internal relationships we discover things, regardless of the fact that it has no other origin than Humanity.

U can call this "objetive constructivism".

The point is that this idea, that "it is the same meaning and is repeated in different minds" is simply false. Each mind relates to the same words in ways exclusive, and unique to that mind. We might say that it is "essentially the same", but we cannot ignore the accidentals which actually make it not the same. — Metaphysician Undercover

It is not false. You are pointing out particular accidents to say that we are not referring to the same thing. But obviously in the act of communication an identity and repetition must take place so that there is a minimum of understanding, this is the meaning. If you say to a Greek and an Egyptian to give you 5 units of that fruit and not 4, they will probably both give you the 5 units; Well, this fact is not a simple coincidence and must be explained. But obviously we cannot explain the same from what is different. We cannot explain, for example, why the Egyptian and the Greek acted in the same way based on the sound differences that each one heard, on their culture wich they belong, on their language, etc.

Maybe you think it's not relevant because you're not understanding it very well. For example, if you don't talk about neuronal synapses, you can talk instead about cognitive processes, or psychological acts. So what I have said about neural processes a fortiori is said of any theory that attempts to reduce (reductionism) one field to another. — JuanZu

I still don't know what you are trying to say JuanZu. My point was that one is prior to the other, as the cause of the other. Minds are prior to ideas as the cause of ideas. Since ideas and minds are subjects of the very same field, there is no attempt to reduce one field to another here, and your supposed "a fortiori" assertion is irrelevant. You seem to be wanting to claim that ideas are prior to minds, so please address the arguments I've made, instead of attempting to change the subject and using that very change of subject as the basis for your claim of a fortiori.

I did. As I have exposed an internal relationship between the elements of a closed field, in this case geometry. — JuanZu

Geometry is not a "closed field", there is no such thing as intelligible objects which exist in total isolation from others. So geometrical terms get defined by a wider field of mathematics, and concepts of spatial dimension. This issue is often addressed by philosophers, such as Wittgenstein in On Certainty, because it appears like it may produce an infinite regress of meaning, leaving no concepts truly justified as "ideal", in the sense of perfect, absolute certitude.

Or can u say that geometry theorems are different through different cultures? ). — JuanZu

Yes, geometrical ideas have been very different in different cultures. All you need to do to find this out, is read someone like Plato, where it is described how the different geometrical concepts were derived from different parts of the world, Egypt and Babylonia for example, and from there the ideas spread to other parts of the world like Greece, and what is now Italy, where they were assimilated through the process of working out differences, inconsistencies and incompatibilities.

A more modern, and also very clear example, can be found in numerical systems. Currently we use what is known as "Arabic Numerals". This numeral system came to supplant the use of "Roman Numerals" in the western world. It is not the case that these two are simply different names for the same conceptual system, because these two conceptual structures were completely different, as is plainly evident from the absence of the zero in the Roman Numerals. I admit that this example is not specifically "geometry" but it is related, and it gives very clear evidence of how highly logical theorems very clearly vary through different cultures.

Now, you will say "but geometry does not represent anything and is something created." Quantum physics is also something created, logic is too. But of course the fact that it is something created does not prevent it from being something objective (even if we follow ur argument no one can say that a computer or a sintetic chemical element is non-objective just because it's artificial) . — JuanZu

Why are you arguing against yourself now? You used "objectivity" as evidence that ideas are discovered, presented or given to us, rather than created by us. Now you claim "the fact that it is something created does not prevent it from being something objective", so you've just undermined your entire argument.

Ur argument, if I understand correctly, is based on a sense of objectivity as representation wich grounds it. That is, as the correspondence between the theory and a referent wich is provided by the sensory system. But if we abandon that idea of ​​objectivity as representation we also abandon what you say about geometry as something non-objective. And let me tell you: We have to abandon your sense of objectivity as a representation or as a necessary link between theory and an empirical reference that must correspond to. In the case of geometry it can be said that it is its own reference, and to the extent that we discover its internal relationships we discover things, regardless of the fact that it has no other origin than Humanity.

U can call this "objetive constructivism". — JuanZu

Remember JZ, you introduced "objectivity". I'm happy to go ahead without that term, as something irrelevant, but your claim was that being "objective" implies that concepts are not created, but discovered. You said that the reason why a right triangle is "objective" is because it gives itself to us, or presents itself to us as this type of an object. So you are very clearly saying that being "objective" is what implies, or justifies your claim that the right triangle is a discovered (natural) object rather than a created (artificial) object.

In my opinion the term "Real" has no place in the discussion because a thing like that, a thing like a triangle simply "gives itself" and presents itself to us as an object of study, without being able to be reduced to a psychological act. To say that there is an incommensurability in its being does not add to or take away anything from the fact that it is presented and given to our knowledge and has effects on it. That is why it is objective, since an internal relationship can be established, whether one of incommensurability, which tells us what a triangle like this – is. — JuanZu

That is what you said.

It is not false. You are pointing out particular accidents to say that we are not referring to the same thing. But obviously in the act of communication an identity and repetition must take place so that there is a minimum of understanding, this is the meaning. If you say to a Greek and an Egyptian to give you 5 units of that fruit and not 4, they will probably both give you the 5 units; Well, this fact is not a simple coincidence and must be explained. But obviously we cannot explain the same from what is different. We cannot explain, for example, why the Egyptian and the Greek acted in the same way based on the sound differences that each one heard, on their culture wich they belong, on their language, etc. — JuanZu

With respect to the identity of an object, each accidental of that object must be accounted for, or else two distinct objects, with different accidentals would have the same identity, and therefore be the very same object. Therefore in any instances when the accidentals differ, as not being the same in each of the instances, we must conclude that the two objects are distinct objects and not the same object. This is derived from the law of identity.

Isn't the limit something that is imposed on us from the things themselves? (I.E. imagine a perfect triangle-square) We cannot impose that limit on ourselves at will, it is shown as something foreign to our will. — JuanZu

In the case of the constitution of a real spatial object via the synthesis of perspectival adumbrations, passage to the limit never succeeds in fulfilling the idea of the object as a unitary identity. We strive for this fulfillment through our continued interest in the object , but the self-identical object always remains transcendent to what we actually experience. In the case of a geometric ideality like a straight line or circle, passage to the limit assures an exactitude because mathematical shapes are free idealities, whereas real spatial objects are bound idealities.

Mathematical idealization is free, unbound (within the strict limits of its own repetition); no contextual effects intervene such as was the case in the attempt to constitute a real spatialobject. Contextual change implies change in meaning, and a mathematical ideality can be manipulated without being animated, in an active and actual manner, with the attention and intention of signification. Such an ideality can be repeated indefinitely without alteration (passage to the limit), because its meaning is empty. In the case of a bound ideality, what repeats itself as self-identical returns to itself as `the same' subtly differently each time; the immediate effects of contextual change ensure that alteration is intrinsic to the repetition of an intentional meaning. Put differently, we impose the real unity of a spatial object via intention acts, but can never fulfill this intention. We likewise impose the ideal unity of an identically repeatable geometric shape through intentional acts. But in this case we succeed in fulfilling its exact and universal reproducibility because it is an empty , unbounded iteration.

I still don't know what you are trying to say JuanZu. My point was that one is prior to the other, as the cause of the other. Minds are prior to ideas as the cause of ideas. Since ideas and minds are subjects of the very same field, there is no attempt to reduce one field to another here, and your supposed "a fortiori" assertion is irrelevant. You seem to be wanting to claim that ideas are prior to minds, so please address the arguments I've made, instead of attempting to change the subject and using that very change of subject as the basis for your claim of a fortiori. — Metaphysician Undercover

Well, I precisely maintain that they are different fields, not only in terms of validation but in their terms, their relationships and operations. But you are assuming it is the same field (psychological acts) by simply repeating it, ignoring all the evidence I have presented to you and in no way refuting it.

Geometry is not a "closed field", there is no such thing as intelligible objects which exist in total isolation from others. So geometrical terms get defined by a wider field of mathematics, and concepts of spatial dimension. This issue is often addressed by philosophers, such as Wittgenstein in On Certainty, because it appears like it may produce an infinite regress of meaning, leaving no concepts truly justified as "ideal", in the sense of perfect, absolute certitude. — Metaphysician Undercover

you are saying that it is not a closed field but without giving any justification or argument. I, on the other hand, have given "evidence" that you have not even tried to refute: The internal relations between terms of the same type, their semantic difference with respect to the field that you believe is the same. For example, we have hypotenuse and legs, both are straight, both are two-dimensional, etc. I ask you to make an effort to argue more and spread fewer categorical statements.

A more modern, and also very clear example, can be found in numerical systems. Currently we use what is known as "Arabic Numerals". — Metaphysician Undercover

And yet you continue to refer to both cases as "numerals". You have not yet understood that you cannot speak of the different as the same. That is, if you speak of two cases (Greeks and Arabs) as species of the same phenomenon (numbers) , you are only arguing against yourself. I say again, you do not explain the same thing by what is different.

Why are you arguing against yourself now? You used "objectivity" as evidence that ideas are discovered, presented or given to us, rather than created by us. Now you claim "the fact that it is something created does not prevent it from being something objective", so you've just undermined your entire argument. — Metaphysician Undercover

There is no contradiction. In fact, if I can alternate between creating and discovering it is because it is in a certain way undecidable. On the one hand it has human genesis; On the other hand, it has a structure in which terms establish and maintain autonomous relationships that are no longer reduced to human creativity (for example, the Pythagorean theorem).

What you see as a contradiction between creating and discovering is actually a difference between the pair of concepts called "genesis" and "structure." That is, the first geometer may have imagined a line, the first line in the world; However, this line was already the object of a length, and the object of union with other lines that formed a triangle. But then the lines autonomously maintain a relationship with each other, which, depending on the measurement or value of their length, is equivalent to this or that other value. The key here is autonomy and the internal relationship between a set of elements. This relationship between elements can no longer be thought of as a psychological act of the imagination. Why? Because these relationships are said of the elements and not of the imagination. That is why geometry is objective, created and discovered at the same time.

With respect to the identity of an object, each accidental of that object must be accounted for, or else two distinct objects, with different accidentals would have the same identity, and therefore be the very same object. — Metaphysician Undercover

Here I repeat the argument that I have presented in relation to your example of numbers.

Well, I precisely maintain that they are different fields, not only in terms of validation but in their terms, their relationships and operations. — JuanZu

So you're argument amounts to "I stipulate that these fields are different", and you think that this validates your perspective. That's called begging the question.

But you are assuming it is the same field (psychological acts) by simply repeating it, ignoring all the evidence I have presented to you and in no way refuting it. — JuanZu

You've presented exactly zero evidence, only some blabbering about relationships between fictitious imaginary elements. On the other hand I've presented the example of learning, the problem with infinite regress if concepts are only learned, Plato's proposal of "recollection", the problem with this, and Aristotle's resolution to that problem.

you are saying that it is not a closed field but without giving any justification or argument. — JuanZu

I explained why no field is a closed field. You don't seem to know how to read Juan. Or do you prefer just to ignore evidence which does not support what you believe?

And yet you continue to refer to both cases as "numerals". You have not yet understood that you cannot speak of the different as the same. That is, if you speak of two cases (Greeks and Arabs) as species of the same phenomenon (numbers) , you are only arguing against yourself. I say again, you do not explain the same thing by what is different. — JuanZu

Yes, two very different instances of the same type of phenomenon. This implies a difference between the two specified things, and in no way implies that the two are the same thing. However, two different things may be of the same type, so your objection "that you cannot speak of the different as the same" is ridiculous. Two different things cannot be the same, yet they can and often are, said to be the same type. So, very commonly we speak of the different as the same, so long as we maintain the distinction between particular and universal, and recognize that "the same type" does not mean "the same individual".

What you see as a contradiction between creating and discovering is actually a difference between the pair of concepts called "genesis" and "structure." — JuanZu

What I saw as contradiction was that you said a right triangle is "objective" because it "gives itself" and presents itself to us. This was the alternative to my claim that the right triangle was created by us. Later, you said "But of course the fact that it is something created does not prevent it from being something objective."

Therefore we need to conclude that whether or not the right triangle is objective, is irrelevant to whether or not it "gives", "presents itself" to us, or whether it has been created by us. And all this talk about objectivity is just a ruse.

What you see as a contradiction between creating and discovering is actually a difference between the pair of concepts called "genesis" and "structure." That is, the first geometer may have imagined a line, the first line in the world; However, this line was already the object of a length, and the object of union with other lines that formed a triangle. But then the lines autonomously maintain a relationship with each other, which, depending on the measurement or value of their length, is equivalent to this or that other value. The key here is autonomy and the internal relationship between a set of elements. This relationship between elements can no longer be thought of as a psychological act of the imagination. Why? Because these relationships are said of the elements and not of the imagination. That is why geometry is objective, created and discovered at the same time. — JuanZu

So your argument here is worthless. The "autonomy and the internal relationship between a set of elements" is no more likely if the triangle is natural than if it is created.

Furthermore, what you say about "the first line in the world", that " this line was already the object of a length, and the object of union with other lines that formed a triangle", is clearly false. If it is the first line in the world, it is contradictory to say that it is already a union with other lines, making a triangle. This would imply that it is not the first line, but that it coexisted with other lines. But this is impossible, because you described it as the first line in the world, created by the first geometer.

Here I repeat the argument that I have presented in relation to your example of numbers. — JuanZu

The argument which amounts to an ignorance of the difference between 'being the same thing', and 'being of the same type'?

In this regard, Husserl spoke that in iterative moments there must be a sedimentation in which the meaning is recorded to be "revived" by intentionality in different moments and places. Aren't these sediments language, writing, archiving, for example? An ideal object, to be ideal, must be available for the subject. In a certain sense consigned, registered, etc. These sedimentations, such as language, writing, archiving, computing, etc., are not precisely " "empty" until a living intention animates them? And yet they are necessary conditions for meaning to appear in iteration: in an interlocutor, in another culture, in another time, etc.

So you're argument amounts to "I stipulate that these fields are different", and you think that this validates your perspective. That's called begging the question — Metaphysician Undercover

Not at all. I start from the assumption that we are talking about the same field, in order to take that assumption to the limit where it can be demonstrated that they are actually two fields that are irreducible to each other.

You've presented exactly zero evidence, only some blabbering about relationships between fictitious imaginary elements. On the other hand I've presented the example of learning, the problem with infinite regress if concepts are only learned, Plato's proposal of "recollection", the problem with this, and Aristotle's resolution to that problem. — Metaphysician Undercover

Among the evidence is the impossibility of carrying out a process with the same results based on certain terms and operations. The terms and operations of psychology and geometry are radically different. The terms and operations carried out in geometry reveal internal relationships that you cannot discover by exchanging these terms for others in psychology.

I explained why no field is a closed field. You don't seem to know how to read Juan. Or do you prefer just to ignore evidence which does not support what you believe? — Metaphysician Undercover

You didn't . The only thing you said is that geometry objects are not isolated objects. But that's assuming you can delimit the field of geometry from every other field, which is not the case, I assume you can't do that. On the other hand, I have exposed the incommensurability between one field (geometry) and another (psychology). Relative to the field of psychology the field of geometry is closed in the sense that none of its terms, operations and relationships can determine the nature of the field of geometry.

Yes, two very different instances of the same type of phenomenon. This implies a difference between the two specified things, and in no way implies that the two are the same thing. However, two different things may be of the same type, so your objection "that you cannot speak of the different as the same" is ridiculous. Two different things cannot be the same, yet they can and often are, said to be the same type. So, very commonly we speak of the different as the same, so long as we maintain the distinction between particular and universal, and recognize that "the same type" does not mean "the same individual". — Metaphysician Undercover

They are the same insofar as they are numbers, they are different insofar as they are different types of numbers. Have you ever read about being as equivocity, as univocity and as analogy? Well, it seems that you speak from equivocity (all things are different and none can be the same in any sense), but contradicting yourself by using the same numerical system sign. "Things are different in one sense, but in another sense They are the same". Thus, there is evidently no contradiction. Things can be the same as genres, bus distinct as species.

What I saw as contradiction was that you said a right triangle is "objective" because it "gives itself" and presents itself to us. This was the alternative to my claim that the right triangle was created by us. Later, you said "But of course the fact that it is something created does not prevent it from being something objective."

Therefore we need to conclude that whether or not the right triangle is objective, is irrelevant to whether or not it "gives", "presents itself" to us, or whether it has been created by us. And all this talk about objectivity is just a ruse. — Metaphysician Undercover

A geometric object is presented to us and given to us even though it is a human creation. But it is given to us as a set of internal relationships and meanings that transcends the acts of its creation. It is in this sense that it gives itself: Depending on its autonomy, a property of the object that emerges from relationships between the parts of that object that are discovered beyond our will. That is, when we talk about a property of triangles we are talking something about triangles, not something about imaginative acts. It is something that comes up from the thing, not from us. Thats why it presents itself.

We can say that it is something created and discovered for the reasons I have given (genesis and structure). A straight line could perhaps have been imagined once, or imagined by three different people at different times, or simply be an imaginary act repeated three times. That doesn't matter (and it's important that it doesn't matter), the important thing is when those lines entered into a relationship and crossed forming a triangle (three angles appeared). Something like a leg and a hypotenuse appeared and relationships emerged between these elements, regardless of how the lines were created.

The argument which amounts to an ignorance of the difference between 'being the same thing', and 'being of the same type'? — Metaphysician Undercover

Univocality, equivocality and analogy.

I am quite impressed with your posts, but I find them very hard to understand. Perhaps you might write a self-intro in the Intro thread , it might help me understand a little more about your interests.

Thank you. I'll give a try to present that self-intro.

Among the evidence is the impossibility of carrying out a process with the same results based on certain terms and operations. The terms and operations of psychology and geometry are radically different. The terms and operations carried out in geometry reveal internal relationships that you cannot discover by exchanging these terms for others in psychology. — JuanZu

The field we are working in here is philosophy. We are discussing the reality, and objectivity of geometrical objects, that is philosophy. You have assumed that we are discussing two distinct fields, geometry and psychology, and this forms the premise for your argument which proves that these are distinct fields. That is called begging the question.

I really do not see how your other premise, "the impossibility of carrying out a process with the same results based on certain terms and operations" is at all relevant, or even how it is meant to be interpreted. Therefore you need a much better explanation of what you are talking about before this phrase can be admitted as "evidence".

You didn't . The only thing you said is that geometry objects are not isolated objects. But that's assuming you can delimit the field of geometry from every other field, which is not the case, I assume you can't do that. — JuanZu

Obviously you did not understand me, so I will repeat with explanation. I said: "geometrical terms get defined by a wider field of mathematics, and concepts of spatial dimension. This issue is often addressed by philosophers, such as Wittgenstein in On Certainty, because it appears like it may produce an infinite regress of meaning, leaving no concepts truly justified as "ideal", in the sense of perfect, absolute certitude."

To explain in a simpler way for you, all terms and conceptions get defined and understood by a wider context. There is obviously no assumption here that geometry is "delimited", as what is expressed is exactly opposite to that. I am saying that no concepts are actually "delimited", and this has been an issue for philosophers. Wittgenstein said in the Philosophical Investigations for example, that concepts have no inherent boundaries, though a person may create a boundary for a specific purpose.

This I assume would be the case when we define a term for the purpose of a logical operation, as a premise. The issue I am telling you about, is that the understanding, or interpreting of this definition takes us outside the boundaries which the definition is meant to create. So, for example, if we define "right triangle" as a triangle with one right angle, then to understand these terms, "triangle", and "right angle", we must go to a wider context. We can define "triangle" as a plane figure with three sides and three angles, and we may define "right angle" as the angle produced when two lines cross each other and have equal angles on all sides. To understand or interpret these definitions we need to go to a wider context. We need to define "plane figure", "sides", "angles", "lines".

As you can see, at each step of defining the terms, then defining the terms of the definition, and then defining the terms which define the defining terms, we move into a wider and wider context, with an increase in terms to be defined, and an increase in the possibility of ambiguity and misunderstanding. It appears to many philosophers that this need to continually place the terms into a wider and wider context, in one's attempt to understand, would lead to an infinite regress rendering true understanding as impossible.

On the other hand, I have exposed the incommensurability between one field (geometry) and another (psychology). Relative to the field of psychology the field of geometry is closed in the sense that none of its terms, operations and relationships can determine the nature of the field of geometry. — JuanZu

This is exactly why what you are arguing is self-contradictory. First you say geometry cannot be delimited. This means that this proposed "field", geometry has no fixed boundaries. Then you argue that there is incommensurability between this proposed field, geometry, and another proposed field, psychology, and so you conclude that the two fields must be closed. Your conclusion contradicts your premise.

Do you apprehend the blatant contradiction? On the one hand you assume, 'geometry is not delimited. Then from here you say, 'but there is incommensurability between the terms of geometry and the terms of psychology'. So you conclude, 'relative to psychology, geometry is closed'. But this is obviously a fallacious conclusion. You do not have the premise required, which would state that there cannot be incommensurability within the same field. Furthermore, we have all sorts of evidence of incommensurability existing within the same field, which proves that such a premise would be false.

For example, within the field of mathematics there is incommensurability between real numbers and imaginary numbers. The use of imaginary numbers produces all sorts of complexities within the field, making the above mentioned concept of "plane" extremely difficult and complex. The use of imaginary numbers creates the need for a completely different definition of "plane".

Now, we can justly inquire whether the use of imaginary numbers is better described as a mathematical operation, or a psychological operation. We can look at this usage from at least two perspectives, what imaginary numbers actually provide for us within the field of mathematics, and also from the perspective of the psychology behind the desire to create such a thing as imaginary numbers. If there is incompatibility between these two, as you seem to assume, then we can conclude that imaginary numbers do not fulfil the purpose they were intended for.

They are the same insofar as they are numbers, they are different insofar as they are different types of numbers. — JuanZu

OK, now the point is that there is incommensurability between the different types of numbering systems. And, this incommensurability exists within the same field. Therefore your conclusion that fields are closed to each other when there is incommensurability between them, is unsound. Furthermore, your argument that geometry and psychology are distinct fields is also unsound. And, we can conclude that your presumption that these two names are representative of two distinct fields is nothing but a prejudice which is presented a premise for a fallacious argument, due to the fallacy of assuming the conclusion, begging the question.

Have you ever read about being as equivocity, as univocity and as analogy? Well, it seems that you speak from equivocity (all things are different and none can be the same in any sense), but contradicting yourself by using the same numerical system sign. — JuanZu

Did you not read where I explained the difference between "being the same thing", and "being of the same type". I'm really starting to think that you do not even bother to read half of what I post JZ.

A geometric object is presented to us and given to us even though it is a human creation. But it is given to us as a set of internal relationships and meanings that transcends the acts of its creation. It is in this sense that it gives itself: — JuanZu

Now you're finally saying something which appears possibly reasonable, which warrants a thorough investigation. You say that geometrical objects are created, but their meanings transcend their creation. Is that correct, and what exactly do you mean by "meanings that transcends the acts of its creation"?

Let's look at "meaning" to begin with, in its most simple and ordinary sense. When someone uses words, we say that the meaning is what is meant by the author, what the author intended with the words. Do you agree with that? If so, how would you say that "meaning" in this sense, "transcends" the act of creation, which is the act of the author thinking up, and giving physical existence to the conglomeration of words? Would you say that "transcends" is used here in the same way that we might say that one's intention "transcends" one's intentional acts?

If so, then we have your expression of "internal relations and meanings" as transcending the intentional act. But I defined "meaning" as what is given by the act itself, what is meant by the act. It appears wrong to say that meaning could transcend the act, because meaning seems to be intrinsically tied to the act. How could there be any meaning when the act which gives meaning is non-existent? We might be better off to say that "intention" transcends the act, and meaning is what is created by the intentional act, but intention is defined by terms which lead us in a different direction. It is defined by "purpose".

Let's say the "purpose" of the intentional act, or act of creation, transcends the act. And "purpose" implies a completely different type of "relations", which are not spatial relations at all, like what geometry works with. The relations implied by "purpose" is a hierarchy of values and priorities in relation to goals or ends. So, would you agree with me, that if there is a sort of "relations" or even if we might call it "meanings" which transcends the act of creation, these relations are "value" relations, which are distinct from spatial relations, being based in "priority". We might see that mathematics also is based in a type "value" system, and "priority" is paramount in the concept of order which is very important to mathematics.

We can say that it is something created and discovered for the reasons I have given (genesis and structure). A straight line could perhaps have been imagined once, or imagined by three different people at different times, or simply be an imaginary act repeated three times. That doesn't matter (and it's important that it doesn't matter), the important thing is when those lines entered into a relationship and crossed forming a triangle (three angles appeared). Something like a leg and a hypotenuse appeared and relationships emerged between these elements, regardless of how the lines were created. — JuanZu

Let's look directly at what I've identified as the relations which could possibly transcend the human, artificial act of creation, "priority", "order", and "value". If "order" transcends the acts which create mathematical axioms, is it possible, in mathematics, to have a set with no order, or no elements? Wouldn't such an axiom be necessarily false, therefore needing to be rejected as ontological wrong. However, mathematics does employ such axioms. Therefore it appears impossible, because of falsity, to argue that "priority|, "order", and "value" transcend the axioms of mathematics, because these axioms define what those things are.