• Mathematical platonism

    It's
    ...only be grasped by a mindWayfarer
    that is problematic. Again, what might it be for a mind to grasp a number, apart from being able to count to it, add it, or halve it?

    If you can count out seven things, do additions that result in or use seven, double and halve seven... what more is there that you are missing, that is needed before you can be said to have grasped seven?

    I don't think there is anything more to grasping seven than being able to use it. Hence concepts are no more than being able to work with whatever is in question, and thinking of them as mental items in one's head is fraught with complications.
  • Mathematical platonism
    But it doesn't vitiate the fact that the number is independent of any particular mind, but can only be grasped by a mind.Wayfarer

    I don't get that. What is it for a mind to grasp a number, apart from being able to count to it, add it, or halve it?

    Numbers are not things in the head, not mental furniture.
  • Mathematical platonism
    In the Metaphysics, Aristotle identifies multiple senses of "being," which include:
    * Substance (ousia): The primary sense of being, referring to what a thing fundamentally is.
    * Qualitative Attributes: Being in the sense of having certain properties (e.g., "the apple is red").
    * Existence: Being in the sense of "being there" or existing in time and space (e.g. "the apple is on the table")
    * Potentiality and Actuality: Being as a dynamic process, involving what something can become versus what it is.
    Wayfarer

    The last three can be parsed as predications.

    The first is ambiguous, partly about placing something in the domain of discourse and hence making it subject to quantification, and partly about essences, which are more trouble than they are worth.
  • Mathematical platonism
    Philosophical argument, trying to get someone to believe something whether he wants to believe it or not, is not, I have held, a nice way to behave toward someone — Nozick, 13
    But why should that stop us? :wink:

    Maybe the place to start is "Using a term just is using a concept". What if we reply, "Yes, but is using a concept just using a term?"J
    Here I'll reach to my other pet philosopher, Austin.

    The concept "seven" just is being able to buy seven apples, adding three and four, taking nine from sixteen. There is not a something in addition to these that is the concept of seven. So yes, using a term just is using a concept, but we can do stuff without terms, so using a concept is not just using a term. But better than any of these, just drop the use of "concept" altogether. Drop the concept seven and just add three and four.

    The implicit picture is of a "concept of seven" in someone's head that are called when one does things with seven. But if we can add three and four, what further explanatory work is done by the concept?That's why this is muddled:
    Brain; ( number system 1 )
    Brain; ( number system 2 )
    Brain; ( number system 3 )
    Mark Nyquist
    But I'm not sure if Mark is advocating or laughing at the suggestion.

    ...evidently it can be referred toJ
    Waved at, perhaps.
  • Mathematical platonism
    I'm somewhat familiar with Nozick's politics, which have not inspired me to read his wider philosophical work.

    Speaking from this ignorance, if we are going to take philosophical pluralism seriously, shouldn't we avoid the sort of over-arching story found in Philosophical Explanations? Shouldn't we avoid saying that philosophical explanations are thus-and-so?


    But to this:
    The sense of the world must lie outside the world. In the world everything is as it is and happens as it does happen
    Again, this is from the Tractatus, which I take PI to supersede. Roughly, post-PI the "sense of the world" remains unstated, but can be either enacted and shown, or left in silence. In neither case is the sense of the world said.

    So this comes down to what we might mean by "expressible" in "is the sense of the world expressible".
  • Mathematical platonism
    Your reply deserves much more attention.

    You offered as a way forward for the different approaches adopted by @Wayfarer and I. offers the Aristotelian account as paradigmatic, which we might come back to later.

    You phrased the question as about what the three parsings of "is" in a first order language are able to account for in terms of being and existence, and whether there is more to being and existence than these can be grounded in predication, equivalence and quantification. The issue is now "Will it ever be helpful to use the words 'being' and 'existing' to talk about this ground?" but where the issue is one of terminology rather than concept. I have two issues with this. Firstly that we can't long maintain a distinction between concept and terminology, and secondly that our words and actions work directly in the world and not on our model of the world.



    It is difficult to maintain a distinction between what is conceptual and what is terminological, between the structure we accept of how things are and the labels we apply to that structure. This because using a term just is using a concept. This follows immediately from not accepting that there is some thing we can call the "meaning" of the term that is distinct from it's use, but instead looking just to their use.

    Two caveats here. Firstly I put this in terms of use, as per Wittgenstein, but it can equally well be put in terms of truth functionality, so as to more closely approach Davidson.

    And secondly, the use of "terminology" may mislead folk into supposing that that this view takes concepts to be only linguistic, that it is "language all the way down". That's not what is proposed; rather the concept is the doing.That a cat has a concept of "food bowl" is shown by the behaviour it exhibits, by what it does, by how it uses the food bowl. In this regard, language is just more doing, more behaviour. But - and it is an important but - once language comes into play, there is no going back. The rational structures developed on language cannot be rescinded. Concepts are displayed in our actions, including those actions that involve language. Indeed, our concepts are our actions.



    Davidson has shown how trying to explain our behaviour, especially our linguistic behaviour, in terms of conceptual schema leads to irredeemable difficulties. Specifically, that we understand what someone else is doing and why implies that their supposedly different conceptual schema is subsumed by our own. We could not recognise their behaviour as consistent and coherent without thereby making sense of their supposed conceptual scheme. But what this shows is not a similarity in conceptual schemes but that they and we have the same beliefs and act within the very same world. It's not the conceptual schemes that are similar but the world in which we are embedded. Our actions, including our language, are in direct contact with that world.



    This post compresses two very large ideas into a very few words. But it might give someone with the right background in Wittgenstein and Davidson an idea of the direction in which this conversation might head. Others will misunderstand. I can't help that.
  • Mathematical platonism
    Re: the whole quantification thing, this just seems like equivocation.Count Timothy von Icarus
    :wink: Quite the opposite. It's the clearest definition hereabouts. Your Cassius is being a prat.



    Edit: I should add, quantification is only one part of the explanation offered - it includes predication and equivalence and domains of discourse. Quantification tells Brutus and Cassius that we can talk about ghosts. Predication might be used to further say that ghosts are immaterial, imaginary or superstition. Cassius is mistaking quantification for predication.
  • Mathematical platonism
    But that is much nearer to phenomenology and transcendental idealism than it is to direct realism.Wayfarer
    :wink: No. It is direct realism, in that there can be no gap between the talk and what we talk about.

    That's why i haven't participated in @Srap Tasmaner's new thread - there is no model.


    Edit:
    At a certain point we can realize that we now have a pretty adequate conceptual map...J
    There it is again. I have to go with Davidson here and deny that a map sits between us and the territory.

    But real life calls. Later.
  • Mathematical platonism
    ...the factual world only has its intelligibility on the basis of acts of coordination and correlation between events and schemes which assimilate them.Joshs
    Sure. That does not make the world only the result of those "acts of coordination and correlation between events and schemes which assimilate them". Not just any "acts of coordination and correlation between events and schemes which assimilate them" will do. There remains novelty, agreement and error, embedding us in a world that does not care what we believe.
    I’ve forgotten now.Joshs
    Me too.
  • Mathematical platonism
    Sure, we can make new use of antique arguments. But they are not in themselves authoritative; and there are reasons they are antique.
  • Mathematical platonism
    Then it becomes very unclear to me what you were saying way back here, where in rpely to my "π is not private thing in each of our heads, but a public thing that is used openly to make calculations and settle disagreements" you said:

    Pi is like any other word. It is communicated in partially shared circumstances. This circumstance includes your brain processes and my brains processes , along with their embodiment in each of our organisms and the embeddedness of our brains and bodies in a partially shared social environment. None of these aspects
    can be neatly disentangled from the others, but the fact that the meaning of pi is only partially shared between us explains why its use by either of us can always be contested by the other.
    Joshs

    What is your point of disagreement, if there is one?
  • Mathematical platonism
    . But there's no way to extend that to the relationship between brain, mind, and thought.Wayfarer
    How do you know that "There is no way" here? Overstretching yourself, again, it seems. The best you might conclude is that it hasn't been done yet; that's not to say it cannot be done.

    The neuroscience is in a state of rapid development.
  • Mathematical platonism
    You have it exactly backwards. It is the factual world which is dependent on the processes of transcendental consciousness. Husserl was not a realist. The factual world was for him a product of the natural attitude, which concealed its own basis in subjective processes.Joshs
    And yet not just any "processes of transcendental consciousness" will do; the "processes of transcendental consciousness" is itself restricted by the "factual world"...

    It's not either realism or idealism, We construct the facts, from the world.
  • Mathematical platonism
    If the language game were different, the meaning of pi could change even if the description remained the same.Joshs
    You talk as if there were a discrete entity that is the "meaning" of π.

    That's the bit to which I am objecting.

    Whether you use π to find the volume of tanks or the orbital period of a planet, the extension of "π" is the very same. That much is clear.

    That we are doing something different with π does not imply that we are using a different π.

    If in your novel language game the value of π is different, then that is simply not a use of π.

    So extension is clear. Meaning, not so much.
  • Mathematical platonism
    Regardless, hope the point is clear.Wayfarer
    Again, you express a tractatian view, that is not carried forward.

    Thomas preserves an element of the philosophia perennis which has elsewhere been forgotten.Wayfarer
    Forgotten or bypassed? I remain unconvinced.
  • Mathematical platonism
    There's some value in Thomism. But recent posts have relied on appeals to Aristotle and Plato as if they were authoritative; as if that they said it were proof enough.

    This too will pass.
  • Mathematical platonism
    Plato's theory of the mind is outdated.Arcane Sandwich
    You've happened on the forums at a time when the fashion is towards mediaeval thinking.
  • Mathematical platonism
    Nice. That's Tractarian. Can you show that this view was maintained unmodified into the Later period? And if not, how was it modified?

    I'd suggest that "I am my world" is itself something that can only be maintained as part of a community - so "I" has a sense only against "you". If language is not private, neither is the world. I am my world, in relation to others. The sense of isolation or separation associated with solipsism arises from misunderstanding how language works.
  • Mathematical platonism
    Yes, but also their logic is wanting. Peirce because he was prior to Frege, Husserl... perhaps just didn't get it.
  • Mathematical platonism
    I don't disagree. Although the way Husserl expresses it is unnecessarily obtuse. (Edit: and Peirce not much different.)
  • Mathematical platonism
    What I say is that objects exist for a subjectWayfarer
    And my reply is that yes, saying (believing, doubting) that something exists does indeed require a mind.

    But not existing. There is gold in those hills, even if it remains unsaid (unbelieved, undoubted).
  • Mathematical platonism
    you wont find "hu(n)gry" by dissecting a stomachArcane Sandwich
    "Hungry" isn't something stomaches do. Being hungry takes an organism.
  • Mathematical platonism


    @Wayfarer has a point - you will not find seven by dissecting a brain.

    One might conclude that there must be two sorts of things, the mental and the physical. But there are alternatives.

    Wayfarer sometimes says that there are only mental things, but when the problems with this are pointed out, he quickly retracts such a view.
  • Mathematical platonism
    What is denoted by the symbol is an intellectual act, namely, an act of counting. And that act is not an existent, in the sense that objects are existents. This is where the distinction can be made between the kinds of existence of numbers (etc) and sensory particulars.Wayfarer

    Both numbers and chairs exist.

    Where they differ is not in their existence, but in the other properties they have. The chair has a time and place, the seven, no so much.

    It would be an error to think of this as a difference in the way in which they exist, or as a difference in their being (whatever that is).

    But this seems to be an error Wayfarer is prone to.
  • Mathematical platonism
    "Mind is to brain as digestion is to stomach". Searle.

    Is digestion also lumpen materialism?
  • Mathematical platonism
    ...a description of what pi refers to cannot guarantee that what I do with it is the same as what you do with itJoshs

    Sure.

    So what.

    I use π to work out the volume of a water tank. You use it to lay out the design for your garden. We are not here making use of a different thing. You could also use it to work out the volume of the tank.

    That you do something different with π does not suggest that you are using a different π.

    Edit: But this seems to be the implication of your approach. You can disavow that, if you like. It would be good if I were wrong here, since it might lead to some agreement between us.
  • Mathematical platonism
    Things are not pragmatism and convention all the way down becasue at some point we must simply act; we make it so.
  • Mathematical platonism
    The extension of π, what it refers to, is the ratio of a circle's diameter to it's circumference. The "sense" or "meaning" of π? If we have what we do with π, what more is there?
  • Mathematical platonism
    I don't find Heidegger of much use. Same goes for most of that school of Phenomenology.

    the meaning of pi is only partially shared...Joshs
    But that's not quite right - π refers to the ratio of the diameter to the circumference of a circle; that's it.

    Moreover, the idea of meaning as shared is decrepit. Meaning is something we do. Or better, stop looking at meaning and look instead at use.
  • Mathematical platonism
    which means that they are brain processes occurring inside the living brain of a member of the biological species homo sapiens.Arcane Sandwich

    There's a simple argument to show that this is not so.

    If π is a brain process in your brain, and also a brain process in my brain, then it is two different things.

    But if that were so, when I talk about π I am talking about a quite different thing to you, when you talk about π.

    This is a cut-down version of the private language argument. π is not private thin in each of our heads, but a public thing that is used openly to make calculations and settle disagreements.
  • Mathematical platonism
    (existence) is a property. It is something that material objects have. It is the property of having a spatiotemporal location (which can be fuzzy or clear-cut, it doesn't matter).Arcane Sandwich

    "A is at (x,y,x,t)".

    Therefore something is at (x,y,x,t).

    But π is not at (x,y,x,t); are you willing to conclude that π does not exist?

    There are genuine problems with treating existence as a property, some brought out in free logic, some accounted for in ordinary first-order logic. There are reasons that quantification is different to predication. Reasons first order logic works with "∃(x)" and not ∃!x. Foremost are perhaps the difficulties in applying extensionality to existence if it is treated as a predicate.

    Extensionality is simply the idea that if two predicates range over the same individuals, they are the smae predicate. If f={a,b,c} and g={a.b.c} then f=g. If we allow ∃! to be a predicate of this sort, then does it includes everything? What things are not in ∃!? The elements of ∃! are the domain of discourse.

    I don't know how Bung deals with this, but in free logic is leads to there being two domains, one of things that exist and one of things that do not. And it gets a bit weird.

    So if ∃! is a property, it is not like (f,g,h...) and the other properties of first order logic.
  • Mathematical platonism
    Nice work. I'll go along with that.

    I baulk at your distinguishing "conceptual" from "terminological". Our terminology sets out our "conceptual framework" as it were.
  • Australian politics
    Canberra. Only got to 30℃ yesterday.

    Stay out of the smoke.
  • Mathematical platonism
    What does that post say? Is it in some way a counterproposal? How?
  • How can one know the ultimate truth about reality?
    Have you found philosophy useful?Tom Storm
    Well, yes, but not in any grand sense of providing an understanding of the whole of life or such. More in a piecemeal, day-to-day way. More by showing what's not right than by showing what 's right.
  • Mathematical platonism
    , , my contribution to rebutting the centrality of a being/existing distinction is to point out the three translations of "is" in first order logic - predication, equivalence and quantification. Is there something that is not covered by these but is available in being or existing?
  • Hypostatic Abstraction, Precisive Abstraction, Proper vs Improper Negation
    Not so much. Reminds me a bit of General Semantics.

    Happy new year.
  • How can one know the ultimate truth about reality?
    I have known many people with psychosis whose reality differsTom Storm
    Yep. I'd say that their beliefs differ, rather then their reality. When I worked with such folk one approach was to gently show them how their belief didn't match what was going on, or what others thought, or as least wasn't getting them what they wanted. We called it a "reality rub" - an LSCI term.

    While I never worked with the level of psychosis you work with, isn't the objective much the same - to bring about some set of beliefs that are at least a bit more functional?
  • Hypostatic Abstraction, Precisive Abstraction, Proper vs Improper Negation
    Cheers. Suspected so. But I advocated none of those things you list. I'll go over what I said once again, with a slightly different approach.

    Hypostatic Abstraction is taking a predicate and turning it into a relation. That works for some, but not all, predicates. So "The cat is on the mat" can be parsed using one individual, the cat, and saying that the cat is one of the things on the mat. Or it can, by Hypostatic Abstraction on "....on the mat", be parsed as a relation between two individuals, the cat and the mat. Roughly, we take "On the mat(cat)" and use Hypostatic Abstraction to change that to "On(cat, the mat)".

    That works becasue we can treat the mat as an individual.

    But if we take "Honey is sweet" and try the same thing, we end up with your has(honey, sweetness); a mess. What is the "has" here? And the reason it becomes a mess is...

    Sweetness is not an individual.

    To treat sweetness as an individual is to treat a group of things as if it were an individual - to hypostatise.
  • How can one know the ultimate truth about reality?
    Not quite following - the latter, so you prefer there be at most one reality; but which includes both subjective and objective realities?

    And this makes things simpler? Again, I don't think the objective/subjective dichotomy is of much use, nor that it can be tightened up. We can mostly get by without it.