Yes; so an object with no start is a non-existent object; IE infinite time is impossible. Same argument for infinite space. — Devans99
Singularities are nasty beasts, and there's a better reason for eschewing them than past experience: singularities blow up your model in the same way that division by zero does (division by zero is one instance of singularity); they produce logical contradictions. — SophistiCat
That’s not correct, they make recourse to the limit concept which is not the same as actual infinity. — Devans99
If you accept relativity as pretty close to the truth you necessarily must accept that space is infinitely divisible (basically true in quantum mechanics too). Hell, a large chunk of quantum mechanical interpretations are relativistic as well so I don't even see the objection here.I believe and so I thought did everyone that relativity is a close approximation only of the large scale universe. The plank length is very small so reality is approximately continuous hence the theory works so well. — Devans99
But numbers just exist in our mind and our minds have finite capacity so numbers are finite in that sense. — Devans99
There is a big difference adopting the maths because it is a useful model and accepting it as the actual metaphysics. And it should be telling that the central problems of modern physics/cosmology revolve around finding ways to avoid the mathematical infinities, or singularities, that are contained in the current best models. — apokrisis
I’m not suggesting dropping infinity from maths. It’s fine with the limit concept and set concept. I’m suggesting dropping actual infinity in physics and metaphysics when used as the value for real world quantities. — Devans99
Relativity is an approximation of reality not reality - We don’t know for sure if space is continuous. Anyway continuous space is a Potential Infinity whereas I’m talking about Actual Infinity. — Devans99
There is an argument that the natural numbers are only potentially infinite - we have used finitely many of them so far and that will remain the case. — Devans99
’m hardly the only person to have a problem with actual infinity. The great German mathematician Hilbert posed his Infinite Hotel paradox. Just one of many paradoxes that stem from actual infinity — Devans99
I know it’s possible to construct consistent mathematical systems around infinity; that is not what I’m objecting to. I’m objecting to the use of actual infinity in physical sciences. — Devans99
in many instances and is holding back scientific progress. — Devans99
Many, many paradoxes and speculative theories disappear at a stroke if we are simply willing to acknowledge the actually infinite cannot exist.
There are strong arguments against the actually infinite. For example, no matter how many times you add one you never reach infinity so actual infinity is impossible to achieve.
On paradoxes, for example, Zeno’s paradoxes, there is a very simple solution if you take the view that the actually infinite is impossible: — Devans99
In the physical sciences we used to be quite strict with infinity:
- used only as approximation of very large/small
- indicate of logic error when occurs elsewhere
- even in maths infinity = divide by zero = logic error — Devans99
But I guess belief in the actually infinite keeps cosmologists in a job for an actually infinite period of time... — Devans99
Simply put, should we let evolution do what it does best which is filter out the weak? — intrapersona
Good point. So, we can agree that the real world is logically prior to any possible world. — Dfpolis
So, when you say "if the laws of physics were different," you are excluding from S any proposition specifying the actual laws of physics, the evidence leading us to them and their implications. Thus, my definition is perfectly suited to your example. — Dfpolis
My objection is that the construction of possible worlds does not add to our knowledge of the real world, which remains the same (except for our mental state) no matter what we imagine. In other words, imagining a possible world can give us no new data on the real world, which alone is relevant to understanding our experience consistently. — Dfpolis
Why bring in a construct of dubious ontological status? Why not be more parsimonious and say it means "I see nothing to prevent me from being a doctor"? What does the construct add to this besides an unnecessary discussion of the ontological status and semantics of possible worlds? — Dfpolis
Yes, but not in any essential way. Think of all the things we imagine that do not turn out. That some imagined possibilities become actual does not justify the claim that all imagined worlds are possible or self-consistent. — Dfpolis
"Our sensory representation of an object" is just another name for the modification to our sensory state brought about by sensing that object. What else can it be? — Dfpolis
Of course, this is blatantly false. It's like saying, if we have a noisy connection, we aren't talking to our mother. In other words, it's nonsense. — Dfpolis
Hardly! I've explained many times now that since they are not actual, possible worlds aren't "there." I've made it clear that their only existence is intentional -- the unparsimonious imaginings of overwrought philosophical minds. — Dfpolis
It is the name of the concept because the employment of the tool requires one to construct, or at least recognize, worlds that are possible. — Dfpolis
My point is simple: Independently of whether or not there is such a thing as modal logic, only one world exists simpliciter -- ours. Thus, unless you do add "possible" to "world," consideration is restricted to our actual world. So, using your definition, if p is false in this world, it is impossible. Appealing to modal logic is irrelevant misdirection and distraction. — Dfpolis
Which means that "Venus" picks out multiple objects (one real, many imagined) and so it is a universal, not a proper name. The only alternative is to say that an imagined Venus is numerically identical with the actual Venus -- but to say this is to deny the difference between reality and fiction. — Dfpolis
But, it may still be the condition that specifies to whom the proper name is assigned. If we are to pick out which object to call "Dennis" or "Venus" in a modified world we need a well-defined set of criteria. Lacking such criteria, who or what is designated by these names in some possible world is indeterminate. What if we imagine a new second planet; is it, or the third planet, to be called "Venus"? You may choose to ignore such niceties, but if you do, the possible worlds construct is ill-defined. — Dfpolis
Inclinations are not a species of modality. They are actual. They determine how an object will act in well-defined circumstances. They are no more "modal" than the laws of nature. If we bring two particles of the same charge next to each other, they will exert a repulsive force according to Coulomb's law. That is a fact about the contingent structure of nature which requires no reference ot possible worlds. — Dfpolis
This is like saying that a map with a misprint is not worth anymore than a possible map. — Dfpolis
P is possible with respect to a set of facts or propositions, S, if P does not contradict S.
I do think "facts" should be restricted to intelligible reality. — Dfpolis
There is no claim of infallibility here. If you think there is, explain how.
The actual world is actual because it acts to inform us. Merely possible worlds do not act, let alone act to inform us. Instead, we inform (or perhaps misinform) them. — Dfpolis
First, it is unnecessary. As we can have no epistemic access to any world but our own, actual world, anything we can learn, we can learn from the real world.
We have no access to any possible world. We only have access to our imagination, which can easily be inconsistent. What we know of the actual world cannot "easily fail" if we exercise due diligence. It fails occasionally, but it is usually interpretations and constructs that fail rather than experiential data. — Dfpolis
I said that a sensory object's modification of our sensory state is identically our sensory representation of the object. I said that the object informing the subject is identically the subject being informed by the object. — Dfpolis
It is the name of the concept because the employment of the tool requires one to construct, or at least recognize, worlds that are possible. — Dfpolis
This is inadequate as, unless P is actually true, there is no world in which P is the case. What you need to say is "P is possible if there is at least one possible world in which P is the case" -- and that is circular. — Dfpolis
Still, they are not our world, as, if they are different in any way, they are not identical to our actual world. Any world that is not identical to our world is a different world. As each is a different world, each (actual or potential) object in them is a different object from any object in out actual world. — Dfpolis
When I use the notion of a rigid designator, I do not imply that the object referred to necessarily exists. All I mean is that in any possible world where the object in question does exist, in any situation where the object would exist, we use the designator in question to designate that object. In a situation where the object does not exist, then we should say that the designator has no referent and that the object in question so designated does not exist — Kripke
Objects are individuated by the network of relations that contextualize them. If you change one relatum, you change the object's individuation conditions. So, the individuation conditions may not return the same object. E.g. if I am the oldest child in the real world and in the possible world I have an older brother, the individuation condition of being the oldest child will not return me. — Dfpolis
Counterfactual propositions can be judged on the basis of real-world potencies. Steve would have enjoyed the trip even if he did not go on it because he is actually disposed to enjoy such trips. If we did not know his relevant dispositions, we could not say whether he enjoyed the trip or not. So, there is no need for possible worlds talk to deal with counterfactuals. — Dfpolis
not require that everybody else also deal with their choice. Even if 1 million English speakers out of the 1.5 billion people who speak English reject gender,it's still their problem, not mine. — Bitter Crank
This seems an attempt to give possible worlds the same epistemological status as the real world, hence my justification of direct epistemic access. — Dfpolis
Facts are actual, not merely possible. Possible worlds might be a consistent set of posits, they are not a consistent set of facts.
Yes, I used "possible" -- not essentially, but to avoid circumlocution. So, here's the same definition restated: "P is possible with respect to a set of facts, S, if P does not contradict the propositions expressing S."
If I didn't consider objections, I wouldn't have said "reliable." Yes, it's doing a lot of work, but that doesn't mean that we can't have true knowledge, where "truth" is understood as adequacy, not as exhaustiveness or infallibility. I've made no claim of infallible human knowledge, so the notion of infallibility is a straw man -- effectively replacing human knowledge with divine omniscience. Primarily, "knowing" names an human activity, so requiring infallibility as you seem to is a bait and switch tactic. — Dfpolis
First, it is unnecessary. As we can have no epistemic access to any world but our own, actual world, anything we can learn, we can learn from the real world.
If you can't see that using possible worlds as the ultimate basis for defining possibility is circular, I can't help you. — Dfpolis
A "Venus" in another (possible) world is not our Venus. Therefore, one can only be call both "Venus" by equivocation or by universal predication. — Dfpolis
But, in my example, the terms are referential via the same types of experiences that give them reference here. Each rigid designator names is appropriate object: There are morning and evening stars and a second planet. It is just that the references are not what you want them to be. You response will define my possible world out of consideration. So, again, the conclusion is based on how you choose to construct a set of possible worlds, not on any observable facts of the matter -- and that is precisely my objection. — Dfpolis
A plural pronoun for a singular meaning. Alright it's common in use when we don't know who we're referring to. But it gets too contradictory when we do know, and we use a plural pronoun to refer to one person. ...and it gets even more incongruous, contradictory and funny-sounding when we use a singular verb with "they". — Michael Ossipoff
So, to say that we do not perceive what we are perceiving is an oxymoron and an abuse of language. — Dfpolis
A consistent "set of facts" is one way of articulating what a possible world is so I don't even know what you think you're arguing against at this point.Yes, I used "possible" -- not essentially, but to avoid circumlocution. So, here's the same definition restated: "P is possible with respect to a set of facts, S, if P does not contradict the propositions expressing S."
No, a circular definition is no definition, whereas my proposal is an actual definition. — Dfpolis
Naturally "reliable" is doing all the work here, being used to obfuscate the fact that there's no guarantee that perception maps to reality such that we can have an infallible means by which to say some experience is reliable. It's like you've never considered any objection to your views ever.By "reality" we mean what's revealed in reliable experience. So, to say that what we experience is not "real" is an oxymoron — Dfpolis
Yes, most of which are modal concepts, hinging on possibility and its correlative, necessity. So, yes, possible worlds talk is circular. I have seen "necessary" defined as true in all possible worlds. Since "necessary" means the contrary is not possible, this is circular. — Dfpolis
First, proper names name one, not multiple, individuals. So, to say it's nonsense to say that "Venus" names the same object in every possible world because Venus does not exist in every possible world. — Dfpolis
As I pointed out in my critique, your analysis does not consider all possible worlds, only those consistent with certain contingent facts. As you are constraining possibility with contingent facts, the result is only necessary contingently, not metaphysically necessary. For there are possible worlds in which the light in the morning sky has a different source than the light in the evening sky -- even though they both exist, along with a second planet from the sun. — Dfpolis
That example is of something nobody would ever say and expect to be taken seriously. I don't regard the lack of applicability to something nobody would ever seriously say as any reason to discount a definition. — andrewk
My understanding is that the modality the possible worlds paradigm seeks to explain is not the fancy modality of modal logic, but the modality of everyday speech, when we say something is possible, impossible or certain. — andrewk
There's no need for possible worlds in that interpretation. I can't personally see any value in the possible worlds paradigm. — andrewk
For example, an object's modification of our sensory state is identically our sensory representation of the object. As one state belongs both to the sensed object and to the sensing subject, there is an existential penetration, not a gap. — Dfpolis
If you do not understand "possible" or "necessary" you will not understand "possible world." — Dfpolis
I do not define "possible" in terms of worlds. P is possible if P does not contradict the set of propositions which it is possible with respect to.
Further "alternate world" does not mean "possible world." I may imagine any number of alternate worlds that are not self consistent, and so impossible. If you want to bring in the concept of self-consistency, you may, but then you're not defining modality in terms of a set of worlds, but following my definition of the last paragraph.
Yes, it is, because it leads back to circularity. To define any type of possibility you must specify what makes a world "possible" in that way -- which means that you need an independent definition of that mode of possibility -- in other words, the worlds cease to be a primitive, and are merely an unparsimonious wart on your theory. — Dfpolis
Now you can say that "Hesperus" and "Phosphorus" are "rigid designaters," but there is no intelligible property that allows us to determine one way or the other if they are. — Dfpolis
Is there an a priori possible world in which one planet appear in the sky in the evening and another in the morning? I don't see why not — Dfpolis
Hesperus = Phosphorus’ is necessarily true if true at all because ‘Hesperus’ and ‘Phosphorus’ are proper names for the same object. Like other names, Kripke maintains, they are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world. The object that ‘Hesperus’ and ‘Phosphorus’ name in all possible worlds is Venus. Since ‘Hesperus’ and ‘Phosphorus’ both name Venus in all possible worlds, and since Venus = Venus in all possible worlds, ‘Hesperus = Phosphorus’ is true in all possible worlds.
— SEP
Clearly, the conclusion is nonsense, because "necessarily," does not even follow the norms of possible worlds talk. There are many worlds that seem perfectly possible where this is not so, but they are excluded by hypothesis and arbitrary dictate. — Dfpolis
First, it is unnecessary. As we can have no epistic access to any world but our own, actual world, anything we can learn, we can learn from the real world. — Dfpolis
Second, if the purpose of possible worlds talk is to define the meaning of modal statements, it is circular. If a person does not understand modality, they will not understand the meaning of "possible worlds."
Third, speaking of worlds as simply "possible" allows one to confuse logical, physical and ontological possibility. — Dfpolis
If possible worlds talk is nonsense, then rigid designators are undefined.
A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else. — SEP
There is no ''discernible'' difference between two electrons, for example. So, identity, as in uniquness, is a problem for electrons. Am I getting your point? — TheMadFool
So, if at all there's a problem with the concept of identity it lies with our inability to see the difference between electron A and electron B. It's subjective. But we know there IS a difference in location between A and B. That's objective.
Why do you think the Law of Identity is required in classical logic? I'm guessing here that, as one of the three laws of thought, it is a necessity for logic. — TheMadFool
Without this basic agreement conversation would be impossible right? — TheMadFool
We allow the usual connectives, quantifiers, an identity relation symbol, and punctuation symbols. For one of the kinds of terms (variables and constants), let us say T p T2, ..., terms of the first kind, we allow that identity holds as usual. In the intended model they represent the individuals. For terms of the second kind, tp t2, ..., identity is not an allowed relation. In the intended interpretation those terms denote non-individuals, items with no identity conditions
Do you mean that sentence to be taken as truth? — Heiko
"Quasi-set theory Q is a first-order ZFU-style set theory. Its underlying logic is just like first-order classical logic without identity (the system L mentioned before), with a significant difference: the semantics for that system L underlying Q is described in a non-reflexive metalanguage; just like classical logic has a semantics developed in classical set theory, this particular system of logic (i.e. L) has a semantics developed in a non-reflexive set theory (more on that topic soon). So, the system in question is not exactly classical logic, but it formally coincides with classical logic, although it is semantically different (since its semantics is provided in a non-reflexive metalanguage)." — Classical Logic or Non-Reflexive Logic? A case of Semantic Underdetermination
"This is also connected with a second point. What exactly is meant when we say that
we deny a tautology (or a logical law, or a logical necessity)? In denying that an axiom
of classical logic is valid in general, don’t we have to accept that this ‘axiom’ is false
in at least one interpretation of an alternative system in which the same formula may
be expressed? Consider, for instance, intuitionistic logic. In denying the validity of
some instances of the law of excluded middle, it is not the case that intuitionists accept
its negation in its place. However, they do accept that the law may be false sometimes
(mostly when we deal with infinite collections)."
[...]
"As we have said in the previous section, in non-reflexive logics we do not accept
the negation of the reflexive law of identity. Also, we don’t have to accept that it must
fail in at least some interpretations. Rather, we adopt its restriction in the form of
its inapplicability. Here, ‘inapplicability’ is couched in terms of identity not making
sense, not being a formula, for some kinds of terms. Recall from our discussion in
the previous section that this is the formal counterpart of the idea of something not
having TI. So, if this is correct, the link between metaphysics and logic that underlies
the non-reflexive formulation of the RV is reasonable, in fact, but it does not go in the
same lines as we think it is reasonable to reject some classical principles of logic in
any non-classical logic with the same vocabulary."
Some yes, but mostly it's binary. Planes either fly or they don't, etc. — gurugeorge
That's my point - what they get from those things isn't very good, it would be better if they got things from clever people who had actually spent a lot of time thinking about them.
That's begging the question - we may not, but do we need to? Maybe we need to. Maybe a consistent, structured picture is better than an inconsistent, haphazard one. — gurugeorge
Why not? Who would be a better person to ask so that you, as a philosopher, could be more informed about the topic and be able to incorporate it into your big picture?
But how the ordinary world behaves is of concern to the vast majority of people in their everyday lives, and part of philosophy's job is (or Rand and I would say ought to be) to give ordinary people in their everyday lives some sense of the big picture - otherwise, in lieu of a rational big picture, they'll accept an irrational big picture, or flounder around in a state of permanent anxiety. — gurugeorge
That's true of basically every field though. I'm not going to hit up any random physicist for, say, particle physics questions. This seems like an issue with it any real resolution. If we want to curb specializiation we will have to stop drilling down on the very debates that drive the numerous parts of philosophy. And that seems unlikely to produce novel developments in those areas. Interdisciplinary work is all well and good.All I'm saying is that the discipline is skewed too much to specialization, — gurugeorge
Well, andrewk. Firstly, I'm not a theologian. I'm a metaphysicist. — Lucid
In a nutshell, non-reflexive systems of
logic are systems that violate the so-called ‘Reflexive Law of Identity’ in the form
∀x(x = x). In its ‘metaphysical reading’, the Reflexive Law of Identity is known as a
version of the ‘Principle of Identity’, roughly stating that everything is self-identical.
Versions of this law are restricted in systems of non-reflexive logic, and those systems
are said to incorporate in a rigorous fashion the idea of entities somehow losing their
identity.
Sure there are alternative logics, but the question of interest is which form of logic does the world happen to behave in accordance with? At the level of the middle-sized furniture of the world, at least, it seems to be good old-fashioned binary logic. — gurugeorge
And that's something philosophers can do, but the question is whether it's worth doing - or whether philosophers doing that has been simply an artifact of the academic system. — gurugeorge
What I ''feel'' is that the Law of Identity is required in logic. May be it's only classical logic that requires it because if you deny that water=water then how are we to have a meaningful discussion on water? Isn't consistency in the meaning of words and terms a requirement for sound argumentation? — TheMadFool
We begin by recalling the infamous Problem of the Identical Particles. According to a widely held interpretation of non-relativistic quantum mechanics, there are many situations in which one cannot distinguish particles of the same kind; they seem to be absolutely indiscernible and that is not simply a reflection of epistemological deficiencies. That is, the problem, according to this interpretation, is seen as an ontological one, and the mentioned indiscernibility prompted some physicists and philosophers alike to claim that quantum particles had "lost their identity", in the precise sense that quantum entities would not be individuals: they would have no identity. Entities without identity such as quantum particles (under this hypothesis) were claimed to be non-individuals."
If, in a discussion, the meaning of ''sex'' changes from gender to intercourse we would have a problem:
Name: John Smith
Age: 24 years old
Sex: Daily with my partner OR Male??!!