I don't doubt that such sources are authoritative in their own right. I think that such treatment is a little outdated in style, because the mathematics skip a little modern abstraction, in pre-Russellian (pre-Frege) manner of thought. I do not oppose the dot product and metrization you provide. It indeed fits the axiomatic requirements. Affine spaces can be defined over n-tuples (as both point and product spaces) and that Cartesian coordinate systems can simply be rigid transformations over some preferred innate coordinates. However, I have something else in mind. Something akin to the Wikipedia definition. I agree that it comes from a much less reliable source, but it is what I mean.Here's what Euclidean space is. My reference here is for example Calculus on Manifolds by Spivak, page 1 — fishfry
Inner product space over the real numbers does not imply a vector space of n-tuples, but simply that the scalar field of the vector space are the reals. That allows us to use real numbers in the Cartesian coordinate system, without worrying of the underlying units of measurement that correspond to the unit distance stride in our point space.A Euclidean vector space is a finite-dimensional inner product space over the real numbers.
A Euclidean space is an affine space over the reals such that the associated vector space is a Euclidean vector space. — Wikipedia
I personally do not object to extra formalism, if it makes the assumptions more explicit. But I see how you may feel this way.The rest of what you wrote is overloaded with what software developers would call cruft. — fishfry
Then the distance in your point space is inherently unitless, and the angles are synthetic. In the OP's case, the answer then would be that the hypotenuse length is also unitless. The units do not come from the metric, which is just a number, but from the nature of the unit vectors, which in the case of an n-tuple are just numerical. But for many applications, there are underlying units. Sure, you can informally make the association, but if you were willing to formalize it, it would be stated explicitly in the point and inner product spaces. For example, your vectors would be currency or distances, your points would be capitals or locations, etc.There is no underlying point space, the n-tuples ARE the points. — fishfry
I'm not sure I get that. You riddle me too hard a riddle there, I'm afraid.What's, for you, the next best thing to say? — TheMadFool
I agree with the fact that we can define the dot product as you specify, but we need inner product as well, or we are just manipulating unitless numbers that don't correspond to anything.I assume you agree. — fishfry
To some extent. But I was saying that there is one more hop (probably) in my mind to how this intuition translates to Cartesian coordinates. We first justify the requirements of the affine spaces with the constructive proofs, such as the properties of the inner product in the inner product space. Then we assign n-tuples to the points in the point space, proving that we preserve the inner product with the dot product. Since, in the OP's question there is no inner product, just dot product, there is nothing to preserve and no Pythagorean semantics to be had. We either have arbitrary assignment of numbers to points somewhere, in some semantic domain, or we work with numbers as our semantic domain, and those numbers have no units.Is that what you're saying, that we need the ancient geometric intuition to ground the modern analytic approach? — fishfry
I still want to be certain that you concur with me on the definition of Cartesian coordinate systems.No that's not true. We define R2 as the set of ordered pairs of real numbers. Then we define the usual Euclidean Euclidean distance, and we define the usual dot product. — fishfry
(a + b) (a + b) = a ^ 2 + b ^ 2 + 2 a * b
I don't see it that way really. We still come from the geometric perspective, to define angles and distances in one way or another, and only then we have the privilege of calling an n-tuple of points being from a Cartesian coordinate system. Cartesian coordinate systems come with semantics that need to be defined apriori. They are not just mechanical assignment of pairs of numbers to some arbitrary point space.And in modern math we start with a 2-dimensional coordinate system and define the Euclidean distance. — fishfry
My point is that you need to have the concepts of "angles" (so that they can be equal), "directions" (so that you can make the points on your lines aligned, i.e. colinear), "distances" apriori, before resorting to analytic geometry. (And formally, we would call that an affine space today. Although the terminological designation would not be present historically, the ideas would be the same.) It would be backwards thinking if we started with pairs of numbers, declared them to be the Cartesian coordinate system for implicit space of entities and finally tried to infer a sensible explanation of the nature of the metrics of those entities.A right angle (if I remember my high school geometry) is when you have a line intersecting another line and making equal angles on each side. — fishfry
How did you come to the realization that the angle is perpendicular when constructing your mathematical model of the problem domain? What property in the actual domain of application of your model prompted the idea? If you were not concerned with any domain when you constructed the model, how do you come to need to ask semantic questions now?If memory serves, Pythagora's theorem works only for right triangles and yes the axes that I used are perpendicular and yes there's a right triangle (3, 4, 5) formed. — TheMadFool
Xenophobia and ingroup mentalities run strong in our genes. Religion is another trigger that we might not have otherwise had, but we would have found other reasons to be xenophobic.- justification for prejudice — Tom Storm
This I also believe is unjustifiable epistemic error for a sensible human being.-Justification for bigotry — Tom Storm
This appears to be gradually weeded out, albeit very slowly. I think that it is prevalent in violence-prone subcultures and strata of society, where they are practicing violence to defend all sorts of personal subscriptions.-justification for violent behaviour — Tom Storm
I wish I wrote that. Even someone like Jordan Peterson, who is a hardliner cultural and religious conservative describes a lot of the religious texts as mythos. However, being a pragmatic utilitarian, he seems to perceive them as socially constructive mythos. I have never heard him express the need to have the degree of metaphysical skepticism that he himself has. His claims to be a Christian, who does not believe in God, but acts as if there is one. Or, differently put, that he is raised and remaining under the influence of the Judeo-Christian system of moral values. Being a psychologist, he has also discussed the compulsive nature of knowledge-gap-filling. It isn't something you can easily turn off, and turns on automatically whenever you are faced with the need to ascribe features to unknown parts of reality. It seems to me that certain advocates of organized theism are themselves rather aware of our cognitive biases, but contented with the population at large being a naive recipient of the religious benefit.Rather, we're prone to a variety of known cognitive biases or "features", like apophenia, patternicity, personification (abductive), autosuggestion (and the reiteration effect), knowledge-gap-filling, confabulation, wishful/magical thinking. — jorndoe
I am always coming back to the idea that we are applying induction "on faith". We can argue that our practice is confirmable, but that is also inductive retroactive argument. It only demonstrates the internal consistency of empiricism. Or similarly, with statistics, we use chances to justify our decision making. But in the end of the day, we are not actually observing chances, we are observing satisfactory outcomes and apply confirmation bias. If we consider such intuitions productive for science, can we really disallow religious intuition and biases, as possibly being truthful. As challenging as such concession might be to empirically grounded person. I would not consider asking that we accept them or not to critique their internal inconsistencies and methodological errors (such as lack of hesitancy), but still.We learn from accumulating experiences, interacting with it all, ...
We might then extrapolate (induction) and formalize (for deduction), systematically do away with errors (or demarcate domain of applicability), ... — jorndoe
Government = The consequent system of humanity's free and successful interactions per individual. — Gus Lamarch
I wouldn't have noticed. It happened accidentally.I see what you did here — SophistiCat
Pointing to dogs and uttering the word "dog" is an act of providing instances to the audience (here Possibility's daughter) and if that's all that's being done, leaving the audience to figure out what the word "dog" means i.e. it's the audience's job to abstract the essence of a dog from the instances provided. — TheMadFool
This will always be ‘fuzzy’ to a certain extent - a definition seems to be just a linguistically-structured summary or reduction of these patterns. — Possibility
To define something - to state or describe exactly its nature, scope or meaning; to mark out its boundary or limits - is a reductionist methodology that discards qualitative variability or ‘fuzziness’ in the information we have about that something. — Possibility
I was concerned with the possibility of solving the issue as specified and wanted to propose that we break it down into aspects of smaller complexity. I may have come off as assuming some lack of familiarity with the intricacies that are involved.That there are different definitions of truth (correspondence, paragmatic, coherent, etc.) is suggestive...hints at some degree of arbitrariness...something I referred to in the OP. — TheMadFool
It still seems to me that the criterion is not about establishing unambiguously the truth of propositions, but of designing descriptions for a proposition that matches particular experience. The problem does elicit however many considerations involved when matching the descriptions between individuals through exemplification.If truth were abstracted from instances of truth this wouldn't be the case for then that which can be described as the form (Plato?) of truth would be constant, precluding, in my humble opinion, variety in the definition of truth. — TheMadFool
I agree with pretty much everything you said. Philosophy aside, we routinely apply the idea that appearing human indicates experiencing yourself as human. If some ethical or metaphysical stance connects form to substance in this way, we can inquire how using appearances allows us to discern consciousness, what kind of metric separates being sentient from being insentient (number of cells in the brain, organization of those cells). If the metric implicitly exists, we can inquire for some hypothetical justification or explanative devices behind its implicit construction, and hence delve in its micro- and macro- extrapolations. If is it done purely by association with the statistically normative human form, it becomes a rather crude metric for something so decisive and a disguise for hypocritically disinterested viewpoint to me. Social/political/legal conventions are out of convenience or necessity, but while they may never be made precise in practice, we can at least dissect them philosophically.The crux of the issue of whether anything is sentient is that, to be frank, no level or detail of data/information short of directly experiencing consciousness in an other will ever be conclusive and that's impossible (as of now, I must admit). — TheMadFool
Materialism to me has only one consequence, objective reality, meaning agreement between subjects about the nature of compelling external forces. There can be nothing to agree upon, if there is only one subject. The notion of objectivity becomes meaningless to me, if there are not multiple subjects. — simeonz
"Exist" is just another word for having a form. But the only way we define the idea of form is through the account of our interactions, through phenomenology. How can we talk about objectivity vs subjectivity of the form we perceive when there is only one subject. The two ideas are indistinguishable even conceptually to me. But I must say, I see where you are coming from. You are not asking the question epistemically at all it appears and to you the ontic difference is evident. — simeonz
I argued here that if a theory made distinct claim about the world, in a logically consistent manner, it is deserving of its title. Even if it is epistemically indistinguishable to other proposals.Some variants of dualism might be ontically distinguishable, albeit not in a way that can be corroborated. The differences might not be detectable on earth or might be perceivable only through the lenses of hypothetical psychic observer. I accept such notions, because like with solipsism, there is difference between the version of the proposed reality therein and the conventional ones, even if it fails to project into sensory experience. Such description is still irrefutable. I insisted originally that there are different categories of questions that we could ask to distinguish one theory from the rest - ontic, epistemic, ethical and antropological. Some are distinguishable only through some of these questions, but to me, all should be distinguishable in an unambiguous manner as ontic descriptions or they are synonyms to another theory. — simeonz
I think that you suggest that the relationship between B and C (and therefore the entire existence of B) happens in complete physical transparency. Then, how would free will manifest here?Event A - brain event - causes event B - mental event. Event B causes event C - brain event. — Bartricks
Likewise, my reason represents my mind to be an immaterial thing, for it says of it that it makes no sense to wonder about what sensible properties it might have. — Bartricks
"Exist" is just another word for having a form. But the only way we define the idea of form is through the account of our interactions, through phenomenology. How can we talk about objectivity vs subjectivity of the form we perceive when there is only one subject. The two ideas are indistinguishable even conceptually to me. But I must say, I see where you are coming from. You are not asking the question epistemically at all it appears and to you the ontic difference is evident.That's just the thesis. Materialism 'just is' the thesis that there is an objective - that is, 'existing extra-mentally' - reality. — Bartricks
It makes no sense to ask it as unaided self-reflection, but that doesn't mean that through some assisted view (externally) your mind could not see itself better.It is self-evident to virtually everybody. "Is your mind rough or smooth?" makes no sense. It's like asking "how loud is 3?" — Bartricks
I provided an option that afforded it in case you were theist, because otherwise you may not have subscribed to the others. It is related to the mind, as I said, because if matter is inherently spiritual, then it is also conscious. You cannot have soul and not mind, in a theist worldview.I didn't state it because it is not relevant. You can be a theist materialist, a theist dualist, and a theist immaterialist. Theism is the view that God, or a god, exists. It is not a view about the nature of the mind. — Bartricks
If you justify this presupposition as being evident to you, then there is little that can be said about it. It is not evident to me. Nothing wrong altogether (doesn't make us both right either), but it is a difficult debate when the fundamental perspectives of two people cannot align.It does not make sense to wonder what colour, shape, smell, texture, or taste one's mind has — Bartricks
If there is just one mind, what would draw a boundary between the mind simply being compelled by unnatural forces and the mind being part of a physical world? Those two options become distinguishable only terminologically. There is no other sense of distinction between them.No, that's just confused. Solipsism is a view about the number of minds that exist. It is 'not' a view about the nature of the mind. One can be a materialist solipsist, one can be a dualist solipsist, one can be an immaterialist solipsist. — Bartricks
You didn't state whether you are theist, so I provided a theist option.What? I made arguments in support of the view that our minds are not sensible objects. No premise in any of my arguments (I gave 2, I have 14 - and what I am about to say is true of all 14) assumed a position on deities. — Bartricks
What is the problem? I thought that the problem is how can the mind exist. It solves that problem.There's nothing to be said for it. It doesn't solve any problems. It's just silly. — Bartricks
You said that your mind tells you that it doesn't have colors. I wanted to tell you through analogy that the mind may have features that it cannot perceive unaided. The same way we cannot perceive that we have face without mirror. (Or photo, or description from another person.)I am afraid I don't know what you mean or what your faces analogy was supposed to illustrate. — Bartricks
The problem is that if you intend to include free will, B must also affect A. We need to corroborate this, and if we cannot perceive it, then it appears to be just your axiom. Which is fine, but little can be debated here. It cannot be confirmed.When I ask for evidence that the mind is the brain, that's all I'm ever given. Yet it rests on a simple mistake: the mistake of thinking that if A affects B, A 'is' B. — Bartricks
This would be panpsychism, wouldn't it?And b) even if it wasn't a rubbish objection, it would not imply the mind is a sensible thing, so much as that sensible things are in fact made of mental states. — Bartricks
Solipsism denies an objective world. Materialism and dualism both require it.Solipsism is not a view about the nature of the mind, but the number of minds in existence (it is the view that there is precisely one mind in existence - your own). Solipsism, then, is neutral between materialist and immaterialist views about the mind. — Bartricks
It can have implication about the mind, because it spiritualizes matter, making it conscious. In other words, it can become a theistic version of panpsychism.Pantheism is a view about God. So quite why you're raising it I do not know. — Bartricks
What is so silly about it? You can have mind and it can be the result of your material embodiment's innate ability for experience.And panpsychism is just silly and not implied by any of the arguments I gave. — Bartricks
I ask many times - why dualism and not solipsism, pantheism or panpsychism? You can have shapes and colors (which are just relations of some kind, nothing brutal), while still perceiving those shapes and colors. As an analogy, when we look at other people, they have faces, but we can never see our face directly. Why then assume that self-description should be innate quality?Sensible objects have colours, shapes, sizes, smells, tastes. But my reason assures me that it is positively confused to think of my mind as having any of these qualities. So my mind does not appear to be a sensible object. It may still be, of course, for appearances are sometimes deceptive. But where's the evidence?
My reason also tells me that I have free will, yet tells me at the same time that I would not have free will - not of the robust responsibility-grounding kind that it insists I have - if everything about me traces to external causes. Yet if I were a sensible object, everything about me would trace to external causes. So my reason tells me, once more, that I - my mind, that is - am not a sensible object.
And on and on it goes - there are loads of these arguments (I think I have about 14). They're not decisive, admittedly. But each one counts for something - each one is some evidence, prima facie evidence, that our minds are not sensible objects.
What countervailing evidence do you have that our minds are sensible objects? — Bartricks
Some variants of dualism might be ontically distinguishable, albeit not in a way that can be corroborated. The differences might not be detectable on earth or might be perceivable only through the lenses of hypothetical psychic observer. I accept such notions, because like with solipsism, there is difference between the version of the proposed reality therein and the conventional ones, even if it fails to project into sensory experience. Such description is still irrefutable. I insisted originally that there are different categories of questions that we could ask to distinguish one theory from the rest - ontic, epistemic, ethical and antropological. Some are distinguishable only through some of these questions, but to me, all should be distinguishable in an unambiguous manner as ontic descriptions or they are synonyms to another theory.I'd be a little less polite and add "...or how it distinguishes its description even conceptually from..." ANY theory with no proof, including any conspiracy theory you could concoct. ps - I will NOT that discuss that topic here, just using it to make a point. — GLEN willows
I would claim that if a proposition is not elaborated in terms that can be experienced, witnessed somehow, we cannot truly call it a hypothesis. I concur that it may be presumptive to insist that the terms refer to material aspects of life, but if they do not, the only way in which the proposition can be corroborated (on earth anyway) is through spontaneous agreement of intuition. Which doesn't appear to be all that effective for the philosophy on dualism, because it remains a divisive subject. If the proposition is not elaborated, it can be part of the discourse, in the positive or in the negative, but since it cannot be asserted even in principle, it is not a hypothesis. Second, a theist or a spiritualist is not claiming a hypothesis, but making a conjecture, even an assertion. According to my views, even materialists do that all the time - make conjectures based on unproven assumptions - but they are at least compelled to do so from emancipated forces in the external world. (And I don't mean just empirical evidence, but also sustained practices, biological dispositions.) I fail to see the motivation of a dualist to decide against the other choices - solipsism, intersubjective idealism, panpsychism and pantheism and claim dualism in particular. There doesn't seem to be enough particular arguments for it stemming from experience, in contrast to the other choices. It appears to be based on personal bias. Thirdly, if a hypothesis of dualism makes no physically tangible claims, then I fail to see how it distinguishes its description even conceptually from solipsism. I am not saying that all variants are like that. But certain flavors of dualism, particularly theistic dualism, are not even trying to be definite. (They rely on an "either you get it, or you don't" style of persuasion. Granted, life is like that in the end, based on intuition, but apparently the message does not translate well to everybody, so we have a problem for the philosophical debate.)But is this at all necessary? Isn't it possible that dualist hypotheses with connectivity CAN be constructed without anyone asking but where is this theory in space and how can I grasp it with my fingers? — magritte
The point was that you appear to think of two different references "the feeling of love" and "the synaptic activation of love" as referring to different phenomena, because they are differently expressed. I was remarking that this is not necessarily so. If it is correct that self-reflection manifests as a second order mental activity in a separate set of synaptic connections, there could be any number of synaptic expressions (and linguistic expressions) referring to the one unique original mental process, if those references are produced through different congnitive loops - internal cerebral loop, sensory loop of immediate observation of behavior, sensory loop of aided observation of the underlying physical causes. You are essentially asking, how can "the king" and "Arthur" refer to the same thing, if obviously they embody different ideas. That is because the same referrent is designated through different perspectives. And, if my neuroscience hypothesis is correct, those perspectives are second-order synaptic expressions, different from each other and the expression of the original phenomena, but amorphous. As a side note, not all animals can come to the realization that they are their image in the mirror. (Edit: I meant, that they are the object perceived through the image in the mirror. I hope that we wont have to start an argument over the semantics of the "image".) Thus, understanding that multiple references acquired though different cognitive pathways have the same referrent is an evolved feature of select number of species. (I think dolphins and guerillas or chimps, I am not sure.)Sure but I don't see what that has to do with anything. The emotion of love is represented differently in the brain from the concept of love. Ok.... Now what? — khaled
Having the least amount of presuppositions is the most rationally correct approach, indeed. But it is also the least useful in practice, and philosophy, albeit the most abstract of sciences, still has some interest in its utility in the pragmatic sense. It is very important philosophically to explain what the assumptions are and to investigate their significance, so I am not dismissive of solipism at all, but extreme reductionism results in absurdism. Ultimately, everything lies on some amount of blind conviction. For philosophical purposes, I contest even "cogito ergo sum" (even though I wont go there, because I know I will sound delirious), but like Hume, I don't live that way.But my contention is that many phil. theories THEMSELVES lead to solipsism. — GLEN willows