• Janus
    12.8k
    But I was, in the part you quoted... so you are not addressing that?

    "The cat is on the mat" supposes cats and mats.

    The relevance is that such stuff is already an interpretation.
    Banno

    I don't see what cats being on mats has to do with declarations. Declaratives maybe, I suppose. In any case you should know from many previous posts that I am in agreement with Husserl and Heidegger, (they being, as far as I know, the first philosophers to point it out) that all seeing is "seeing as" or in other words that all perceptions are always already interpretations.

    So, nothing controversial there in what you say.
  • Srap Tasmaner
    3.9k
    Donald Hoffman has a lot to answer for.Tom Storm

    Well, it's early days, and if these beetles survive it stands to reason that the individuals that did not try to impregnate beer bottles will be represented in coming generations at substantially higher rates than those that did. That might be luck. Or it might be that some beetles have a slightly more elaborate criterion for mate identification that excludes beer bottles. So the beetle population should gradually steer away from this particular dead end.

    I can't take Hoffman seriously, so I haven't looked to see whether his model allows this sort of refinement. I don't think evolutionary biologists were committed to a view that species jump to knowing everything all at once.
  • Metaphysician Undercover
    10.4k
    There are only two feelings, pain and pleasure, each with varying degree.Mww

    You start off with a false premise. "Feelings" are sensations and there is many different sorts of them, often involving neither pleasure nor pain. Consider sight, sound, or even taste which is a tactile sensation. Many tastes, like spices for example are neither pleasant nor painful. The same is the case for all the different senses, there are many different sensations which are neither pleasurable nor painful. The sense of touch for example, you can feel around, looking for something with your hand, or feeling your way in the dark, and these feelings are neither pleasurable nor painful, though they are informative. That a particular feeling is peasant, or painful, is a judgement.

    Whether or not all that is granted, it nonetheless authorizes us to say judgements are limited as constituents of our moral disposition, in that because we are this kind of moral agent we will judge good and bad in this way.Mww

    Sure one's judgements are based on one's disposition, but generally speaking we judge good and bad according to how we were taught, not according to what we feel. That is what constitutes our moral disposition, how we've been trained, not how we feel. I don't know why you deny this. And this is how our moral judgements extend far beyond our personal feelings. We make moral judgements concerning principles which have no feeling about at all.

    Now, again, best to keep in mind this kind of judgement is aesthetic, representing a feeling, as opposed to discursive, which represents a cognition. We often do good things that feel bad, as well as do bad things that feel good. From that it follows that the judgement of how it feels subjectively to do something, is very different than the judgement for what objectively is to be done.Mww

    I don't understand this. It seems to be completely inconsistent with what you've been saying. Perhaps you could explain. If "good" and "bad" are solely determined by what feels good, and what feels bad, how is it possible that one could do a good thing which feels bad, or a bad thing that feels good? And what do you mean by "the judgement for what objectively is to be done"? How does objectivity enter morality in your mind?

    Simple example of how we do this, instead of all this concept juggling:

    (1) It is necessary that the book falls if and only if it is not possible that the book does not fall.

    (2) It is possible that the book falls if and only if it is not necessary that the book does not fall.

    "Not" seems to be used in two ways, but it really isn't; under this scheme it is always a proposition-level operator, just like "possibly" and "necessarily". You build necessary this way:
    Srap Tasmaner

    You are just stating the same thing as the last post, in a different way, so the result is the same question i brought up at the end of the last post.

    But "not" is definitely used in two different ways. When you say in (1), "not possible", "not" negates "possible" in the sense of proposing an opposite to "necessary". But when you say "does not fall", here "not" does not negate "fall" as an opposite to "fall" it simply says that the action does not happen. To say in particular, "a fall does not happen", and to say in general, "a fall is not possible", is to use "not" in two distinct ways. "Fall" is a verb, "possible" is an adjective. But the use of "not" is beside the point.

    All you have here is the meaningless, circular definition, which I objected to earlier. "Necessary" is defined as "not possible", and "possible" is defined as "not necessary". But this is not truthful for the reasons I've given. "Necessary" is properly opposed to "impossible", as I've explained. And "impossible" cannot be opposed to "possible" because this would make "necessary" and "possible" the same. So we need to put "possible" in a place distinct from the category which contains those opposites, necessary and impossible.
  • Banno
    18.6k
    so long as it’s “we” who decide, it’ll do.
  • Srap Tasmaner
    3.9k
    the opposite of necessary, necessarily not (impossible)Metaphysician Undercover

    I'll address this, since it's clear enough.

    You are making what I would consider a scope error.

    The opposite of "The car is blue" is "It is not the case that the car is blue," which we can also express as "The car is not blue" because there is only a single level here. (And note this doesn't imply that there is a color we call in English "not blue".)

    But suppose our sentence is embedded in another:

    (a) "Sheila knows that the car is blue."

    What's the opposite of that? Is it

    (b) "Sheila knows that the car is not blue"

    or is it

    (c) "Sheila does not know that the car is blue"

    It's (c). To find the opposite we must negate the outermost, enclosing scope "Sheila knows that ...", not the inner scope "The car is blue". The opposite of knowing something is not knowing it, not knowing the opposite. Everyone knows that.

    So it is with modal operators. If I say

    (1) It is possible the car is blue

    the opposite of that is

    (2) It is not possible that the car is blue

    negating the outermost scope. We do not push the "not" into the scope of "It is possible that ..." producing

    (*3) It is possible that the car is not blue

    anymore than we do with "Sheila knows that ..." That's a scope error.

    The opposite of

    (4) Troy believes that Sheila said that it's possible that Dave knows today is my birthday

    is simply

    (5) Troy doesn't believe that Sheila said that it's possible that Dave knows today is my birthday

    We're spoiled for choice as to where else to stick in our "not", but all the others are wrong. You negate the outermost scope and there's your opposite. Here are all the others, they all mean something different, and none is the opposite of (4):

    (*6) Troy believes that Sheila didn't say that it's possible that Dave knows today is my birthday
    (*7) Troy believes that Sheila said that it's not possible that Dave knows today is my birthday
    (*8) Troy believes that Sheila said that it's possible that Dave doesn't know today is my birthday
    (*9) Troy believes that Sheila said that it's possible that Dave knows today is not my birthday
  • creativesoul
    10.8k
    Well, some species of primates use specific vocalizations as alarms for specific predators sighted in the immediate vicinity. It's also my understanding that not all communities of some species do this, or have the same vocalizations for the same predators.

    That certainly seems like a case of naturally emerging language use to me.
    — creativesoul

    I can't see the relevance of what you are saying here.
    Janus

    You asked about other animals using language. I offered an example. I do not believe that you do not see the relevance.

    It's certainly not the only one. As others have mentioned, dogs will ask for food. My ducks do the same. There are specific behaviours to support all this. Reasoning to boot. Logical argument to bolster.

    Are you denying that these are examples of language use?



    There are many examples and kinds of animal signalling.

    I take it that you're saying that the primates mentioned heretofore are not language users, but merely signaling, and that signaling does not count as language use.

    This presupposes a criterion for what counts as language use.

    I'd like to see the one you're putting to use.





    Only humans, as far as is known, are capable of symbolic language and linguistically mediated thought.

    Unhelpful nonsense. Speaking of anthropomorphism.

    Language does not have agency. All things that are capable of mediation do. Mediation is done for the sake of mediating. Language does not mediate. There are no linguistically mediated human thought.

    Language creation and subsequent use influences and enable the richness and depth of human thought.

    We are not the only language users living on the face of the earth.

    Whatever you are calling "linguistically mediated thought" is neither the only nor the simplest kind of thought humans have. Likely it is one of the most complex.
  • Luke
    2.1k
    All you have here is the meaningless, circular definition, which I objected to earlier. "Necessary" is defined as "not possible", and "possible" is defined as "not necessary". But this is not truthful for the reasons I've given. "Necessary" is properly opposed to "impossible", as I've explained. And "impossible" cannot be opposed to "possible" because this would make "necessary" and "possible" the same. So we need to put "possible" in a place distinct from the category which contains those opposites, necessary and impossible.Metaphysician Undercover

    Metaphysically speaking, I take these terms to mean:

    1. Impossible = cannot occur
    2. Possible = can occur
    3. Necessary = must occur

    This does not make "necessary" and "possible" the same. It opposes the concepts of 1 and 2 to each other, and the concepts of 2 and 3 to each other. This does not require "possible" to be in a distinct category.
  • Janus
    12.8k
    Are you denying that these are examples of language use?creativesoul

    I was referring specifically to symbolic language, to linguistic competency.

    Unhelpful nonsense. Speaking of anthropomorphism.creativesoul

    Whatever you are calling "linguistically mediated thought" is neither the only nor the simplest kind of thought humans have. Likely it is one of the most complex.creativesoul

    There is no point making bare assertions such as "unhelpful nonsense" without explaining why you think so. That is truly unhelpful.Same with the accusation of anthropomorphism; quote what I have said and explain why you think it is anthropomorphic if want an actual discussion.

    Yes, what I am calling linguistically mediated thought is neither the only or the simplest kind of thought, on the contrary it is the most complex: in that it is rich in symbols which allow us the think counterfactually, reflexively and self-referentially; what on Earth led you to think I was claiming otherwise? You seem to be making my argument for me.
  • creativesoul
    10.8k
    We don't really know what animal understandings are like, as to that we can only surmise in our human ways.Janus

    That's not true.

    I know when my cat wants treats. She behaves in certain ways. She will even lead me to the food bowl. She will sometimes sit in silence for ten minutes or more right beside the treat dispenser on the floor waiting for the moment I make eye contact with her. Then she meows and rubs her side around and across my leg and often purrs while I dispense the kibbles into the bowl. The sound of kibbles hitting the sides of her bowl is important to her too. The quantity of kibbles, not so much. Most times, she will not eat until after I gently stroke her from head to tail. Her tail almost always does this little shimmy thing at the end as she steps out of the stroke and into her feeding position.
  • creativesoul
    10.8k
    There is no point making bare assertions such as "unhelpful nonsense" without explaining why you think so. That is truly unhelpful.Same with the accusation of anthropomorphism; quote what I have said and explain why you think it is anthropomorphic if want an actual discussion.Janus

    I suggest you reread the post. What you ask for was already given.
  • creativesoul
    10.8k
    Yes, what I am calling linguistically mediated thought is neither the only or the simplest kind of thought, on the contrary it is the most complex: in that it is rich in symbols which allow us the think counterfactually, reflexively and self-referentially...Janus

    So, any and all attribution of such thought to non humans is anthropomorphism at work. I agree there. Not all language use involves using meaningful marks.

    The alarm screech symbolizes danger. The creatures using the screech connect the two and become language users as a result. The screech becomes meaningful with use.

    All 'linguistically mediated thought' involves language use. Some non human animals have language. Thought they have that involve language use are 'linguistically mediated thought'. The sounding of the alarm is a 'linguistically mediated thought' because it is a thought consisting of correlations drawn between the vocalization and danger. Becoming aware of danger by virtue of knowing what an alarm sound means is linguistically mediated thought.

    We cannot draw and maintain the distinction between the sorts of thoughts that we have and the sorts of thought that other language using animals have with the notion of 'linguistically mediated thought'.
  • Metaphysician Undercover
    10.4k
    Metaphysically speaking, I take these terms to mean:

    1. Impossible = cannot occur
    2. Possible = can occur
    3. Necessary = must occur

    This does not make "necessary" and "possible" the same. It opposes the concepts of 1 and 2 to each other, and the concepts of 2 and 3 to each other. This does not require "possible" to be in a distinct category.
    Luke

    Yes, that's exactly the problem. If (1) is defined as opposed to (2), and (3) is defined as opposed to (2), then (1) and (3) must have the very same meaning, by definition. Obviously though, "impossible" and "necessary" do not have the same meaning. Therefore we need a fix for this problem. My proposal was to put "possible" in a different category from "necessary" and "impossible" which are properly opposed, because "possible" I believe cannot be properly opposed to "necessary" due to our conception of "impossible"

    You are making what I would consider a scope error.Srap Tasmaner

    I really do not think that this explains the issue. Allow me to describe the problem more clearly if you will. The issue is with the definition of "necessary". If we propose to define "necessary" in relation to possible, as you did in the last post, then we also have to allow that it has a relation to impossible. The same sense of "necessary", in common usage has a relation with possible and also a relation with impossible (not possible). So if we simply define "necessary" as opposed to possible then we do not provide an accurate (truthful) representation of "necessary" because we do not provide a position for impossible. "Impossible" has been excluded from having a position in the schema because necessary has been opposed to possible.

    (2) It is possible that the book falls if and only if it is not necessary that the book does not fall.Srap Tasmaner

    So, look at this rendition of "possible", produced from your (1) where necessary was defined as opposed to possible. We can pinpoint the inaccuracy here. The phrase "it is not necessary that the book falls" is actually ambiguous because it implies (a) it is impossible that the book falls, and (b) it is possible that the book falls. I think you'll agree that (a) is very different from (b). However, your proposal excludes (b) by saying that we must allow (a) only, through definition.

    What this proposal does is that it removes "impossible" from the schema through a faulty definition of "possible", induced by the prior definition of "necessary". Everything is either necessary or possible. There is no such thing as impossible. And this is very evident in what we refer to as "logical possibility", anything is possible. So "logical possibility", produced by this means, provides no real defined sense of "impossible", and this is why it does not provide us with a truthful or accurate representation of reality.

    Now, we might account for this by saying that impossible is a form of necessary. This appears to be the most accurate way to go. But then we need to distinguish within our definition of "necessary", the difference between what necessarily is, and what necessarily is not. And, the real issue is that when we proceed from here to establish a relationship between each of these two and possibility, we have to respect the fact that one is the inverse of the other, so they cannot have the exact same relation. This inversion becomes very evident in probabilities. The more precise, or particular, the individual specific identified thing is, i.e. that which we want to relate to "necessary" (in its two senses of is and is not), the more certain we can be in the sense of is not, and the less certain we can be in the sense of is. This is why philosophical skepticism concerning claims about "what is", cannot be eradicated, while we can readily dismiss claims about "what is not", nothingness.
  • Luke
    2.1k
    Metaphysically speaking, I take these terms to mean:

    1. Impossible = cannot occur
    2. Possible = can occur
    3. Necessary = must occur

    This does not make "necessary" and "possible" the same. It opposes the concepts of 1 and 2 to each other, and the concepts of 2 and 3 to each other. This does not require "possible" to be in a distinct category.
    — Luke

    Yes, that's exactly the problem. If (1) is defined as opposed to (2), and (3) is defined as opposed to (2), then (1) and (3) must have the very same meaning, by definition.
    Metaphysician Undercover

    Why? I've already defined them above and you can see that they don't have the very same meaning. If 1 and 3 must have the same meaning, then my definitions must be incorrect. So, how are they incorrect?

    Therefore we need a fix for this problem.Metaphysician Undercover

    Or else your assumption that they must have the very same meaning is faulty.
  • Srap Tasmaner
    3.9k
    Metaphysically speaking, I take these terms to mean:

    1. Impossible = cannot occur
    2. Possible = can occur
    3. Necessary = must occur

    This does not make "necessary" and "possible" the same. It opposes the concepts of 1 and 2 to each other, and the concepts of 2 and 3 to each other. This does not require "possible" to be in a distinct category.
    Luke

    This is not a happy use of "opposes"; see below.

    Yes, that's exactly the problem. If (1) is defined as opposed to (2), and (3) is defined as opposed to (2), then (1) and (3) must have the very same meaning, by definition.Metaphysician Undercover

    Unless by "opposed to" you mean something different from "is the opposite of," or by "is the opposite of" you mean something besides "is the negative of," then this is another scope error. We have

    Possible (◇)

    Then there's "impossible," which is just

    Not Possible (~◇)

    The opposite of impossible is

    Not Not Possible (~~◇)

    which is of course just Possible (◇), unless we're contemplating an intuitionistic logic, and we're not. That just leaves necessity, which we get by putting a negative inside:

    Not Possibly Not (~◇~)

    To complete the set of possibilities, we could mention

    Possibly Not (◇~)

    which obviously tends to run alongside Possible (◇), without being it's opposite. (It's the opposite of Necessary.)

    Evidently, you agree with the use of negation to produce opposites, or you wouldn't have said that two opposites of one thing must be the same thing. But you're not paying attention to what you negate to produce the opposites; you're not paying attention to scope.
  • Srap Tasmaner
    3.9k
    We could, if we liked, take impossibility as our primitive. Then we would have

    Impossible
    Possible = Not Impossible
    Necessary = Impossibly Not

    since the necessity of P is just the impossibility of P's opposite.
  • Luke
    2.1k
    This is not a happy use of "opposes"; see below.Srap Tasmaner

    Possible is opposed to Not Possible. Isn't Possible also opposed to Not Possibly Not?
  • Srap Tasmaner
    3.9k
    Possible is opposed to Not Possible. Isn't Possible also opposed to Not Possibly Not?Luke

    Meaning what? What does "opposed to" mean? Does it mean distinguished from, or actually is the negative of? I take opposite to indicate the negative, and anything else is ambiguity we can do without.

    So, no, Possible (◇) is the opposite of Not Possible (~◇), and nothing else.

    The opposite of Necessary (~◇~) is Not Necessary (◇~).

    While we're here, we can do "necessarily not," which MU mentions now and again: that's ~◇~~, which reduces to Not Possible (~◇), or impossible, which, duh. So we can also say that the opposite of Possible is Necessarily Not — and it isn't anything else.
  • Luke
    2.1k
    So, no, Possible (◇) is the opposite of Not Possible (~◇), and nothing else.

    The opposite of Necessary (~◇~) is Not Necessary (◇~).
    Srap Tasmaner

    Not Necessary (◇~) is equivalent to Possibly Not (◇~).

    It is unclear to me why Not Necessary (◇~) is not also equivalent to Possible (◇).
  • Mww
    3.4k
    There are only two feelings, pain and pleasure, each with varying degree.
    — Mww

    You start off with a false premise. "Feelings" are sensations and there is many different sorts of them, often involving neither pleasure nor pain.
    Metaphysician Undercover

    Your “feelings” related to sensation are not my feelings related to emotional status.
    ————

    How does objectivity enter morality in your mind?Metaphysician Undercover

    Objectivity doesn’t enter morality itself, but only manifests as a determined physical act occurring in response to a subjectively determinable moral situation.

    what do you mean by "the judgement for what objectively is to be done"?Metaphysician Undercover

    What is to be objectively done, is performance of some physical act. In the same way that we judge what an object is, that which is given to perception from the world, for which it is the cause, so too do we judge what we put in the world, for which we are its cause. In the former we are affected by the world, in the latter our acts are effects on the world. In both circumstances are found congruent empirical conditions, insofar as both are directly related to the world, which makes explicit....logically explicit, that is.....they both follow from the same kind of judgement, which is called discursive.

    Do you see the classic “is-ought” moral dilemma here?
  • Srap Tasmaner
    3.9k
    Not Necessary (◇~) is equivalent to Possibly Not (◇~).Luke

    Yes, and I should add I think that matches our intuitions: if something isn't necessarily the case, then it's possibly not the case.

    It is unclear to me why Not Necessary (◇~) is not also equivalent to Possible (◇).Luke

    The problem is necessity.

    Saying something is true might seem to entail that it could be false, but it doesn't, because what you're saying might be necessarily true. 3 + 4 is 7 doesn't entail that 3 + 4 might not be 7.

    So it is with possibility: to say that P is possible might seem to entail that ~P is also possible, but we can't do that because it may be that P is necessary, and that's why it's possible. Same as above: it is possible that 3 + 4 is 7, because it is, and it is necessarily.

    Does that make sense?

    It is absolutely true that we tend to reach for "possible" in epistemic situations that have a kind of constructivist flavor to them, that we say possible when it's all we know, and we don't have actuality or necessity in hand. (That's what I mean by "constructivist" there, that we use possible when we have not demonstrated actual or necessary.) So in a lot of cases where we want to say "possible" we really want to say "possibly not" too as a way of covering our bets; but that's a mistake: we need to demonstrate possibly not, because for all we know it will turn out possibly not isn't actually an option.

    Of course that only matters if you're working in a domain where necessary makes sense, and for a lot of the everyday matters of fact we deal with, we often assume we can rule out necessity. "He might be on time," in everyday reasoning, does seem to entail that he might not. Whether we should make those assumptions, I dunno.
  • Joshs
    3.9k


    I had thought that creativesoul was claiming that there were other species who were capable of symbolic langauge, though, which would be something else altogether.Janus

    Did you mean something different than this?

    “Evidence that an animal is capable of some degree of symbolic, human language processing supports the argument that the animal's consciousness is to some degree human-like.”


    One can , of course, distinguish between ‘capacity for’ and natural use of symbolic language. Bonobos have been shown to have this capacity, but only demonstrate it in artificially induced situations prompted by humans.
  • Luke
    2.1k
    It is unclear to me why Not Necessary (◇~) is not also equivalent to Possible (◇).
    — Luke

    The problem is necessity.

    Saying something is true might seem to entail that it could be false, but it doesn't, because what you're saying might be necessarily true. 3 + 4 is 7 doesn't entail that 3 + 4 might not be 7.

    So it is with possibility: to say that P is possible might seem to entail that ~P is also possible, but we can't do that because it may be that P is necessary, and that's why it's possible. Same as above: it is possible that 3 + 4 is 7, because it is, and it is necessarily.

    Does that make sense?
    Srap Tasmaner

    Not really. I asked about non-necessity - why it's not equivalent to possible/possibly - and you've responded that we need to beware of necessity...? But I'm assuming non-necessity.
  • Srap Tasmaner
    3.9k
    I asked about non-necessity - why it's not equivalent to possible/possibly - and you've responded that we need to beware of necessity...? But I'm assuming non-necessity.Luke

    Ah, okay, I see what went wrong now.

    My point was that we don't derive Possibly ~P from Possibly P, because for all we know Necessarily P.

    Here you have Not Necessarily P

      ~▢P

    and you want to know why it's not equivalent to Possibly P

      ~▢~P

    We could try proving that, but we don't have any axioms, so let's try an example.

    I've got my usual urn of marbles, and I tell you that the marbles in the urn are not necessarily red. You can conclude, given that the urn is not empty, that there is at least one marble in the urn that is not red. Good so far? By restricting our domain to an urn of marbles, we get to cash out the modal claims as quantifiers. Can you conclude that at least one of the marbles is red, that the urn contains a mix of red and not red? No, you cannot. "There is at least one non-red marble in the urn" is the entirety of what you know; it is a complete translation of "The marbles in the urn are not necessarily red."

    Of each marble in the urn, it is false that it must be red. Clearly, that condition can be satisfied by it being false of every marble in the urn that it is red. (That is, it being true of no marble in the urn that it is red.) If this turns out to be the case, we would have that it is necessarily false of each marble that it is red. That's consistent with it not being necessarily true of any marble that it is red.

    Since Not Necessarily P is consistent with Necessarily Not P, it's not equivalent to Not Necessarily Not P, else we'd have a contradiction. Or we can say: Possibly Not P is consistent with Not Possibly P, so it's not equivalent to Possibly P.

    Sorry this is so repetitive. I'm never sure which may of putting things will be clearest.
  • Luke
    2.1k
    and you want to know why it's not equivalent to Possibly P

    ~▢~P
    Srap Tasmaner

    Isn't Possibly P also ~▢P?

    I've got my usual urn of marbles, and I tell you that the marbles in the urn are not necessarily red. You can conclude, given that the urn is not empty, that there is at least one marble in the urn that is not red. Good so far?Srap Tasmaner

    I wouldn't think it follows from "the marbles in the urn are not necessarily red" that there must be at least one marble that's not red. I would think it follows from "the marbles in the urn are not necessarily red" that it is possible that all marbles in the urn are red, that some marbles in the urn are red, or that no marbles in the urn are red.
  • Srap Tasmaner
    3.9k
    Isn't Possibly P also ~▢P?Luke

    No, it isn't. ▢P ↔ ~◇~P and ◇P ↔ ~▢~P. That's the standard, and it maps onto quantifiers in an obvious way.

    I wouldn't think it follows from "the marbles in the urn are not necessarily red" that there must be at least one marble that's not red. I would think it follows from "the marbles in the urn are not necessarily red" that all the marbles in the urn are (possibly) red.Luke

    Dang. I'll try again.

    We have a set of marbles you're going to pick from. We're going to look at claims about what necessarily results when you pick and what possibly results when you pick.

    If when you pick a marble, you get a red one, without exception, that's necessity. Necessity is like a universal quantifier with a restricted domain. Necessity means all the marbles are red. There's only the one result possible when you pick.

    If when you pick a marble, you at least once get a red one, that's possibility. Possibility is like an existential quantifier with a restricted domain. Possibility means at least one of the marbles is red.

    That might be hard to see at first, even with the analogy to ∃, but suppose you pick all the marbles and not one of them is red. Then we would say it was not possible to pick a red marble from that set. I think that fits our intuitions perfectly. To say it is possible to pick a red marble from that set must mean that there is at least one red marble to be picked.

    Not Necessarily is Possibly Not, so that's our existential quantifier. It says you can pick a non-red marble from the set because there is at least one non-red marble to be picked. If you can't pick a non-red marble, that's because all the marbles are red; that's the situation we say we are not in.

    And it should be clear that saying there is at least one non-red marble in the set is consistent with there being only non-red marbles in the set. That is, Possibly Not Red is consistent with Necessarily Not Red.

    From this we conclude that Possibly Not Red is not the same as Possibly Red, because if it were, we would have to say that Possibly Red is consistent with Necessarily Not Red; we would have to have a set of marbles at least one of which was red and all of which were not red. No go.

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