On Oct 15, 2015, at 4:14 PM, Thomas Johnston <tmj44p@xxxxxxx> wrote:
Oct 15, 2015.
Tom and Pat 1
Original intuition. If I say "Some dogs are friendly", and then later change my mind and say "No dogs are friendly", I'm talking about dogs, in both cases. If I believe that there are dogs when I say that some of them are friendly, I continue to believe in dogs when I change my mind and say that none of them, or perhaps that all of them, are.
FWIW, I entirely agree with your intuition in this particular example, but the point that you seem to miss is that this cannot be due to the logical structure of these sentences, because other examples with exactly the same logical form do not support that intuition. To see this, just exchange the property 'friendly' for something vacuously true of all things. For example: "Some dogs are real", which is another way to say "Some dogs exist", changes its mind to give "No dogs are real", ie no dogs exist. To emphasize: this has exactly the same logical form as your case, but supports a different intuition.
Our shared intuition in the dog example arises from the knowledge that we both share that something can fail to be friendly and still be a dog, ie that Ex. Dx & ~Fx. But that is another fact about the world, not expressed in the original sentence and not entailed by it. It is not part of predicate logic to force me to say something I don't believe.
Of course not.
Tom and Pat – a Counter-Intuition
My Own Counter-Intuition. On the other hand, my intuition also tells me that "No dogs are friendly" can be paraphrases as "Nothing is both a dog and is friendly". And this statement will obviously be true even if there are no dogs. In which case, we must express that statement as a hypothetical, i.e., in a form which does not say "There is", or "There exists". This intuition says that the negation of "Some dogs are friendly" can indeed be expressed without ontological commitment, as: Ux(Dx --> ~Fx), (or, BTW, as (Ux(Fx --> ~Dx).)
If we express the negation of "Some dogs are friendly" this way, negation has caused us to switch from being committed to the existence of dogs, to dropping that commitment.
As, it seems obvious to me, it should. If a sentence S expresses a committment, then its denial ~S should deny that committment, not repeat it. So if I can't find another way to express the negation of "Some dogs are friendly", then I need to drop my original intuition and all this will have been just a tempest in a teapot.
So here's my attempt to formalize the negation of "Some dogs are friendly" without switching from conjunction to material conditionals. I begin by using this paraphrase: "No dogs are friendly". I'm talking about dogs, just as I was when I said "Some dogs are friendly". From this point of view, "Nothing is both a dog and is friendly" is not synonymous with "No dogs are friendly".
Hmm. But surely there are entailments between these. Do you agree that 'no dogs are friendly' certainly at least entails 'nothing is both a dog and is friendly' ? This seems intuitively clear to me, for the latter would be false only if there were a friendly dog. Similar reasoning shows that the reverse entailment also holds: for if nothing is both doggish and friendly, then a friendly dog is clearly impossible. So these two statements entail each other, which means that they have identical truth conditions (they are true or false in exactly the same circumstances: they make identical claims about the world.) So how can you believe one of them but not the other? The former is an awkward paraphrase whose purpose is to support a view of universal quantification in which it does not involve ontological commitment. The latter is a way to talk about all dogs, not just about some of them.
But if it talks about all dogs, then surely its logical form should be something like 'all dogs....', which is standardly rendered as 'forall things x, if x is a dog then....'. Again, this seems kind of obvious. Which part of it do you think is mistaken? (Do you object to the standard rendering of a restricted quantifier ('all dogs...') as a universal implication (Ux Dx -> ...) ?)
So here's my attempt.
Tom and Pat 3
Tom: <<<Why should "All dogs are renates" not be expressed as Ux(Dx & Rx)?>>>
Pat: <<<Because that would then also express "All renates are dogs", by the symmetry of conjunction, and would entail "Everything is a dog", by &-elimination.>>>
Tom: I hadn't thought of that. But the following occurs to me:
Statements have a subject and a predicate. Considering atomic statements, to keep things simple. So "All dogs are renates" has "dogs" as its subject term (aka "NP") and "are renates" as its predicate term (aka "VP").
? Are you saying that the logical form of this should be Renates(Dogs) ? (I hope not) NPs identify types, i.e. universals whose instances are particulars. VPs identify properties/relations, i.e. universals whose instances are not particulars. Particulars (Aristotelian primary substances) exist without dependency on properties; but properties depend on particulars to "inhere in".
This seems very shaky ground on which to try to build a theory. In English, at least, nominalizations allow almost any verb to be treated as a noun. If the verb "shake" must identify a non-particular universal, what does the NP "a shaking" denote? Is not every shaking an instance of the verb 'to shake'? Predicate logic ignores this distinction.
Because it plays no role in assigning truth-conditions of sentences. Dx and Fx, in my examples, are treated the same; both are predications.
Now suppose that this distinction between instances of types and instances of properties is important enough to bring in to our formalisms. Let's use the subscripts "T" and "P" to make the distinction. Then
"All dogs are renates" would be expressed as Ux(Dtx & RPx). And-elimination would ruled out for cases like these.
Why? &-elimination is an inference rule which applies to any conjunctive sentence, regardless of the nature of the conjuncts. The semantic justitification for this rule comes from the truth-conditions for the connective, which are not changed by tinkering with the details of its component sentences.
AFAIKS, nothing is changed by your proposed distinction and its subscripted syntax. Both kinds of atomic sentence are still atomic sentences, and have truth-values just as before, indeeed exactly the same truth values that they had before we made this distinction. So the actual *logic* will proceed in exactly the same way after this change as it did before the change. Standard boolean operators would be restricted to working on property predications only.
What could possibly justify such a restriction, and in any case what does it even mean? Your example sentence, which conjoins a property and a type predication, violates this restriction. Does it itself not have truth conditions? Doing predicate logic like this, the existential quantifier over type predications would say that an individual of the stated type exists. The universal quantifier would say that all individuals of the stated type exist
Why would the meaning of the universal quantifier be changed to that of an existential? And what do you mean by the 'stated type'? The body of a universal sentence might have any form: it need not be restricted to simple syllogistic forms like 'all swans are white'. What would we make of a sentence like Ux Uy ( (Tx & Ty & Bxy) -> Ez (Iz & Szx & Fzy) ) for example, which by the way is one axiom of a simple temporal ontology. which, if there are any such individuals, is a tautology.
(Aside. Well, no. A tautology is *logically* true, ie true in *all* interpretations.) But now both existential and universal quantification carry ontological commitment.
So how would we deny existence? Well, for example, to say "There are no dogs", we would write: Ux(~Dtx). This says that nothing in our universe of discourse is of type; in other words, that there are no dogs.
But if the universal quantiifer asserts universal existence of the type, then why is this not a logical contradiction? What if we wrote: Ex(~Dtx). What would that say? It would say that there is at least one thing in our universe of discourse which does exist and is not a dog, i.e. which is not an instance of the type D.
These are exactly what these sentences mean already, so I fail to see how you can preserve these meanings with your proposed change to the meaning of the universal quantifier.
I do not think that you have a coherent logic defined here yet.
I think this suggestion has two things going for it.
It is not yet stated in enough detail to be treated as a suggestion. I honestly think that you will not be able to make it into a coherent suggestion without it being equivlaent to conventional predicate logic. This space has been very thoroughly explored already. First, when talking about anything, switching from "Some" statements to "All" statements doesn't change ontological commitment. In both cases, if negation isn't used, I'm talking about what I presume exists. If I want to say that nothing of a specific type exists, say dogs, I write: Ux(~Dtx). If my switch involves the deMorgan's equivalence of "Some" to "Not All Not" and "All" to "Not Some Not", I still don't drop, or pick up, ontological commitment.
The second thing this has going for it is that it introduces into predicate logic an important distinction that, to date, predicate logic does not represent, and never has: the distinction between universals (types) whose instances are particulars (Aristotelian primary substances, as I explain in Ch. 5 of BDTP), and universals whose instances are properties of particulars or relations between particulars. This distinction is at the heart of language. Atomic statements pick something out by identifying what type of thing it is, and then saying something about it, which amounts to ascribing a property or relationship to it.
I really have no idea what you are talking about here, but it sounds like a version of sorted FOPC with restricted quantiifers might provide the analysis you are seeking. So instead of - I will use CLIF lisp-style notation for clarity -
(forall (x)((P x) implies foo)
one writes
(forall ((x P)) foo),
ie 'forall x of type P, foo' One thing against this proposal is that it isn't worked out, and there would be a lot of working out to do. How would proofs (inferences) work in this kind of FOPL?
I would suggest starting with a semantics, and try to state truth conditions on sentences, and show how they differ from the conventional ones.
Pat
How would they work in modal predicate logics? Truth be told, I have no idea and I lack the expertise to try to answer these questions. It may be that we have the predicate logic we do because trained logicians have gone down this path some ways farther than I have – far enough to find out that it's a blind alley.
I'll try to respond to some of your other comments soon. In the meantime, if you don't think anything is to be gained by continuing this conversation, I'll understand completely.
Thanks for working so hard to help me understand why predicate logic is as it is.
Tom
On Tuesday, October 13, 2015 9:04 PM, Pat Hayes <phayes@xxxxxxx> wrote:
On Oct 13, 2015, at 10:53 AM, Thomas Johnston <tmj44p@xxxxxxx> wrote:
> Oct 13, 2017.
>
> My intuitions tell me that anyone who asserts "All dogs are renates" believes that there are dogs (i.e. is ontologically committed to the existence of dogs) just as much as someone who asserts "Some dogs are friendly".
I think your intuition needs some pumping with more examples. Try these:
All unicorns are imaginary.
All large unicorns are male.
All composite prime numbers are larger than 13.
Your intuition has some very strange consequences. You claim that (Ux Px -> Qx) entails (Ex Px). But the first is equivalent to (Ux. ~Qx -> ~Px), so it must also entail (Ex ~Qx) So "All dogs are renates" entails the existence of some non-renates. But if so, then "All dogs are real entities" (or some other vacuously true property in place of Q), must entail that some non-real entities exist, which is false. So we can derive a falsehood (perhaps necessarily false) from a truth (perhaps a necessary truth), using your intuitions as a guide.
> Suppose someone else asserts, instead, that "No dogs are renates". Certainly, to do that, that person must believe that there are such things as dogs
?? Of course not. For example: "No blue rainbows have gold highlights." Which, by the way, I believe and am quite sure is true, precisely *because* there are no blue rainbows. Or, a more realistic example, one that actually does arise in some conversations here in the deep south, "No spirit guide will cause you harm."
> and, in addition, believe that some of them are not renates (a false belief, of course).
>
> Now for "Some dogs are friendly", and also "Some dogs are not friendly". In both cases, we all seem to agree, someone making those assertions believes that there are dogs.
>
> Now I'm quite happy about all this. If I make a Gricean-rule serious assertion by using either the "All" quantification or the "Some" quantification, I'm talking about whatever is the subject term in those quantifications – dogs in this case. I'm particularly happy that negation, as it appears in the deMorgan's translations between "All" statements and "Some" statements, doesn't claim that a pair of statements are semantically equivalent, in which one of the pair expresses a belief that dogs exist but the other does not.
>
> But in the standard interpretation of predicate logic, that is the interpretation. In the standard interpretation, negating a statement creates or removes the _expression_ of a belief that something exists.
Well, negating the statement expressing that belief yields another statement denying that belief. Why would anyone expect otherwise? Surely that is the whole point of negation, that not-P expresses the exact opposite of what is expressed by P, so they cannot both be true.
> My beliefs in what exist can't be changed by the use of the negation operator.
So if you say "Foos exist", and I respond, disagreeing with you, "There are no foos", then we are in fact agreeing with one another! Do you really find this a reasonable interpretation? If you do, then what could I possibly say, in order to disagree with you about such a claim of existence?
> Apparently, John's beliefs can, and so too for everyone else who feels comfortable with predicate logic as a formalization of commonsense reasoning, and with the interpretation of one of its operators as "There exists ....".
>
> I usually don't like getting into tit for tats. Those kinds of discussions always are about trees, and take attention away from the forest. But I'll make exceptions when I think it's worth taking that risk (as I did in my response to Ed last night).
>
> So:
>
> From John Sowa's Oct 12th response:
> <<<
> TJ
> > why, in the formalization of predicate logic, was it decided
> > that "Some X" would carry ontological commitment
>
> Nobody made that decision. It's a fact of perception.
I wish John had not mentioned perception here, as it muddies the discussion with irrelevant ideas. It is not a fact of perception. but a fact of the truth-conditions of the sentences involved. You may cite medieval scholars as much as you like, but I would be more impressed by a brief account of what you take the truth-conditions of a sentence of the form (Ux Px -> Qx) to actually be, and show us how this will entail Ex Px.
> Every
> observation can always be described with just two operators:
> existential quantifier and conjunction. No other operators can
> be observed. They can only be inferred.
> >>>
> (1) If all ontological commitments have to be based on direct observation, then we're right back to the Vienna Circle and A. J. Ayer.
>
> (2) And what is it that we directly observe? A dog in front of me? Dogs, as Quine once pointed out, are ontological posits on a par with the Greek gods, or with disease-causing demons. (I am aware that this point, in particular, will likely serve to reinforce the belief, on the part of many engineering types in this forum, that philosophy has nothing to do with ontology engineering. That's something I want to discuss in a "contextualizing discussion" I want to have before I pester the members of this forum with questions and hypotheses about cognitive/diachronic semantics. What does talk like that have to do with building real-world ontologies in ontology tools, in OWL/RDF – ontologies that actually do something useful in the world?
>
> (3) I wouldn't talk about some dogs unless I believed that some dogs exist.
Suppose you believe that dogs do not exist, ie that there are no dogs. And you wish to say this to someone, perhaps to enlighten them about the true nature of their animal pet. What will you say? You have to say something like "There are no dogs", or "Nothing is a dog". Rendered into logic, you have to say Ux.~Dx or ~Ex.Dx. Either way, you have to talk about dogs, in order to deny their existence. So someone might well want to talk about dogs - perhaps it would be better to say, to use dog language - when they do not believe that dogs exist.
> And if some dogs exist, then all dogs do, too.
Clearly this is false. I had a dog once, called Sally. Sally existed. On the other hand, the Hound of the Baskervilles was an imaginary dog. That dog did not exist. Similarly Rin-Tin-Tin was a fictional dog that did not exist.
> Either there are dogs, or there aren't. If there are, then I can talk about some of them, or about all of them. If there aren't, then unless I am explicitly talking about non-existent things, I can't talk about some of them nor can I talk about all of them, for the simple reason that none of them exist. To repeat myself: if any of them exist, then all of them do.
>
> (4) And I am, of course, completely aware that trained logicians since Frege have been using predicate logic, and that, at least since deMorgan, have been importing to negation the power to create and remove ontological commitment.
>
> (5) Here's a quote from Paul Vincent Spade (very important guy in medieval logic and semantics):
>
> "This doctrine of “existential import” has taken a lot of silly abuse in the twentieth century. As you may know, the modern reading of universal affirmatives construes them as quantified material conditionals. Thus ‘Every S is P’ becomes (x)(Sx ⊃ Px), and is true, not false, if there are no S’s. Hence (x)(Sx ⊃ Px) does not imply (∃x)(Sx). And that is somehow supposed to show the failure of existential import. But it doesn’t show anything of the sort .... "
> http://pvspade.com/Logic/docs/Thoughts,%20Words%20and%20Things1_2.pdf
It is worth reading the rest of that footnote. He agrees that (x)(Sx ⊃ Px) does not imply (∃x)(Sx), but points out that (Ux)(Px) implies (Ex)(Px), and that *this* is the real existential import of modern logic.
"The modern equivalent of existential import, therefore, is not: (x)(Sx ⊃ Px) ∴ (∃x)(Sx), but rather (x)(Px) ∴ (∃x)(Px). And that holds in standard modern logic, which is therefore just as much committed to existential import as traditional logic is."
Perfectly correct, but has no bearing on the issue you are raising here.
>
> So Spade approaches this as the issue of the existential import of universally quantified statements. He points out that, from Ux(Dx --> Rx), we cannot infer Ex(Dx & Rx). The rest of the passage attempts to explain why. I still either don't understand his argument, or I'm not convinced by it. Why should "All dogs are renates" not be expressed as Ux(Dx & Rx)?
Because that would then also express "All renates are dogs", by the symmetry of conjunction, and would entail "Everything is a dog", by &-elimination.
Best wishes
Pat Hayes
PS there is a wonderful extended essay here on this general topic: http://plato.stanford.edu/entries/ontological-commitment/
> From John's reply, I think he would say that it's because we can only observe particular things; we can't observe all things. But in the preceding points, I've tried to say why I don't find that convincing.
>
> (6) Simply the fact that decades of logicians have not raised the concerns I have raised strongly suggests that I am mistaken, and need to think more clearly about logic and ontological commitment. But there is something that might make one hesitate to jump right to that conclusion. It's Kripke's position on analytic a posteriori statements (which I have difficulty distinguishing from Kant's synthetic a priori statements, actually -- providing we assume that the metaphors of "analytic" as finding that one thing is "contained in" another thing, and of "synthetic" as bringing together two things first experienced as distinct, are just metaphors, and don't work as solid explanations).
>
> All analytic statements are "All" statements, not "Some" statements. Kripke suggests that the statement "Water is H2O" is analytic but a posteriori. In general, that "natural kind" statements are all of this sort. Well, a posteriori statements are ones verified by experience, and so that would take care of John's Peircean point that only "Some" statements are grounded in what we experience.
>
> I don't know how solid this line of thought is. But if there is something to it, that might suggest that if we accept Kripke's whole referential semantics / rigid designator / natural kinds ideas (cf. Putnam's twin earth thought experiment also), then perhaps we should rethink the traditional metalogical interpretation of "All dogs are renates" as Ux(Dx --> Rx), and consider, instead, Ux(Dx & Rx).
>
> Well, two summing-up points. The first is that Paul Vincent Spade thinks that my position is "silly", and John Sowa thinks that it's at least wrong. The second is that such discussions do indeed take us beyond the concerns of ontology engineers, who just want to get on with building working ontologies.
>
> As I said above, I will address those concerns of ontology engineers before I begin discussing cognitive semantics in this Ontolog (Ontology + Logic) forum.
>
> Regards to all,
>
> Tom
>
>
>
>
>
> On Monday, October 12, 2015 10:49 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
>
>
> Tom, Ed, Leo, Paul, Henson,
>
> TJ
> > why, in the formalization of predicate logic, was it decided
> > that "Some X" would carry ontological commitment
>
> Nobody made that decision. It's a fact of perception. Every
> observation can always be described with just two operators:
> existential quantifier and conjunction. No other operators can
> be observed. They can only be inferred.
>
> EJB
> > I was taught formal logic as a mathematical discipline, not
> > a philosophical discipline. I do not believe that mathematics
> > has any interest in ontological commitment.
>
> That's true. And most of the people who developed formal logic
> in the 20th c were mathematicians. They didn't worry about
> the source or reliability of the starting axioms.
>
> Leo
> > most ontologists of the realist persuasion will argue that there
> > are no negated/negative ontological things.
>
> Whatever their persuasion, nobody can observe a negation. It's
> always an inference or an assumption.
>
> PT
> > on the inadequacy of mathematical logic for reasoning about
> > the real world, see Veatch, "Intentional Logic: a logic based on
> > philosophical realism".
>
> Many different logics can be and have been formalized for various
> purposes. They may have different ontological commitments built in,
> but the distinction of what is observed or inferred is critical.
>
> HG
> > I keep wondering if this forum has anything useful to offer the
> > science and engineering community.
>
> C. S. Peirce was deeply involved in experimental physics and
> engineering. He was also employed as an associate editor of the
> _Century Dictionary_, for which he wrote, revised, or edited over
> 16,000 definitions. My comments below are based on CSP's writings:
>
> 1. Any sensory perception is evidence that something exists;
> a simultaneous perception of something A and something B
> is evidence for (Ex)(Ey)(A(x) & B(y)).
>
> 2. Evidence for other operators must *always* be an inference:
>
> (a) Failure to observe P(x) does not mean there is no P.
>
> Example: "There is no hippopotamus in this room"
> can only be inferred iff you have failed to observe
> a hippo and know that it is big enough that you would
> certainly have noticed one if it were present.
>
> (b) (p or q) cannot be directly observed. But you might infer
> that a particular observation (e.g. "the room is lighted")
> could be the result of two or more sources.
>
> (c) (p implies q) cannot be observed, as Hume discussed at length.
>
> (d) a universal quantifier can never be observed. No matter
> how many examples of P(x) you see, you can never know that
> you've seen them all (unless you have other information
> that guarantees you have seen them all).
>
> TJ
> > But now notice something: negation creates and removes ontological
> > commitment. And this seems really strange. Why should negation do this?
>
> The commitment is derived from the same background knowledge that
> enabled you to assert (or prevented you from asserting) the negation.
>
> > I'd also like to know if there are formal logics which do not
> > impute this extravagant power of ontological commitment /
> > de-commitment to the negation operator in predicate logics.
>
> Most formal logicians don't think about these issues -- for the
> simple reason that most of them are mathematicians. They don't
> think about observation and evidence.
>
> CSP realized the problematical issues with negation, but he also
> knew that he needed to assume at least one additional operator.
> And negation was the simplest of the lot. Those are the three
> he assumed for his existential graphs. (But he later added
> metalanguage, modality, and three values -- T, F, and Unknown.)
>
> John
>
> PS: The example "There is no hippopotamus in this room" came from
> a remark by Bertrand Russell that he couldn't convince Wittgenstein
> that there was no hippopotamus in the room. Russell didn't go
> into any detail, but I suspect that Ludwig W. was trying to
> explain the point that a negation cannot be observed.
>
>
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