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Kripke: Identity and Necessity

Kripke asks if this lectern could have been made of ice. His answer is that it is entirely possible that the lectern before us is made of ice, but that if this were so it would be a different lectern. — Banno

Descartes died in 1650, 9 years after publishing Mediations in 1641; after contracting a cold in the Court of Queen Christina of Sweden.
All his scientific works - on Dioptrics, Meteorology, and Geometry, were written prior to Mediations, and he did no notable scientific works after.
He wrote Principles of Philosophy (1644): and Passions of the Soul (1649), and died in 1650. Given that he withdrew 'O Mundo' from publication; (it was published in 1664 after his death) it's fairly clear he was self censoring. And thus, it's fairly clear what the nature of Meditations is - he didn't write Meditations because that's what he really thought. He wrote it in case the Inquisition came knocking.

I agree he was self censoring.

I'm not sure I agree he wrote the Meditations to stop the inquisition, though. I think he liked both science and philosophy, and that his published philosophy could be read as his response to his circumstances -- I can't work scientifically because of these ideas in place, and so I'll set about doing the philosophical work that needs to be done in order that science might flourish.

Science without philosophical implication; science as a tool with no claim to be a rule for the conduct of human affairs? You might call that flourishing; I call it abuse!

Heh, I've once again not been clear.

I agree Descartes was self-censoring. However, I don't think he was doing so in his philosophy, while he was doing so in his science.

With respect to his science he was self-censoring, but I don't believe he was in his philosophy.

And I'd hesitate to call Descartes' philosophy subjectivist, at least. Seems wrong to me given he wanted certain foundations for scientific knowledge in his philosophy.

the question of whether Kripke was doing analysis or building a metaphysical picture — frank

Yes, the quoted passage shows him doing the former. He's trying to lay out the requirements for a consistent picture, not choosing among pictures -- that would be one way of putting it.

Maybe as we look more deeply into Kripke, we'll see whether this is always his strategy.

That position doesn't make sense to me. If what we see is an hallucination or other phantasm, then our eyes must be, also
— Patterner

If you're at the Overlook Hotel and you see people who shouldn't be there, you should question whether you're hallucinating. — frank

I'm not suggesting there is no such thing as hallucination. I'm saying the thought that reality is of a certain nature, but we hallucinate it is of a different nature, and we hallucinate sense organs to perceive that hallucinated reality, doesn't make sense to me.

It might be interesting to look at Malcolm's approach through the lens of one of the formal intuitionist logics. Perhaps relevance logic would be informative. — Banno

Not sure what formal intuitionist logics or relevance logic exactly means but saw some general descriptions and I wonder if the following two examples from Malcolm's body of work is something you have in mind.

From "Kripke and the Standard Meter",

"I have argued that in relation to actual operation of institution or "language game" of measurement with a meter stick, the sentence 'One meter is the length of S' is not a contingent statement. Do I hold then that this sentence expresses a 'necessary truth'? I would not say this either, especially if a 'necessary truth' is supposed to be something that is 'true in all possible worlds'. Certainly there is no requirement to hold that if the sentence is not a contingent statement then it must be a necessary statement. To think that this sentence should be characterized as either contingent or as a necessary statement seems to me to be looking at it in a wrong way. The sentence, 'One meter is the length of S', is correctly characterized as being, in relation to the institution of metric measurement, the definition of 'one meter' and also as a rule for the use of the term 'one meter'. One can also rightly say that this sentence was used to make a fiat or a decree."

From "“Anselm's Ontological Arguments",

"I do not know how to demonstrate that the concept of God-that is, of a being a greater than which cannot be conceived-is not self-contradictory. But I do not think that it is legitimate to demand such a demonstration. I also do not know how to demonstrate that either the concept of a material thing or the concept of seeing a material thing is not self-contradictory, and philosophers have argued that both of them are. With respect to any particular reasoning that is offered for holding that the concept of seeing a material thing, for example, is self-contradictory, one may try to show the invalidity of the reasoning and thus free the concept from the charge of being self-contradictory on that ground. But I do not understand what it would mean to demonstrate in general, and not in respect to any particular reasoning, that the concept is not self-contradictory. So, it is with the concept of God. I should think there is no more of presumption that it is self-contradictory than the concept of seeing a material thing. Both concepts have a place in the thinking and the lives of human beings."

Heh, I've once again not been clear. — Moliere

No, you're not being clear, you're being intellectually dishonest - admitting Descartes was self censoring, but refusing to draw the conclusion that he wrote Meditations; a subjectivist epistemology in diametric opposition to Galileo's objectivist epistemology, as a defence against potential accusations of heresy.

With respect to his science he was self-censoring, but I don't believe he was in his philosophy. — Moliere

You're attempting to rescue subjectivism as a philosophy by suggesting that Descartes withdrawing a work on physics, and giving up on doing science - are entirely separate from his creation of an alternate epistemology to that described by Galileo i.e. empirical scientific method.

And I'd hesitate to call Descartes' philosophy subjectivist, at least. Seems wrong to me given he wanted certain foundations for scientific knowledge in his philosophy. — Moliere

What would you say after you had hesitated? Descartes Meditations on First Philosophy is the foundational work of subjectivism; cogito ergo sum, I think, therefore I am, establishes the individual's own thought as the foundation of existence and knowledge.

Subjectivism does not offer certain foundations for scientific knowledge. It cuts across the authority of science as objective knowledge; achieved by testing hypotheses with regard to unbiased and replicable observation - by emphasizing the role of the individual in shaping their understanding of the world.

The individual doing science is not doing something with universal implications and application; they're idiosyncratically doing science, and any scientific conclusions they reach may be accepted or rejected as any other idiosyncratic individual sees fit.
Descartes neutered science; and that's why we have nuclear weapons and climate change denial, but we don't have limitless clean energy from high temperature geothermal.

I hope I've made clear how clean the distinction is between syntax and semantics in formal systems. — Banno

You have indeed. And it makes it clear that my question arises around what you call a possible third level "where we seek to understand what we are doing in a natural language by applying these formal systems." Using the Eiffel Tower example, we agree that the fixing of the reference "Eiffel Tower" is a semantic step. We have a rough-and-ready language system that shows us how to pick out objects and name them. On the analogy with formal systems, what part of that rough-and-ready system do we call syntactic? It precedes any talk of naming or interpretation, doesn't it? So I still want a way to characterize the difference between saying "The Eiffel Tower is tall" and "That object [pointing] is called 'the Eiffel Tower'". Yes, the first is a property and the second is not, but where do these statements fall on the syntactic/semantic spectrum?

No, you're not being clear, you're being intellectually dishonest - admitting Descartes was self censoring, but refusing to draw the conclusion that he wrote Meditations; a subjectivist epistemology in diametric opposition to Galileo's objectivist epistemology, as a defence against potential accusations of heresy. — karl stone

Couldn't it be the case that Descartes both censored himself and expressed himself? Or must we say, because he censored himself once all of what he did in his life is an act of self-censorship, including what he said?

Of course I agree with Sam26 that a response is found in a treatment of what it is to doubt, along the lines of Wittgenstein's discussion of hinge propositions, but unlike Sam I reject idealism, along with certain sorts of realism, as a false juxtaposition. — Banno

The answers to the questions of this thread aren't dependent on metaphysics. I'm not juxtaposing anything, i.e., the argument is meant to stand on its own. If, on the other hand, someone were to bring in idealism as a way to answer the question, it might add an important layer, but it's not needed. In this respect, I would agree with Banno, but at some point, this agreement would fail, because my ultimate view of reality does involve metaphysical answers. I have no problem keeping these language-games distinct. Moreover, as much as I enjoy Wittgenstein, I depart from him when it comes to the limit of language. Wittgenstein didn't reject the metaphysical, he just thought that what can be said about the metaphysical is senseless (not nonsense, but senseless) because it goes beyond the world, and language is limited to the world.

No! Not if he was saying black, black, black, err, no I meant white! No! That strongly implies an external influence. And we know what that influence was, and it is contemporaneous. You can propose, I suppose, he had some come to jesus moment, but then display your jesus. Subjectivism is bunk! Science rocks!

So I still want a way to characterize the difference between saying "The Eiffel Tower is tall" and "That object [pointing] is called 'the Eiffel Tower'". Yes, the first is a property and the second is not, but where do these statements fall on the syntactic/semantic spectrum? — J

@banno If I may chime in with a related question. I seem to be missing an understanding about what a property is. I can see that whatever name that object (i.e. the eiffel tower) has is distinct from any of the properties that it has qua physical object. But if "a" refers to a, then it seems to me to follow that a is referred to by "a". So if the former is a property of "a" then the latter must be a property of a? You and @J seem to agree that "a" does have a property of referring to a, but that although a is referred to by "a", that does not constitute a property. I don't see why not. I do see that one could not use it to identity the reference of "a", because it would be circular, but that's a different matter, isn't it?

He's trying to lay out the requirements for a consistent picture, not choosing among pictures — J

That's the idea.

It's not that we can't, or even shouldn't, choose amongst the metaphysical theories. It's that if some metaphysics is not in harmony with the best thinking on modal logic or logic more generally, we ought treat it with scepticism; it has issues to be addressed.

He did at one stage describe himself as an anti-realist, but that seemed to be a result of his toying with truth, a seperate issue to possible worlds.

Subjectivism is bunk! Science rocks! — karl stone

Science does, indeed, rock.

I like it anyways.

Though @karl stone -- you ought respond to

The question really should be, let's say, could the Queen -- could this woman herself -- have been born of different parents from the parents from whom she actually came? — N&N, 112

I guess there fact that there are billions of people in the world who were born of different parents and none of them are the Queen doesn't prove it can't happen. But I'm leaning that way anyway. :grin:

Oh, boy. there's a lot in that post.

Relevant logic uses a variation of the accessibility relation from possible world semantics to model relevance relations between worlds. Together with Kripke's strict conditional this is used to group conditionals together in a way that seeks to overcome the so-called paradoxes of implication.

I'd have to do a bit more work before claiming to see how it works in the examples you give. My thought at the time I made the suggestion was that perhaps the relevance relation might be used to clarify the difference between, say, "heat is molecular motion" and "temperature is molecular motion"; that temperature might be relevant to molecular motion in a way that heat is not. it'd be something like that from a world in which we have temperature, we might only be able to access worlds in which we have molecular motion, but from a world in which we have heat, it might be that we can access a world without molecular motion. It might follow that temperature, and not heat, relates necessarily to molecular motion. I do not have sufficient grasp of the machinery of relevance logic to follow through on this.

What this shows is that we've been ignoring a bit of the theory of possible worlds that is becoming increasingly relevant here. We've been saying that ☐A is understood as "A is true in every possible world". This needs some qualification. These statements are indexed to possible worlds and to the accessibility relation. So a more accurate account is that ☐A in world one is understood as "A is true in every world that is accessible from world one".

We get away with the cut down version by assuming that we are working with the syntax of S5, in which every world is accessible from every other world.

And there's another qualification that is needed, as to the difference change in the use of "contingent" in Kripke's semantics. Previously, "contingent" had a sense of "dependent", so something was contingent if it's being true was dependent on some other fact. That is not so much the case in possible world semantics. A statement will be necessarily true in w₁, as explained, if it is true in every world accessible form w₁. A statement will be possible in w₁ if there is at least one world, accessible from w₁, in which the statement is true. It follows that if a statement is necessary then it is possible. A statement will be impossible in w₁ if there is no world accessible from w₁ in which it is true.

And a statement will be conditional in w₁ if there is at least one accessible world in which it is true, and at least one accessible world were it is false.

The dependence on "dependence" drops out, along with a whole lot of metaphysical baggage and a few proofs that god exists. That's part of the reason there is some resistance against this logic from those of a naive theological bent.

So to the metre rule, and area that is fraught with misunderstanding. Consider this, from your Malcolm quote: "Certainly there is no requirement to hold that if the sentence is not a contingent statement then it must be a necessary statement."

This might be so if we think of contingency as dependence. The length S is dependent on the length of the rod, in the base example.

But in a possible world semantics, if a statement is true, and not contingent, it follows immediately that it is necessarily true. Malcolm, from Kripke's perspective, is mistaken: there is a requirement to hold that if the sentence is not a contingent statement then it must be a necessary statement.


And to god. So for Malcolm, the concept of God, like seeing a material thing, is not inherently self-contradictory. While specific reasoning may be invalid, a general demonstration of non-contradiction is not possible. Both concepts are integral to human thought and life.

See my comments in for a bit more on Anselm. While we might not agree that the idea of a something a greater than which cannot be conceived is self-contradictory, it's not clear that it can be made coherent, either. There is the problem of how to deal with a necessary being without the consequence of modal collapse.

But that's enough for now. Thanks again for your posts.

I'm thinking about the physics, the metaphysics, on the weather, the prior analytics, the posterior analytics, parts of animals, and de anima.

The prior and post analytics serve as his epistemology -- how he goes about making inferences. One by deduction and the other by induction. His treatises on weather, the soul, and the parts of animals too serve as examples of Aristotle applying his epistemology to the world at hand. The physics serves as a precursor to the metaphysics in that it is both a particular and general science since it deals with the topic of change, itself an entry into the study of the most general categories. — Moliere

I mean, that's impressive if you've read all of that. I sure haven't.

I know you've read him and know him -- that's why I thought him a good example for us, and didn't think there'd be anything controversial in comparing his method to modern scientific methods and noting that they are different in what they are doing and arguing. — Moliere

Different in what ways? And what is his method? I asked for your source for your ideas about "Aristotle's view of induction," and you literally pointed to seven different works without giving any specific references. That doesn't help me understand where your ideas about "induction" are coming from.

Yes. Aristotle I'd say I'm most familiar with, and the bit of Kripke we've been referencing in this conversation is something I've read here on the forums. Lavoisier's contribution to science is his meticulous work on making precise instrumentation, which I gather is a clear difference between what both Aristotle and Kripke are doing.

Now, readings get rusty and I make mistakes. But I'm not just using these just because -- Kripke got added to the mix, but Aristotle/Lavoisier is one I've just often thought through as a good comparison for finding a difference. — Moliere

Okay, fair enough. I am not familiar with Lavoisier so that reference isn't informative to me. So you are saying that Lavoisier worked with precise instruments and Aristotle did not? That is the difference I see you pointing to.

When you say this it seems like I must not know how to make a real argument, to your mind. — Moliere

Yeah, given the number of invalid or altogether absent arguments, I don't think you are very strong on argumentation.

I'd rather say that arguments don't reveal truth as much as serve as a check to ourselves -- ah, yes, there I messed up, that inference can't be quite right. — Moliere

So arguments don't reveal truth and we just go around throwing seeds "and see what happens"?

My advice would be to try to understand argumentation better. An argument has a starting point (premises), an ending point (conclusion), and a path from one to the other (inferences). If you aren't providing those to your interlocutor, then there's simply no way for them to engage your philosophical beliefs. For example:

But neither he nor we can make induction a valid move that secures knowledge. — Moliere

That's an assertion. It contains no premises, no inferences, and no conclusion. It is opaque. It is probably just a reference to Hume, but if you want it to be more than an opaque assertion, then you have to explain why you think it is true, or where it is supposed to come from.

:lol:

I don't think that's quite what he meant, but it's funny anyway!

I mean, that's impressive if you've read all of that. I sure haven't. — Leontiskos

Only in english, and years ago. Something like 15 years. I don't doubt that my reading is rusty.

But, yes. I wouldn't bother to say something here unless I had at least some reading, experience, or knowledge that relates.

Different in what ways? And what is his method? I asked for your source for your ideas about "Aristotle's view of induction," and you literally pointed to seven different works without giving any specific references. That doesn't help me understand where your ideas about "induction" are coming from. — Leontiskos

Fair questions.

The posterior analytics deals with induction, by my memory. And I want to add that I think Aristotle's notion of induction is not the same as induction today. But I grant you that I didn't give the specificity you asked for: My reading is certainly rusty.

I feel we're getting closer here now, though, in terms of not talking past one another.

The ways that Lavoisier and Aristotle are different, by my head-cannon at least, is that Lavoisier didn't question the enlightenment premises as much as pursued them and did them well.

***

I think Aristotle's method -- Lavoisier I think didn't invent a method as much as adopted one -- is to review what has been said, demonstrate its strengths and weaknesses, then show his conclusion.

And, on top of that, Aristotle had empirical verification for his conclusions.

For his "view of induction" -- I listed the sources I did because I thought thems would explain it... but maybe not. I can tell you in my own words, though, since that's more relevant to our conversation: Aristotle views induction about objects in the same way we view induction about math. Since there are no other categories he is able to say "this is what that thing is. this is its being" -- but over time we've found that his methods are, while a good guess, not quite right either.

He thinks that the world is harmonious. As I read the metaphysics, at least, all of being is within the mind of God thinking himself. Being is God thinking himself into being by thinking, and the categories apply because we can, through empirical research that climbs up, discover the essence of things.



Now, I could be very wrong in my interpretation, but since you asked for how I understand Aristotle's notion of induction I'm giving an attempt at answering that more clearly.

But, yes. I wouldn't bother to say something here unless I had at least some reading, experience, or knowledge that relates. — Moliere

Okay, well I'm glad to hear that.

Fair questions.

The posterior analytics deals with induction, by my memory. And I want to add that I think Aristotle's notion of induction is not the same as induction today. But I grant you that I didn't give the specificity you asked for: My reading is certainly rusty.

I feel we're getting closer here now, though, in terms of not talking past one another. — Moliere

Yes, well in general when you use a term like, "Aristotle's induction," I need to know what you mean by that if I am going to respond in an intelligent way. That information could be supplied by a reference to a primary source, a secondary source, or by your own explanation of what you mean.

I think Aristotle's method -- Lavoisier I think didn't invent a method as much as adopted one -- is to review what has been said, demonstrate its strengths and weaknesses, then show his conclusion.

And, on top of that, Aristotle had empirical verification for his conclusions. — Moliere

Okay, fair enough.

For his "view of induction" -- I listed the sources I did because I thought thems would explain it... but maybe not. I can tell you in my own words, though, since that's more relevant to our conversation: Aristotle views induction about objects in the same way we view induction about math. — Moliere

Eh, well how do we view induction about math? When you say that I think of inductive mathematical proofs, which do not remind me of anything in Aristotle. So I'm at a loss again.

Since there are no other categories he is able to say "this is what that thing is. this is its being" -- but over time we've found that his methods are, while a good guess, not quite right either. — Moliere

What is wrong about them? If you aren't specific about what is wrong about his method, then I don't see what use it is to claim that his method is wrong, especially when talking to an Aristotelian.

He thinks that the world is harmonious. As I read the metaphysics, at least, all of being is within the mind of God thinking himself. Being is God thinking himself into being by thinking, and the categories apply because we can, through empirical research that climbs up, discover the essence of things. — Moliere

This sort of stuff is too vague for me, Moliere. That last sentence is a doozy.

Now, I could be very wrong in my interpretation, but since you asked for how I understand Aristotle's notion of induction I'm giving an attempt at answering that more clearly. — Moliere

Okay, and that's a good starting point. Thanks for that.

When one critiques a thesis it is crucial that they give a clear exposition of the thesis they are opposing. Here is an example from Aquinas:

Objection 2. Further, the act belongs to the same subject as the habit. Now the habit of charity is in the power of the will, as stated above (II-II:24:1). Therefore the act of charity is also an act of the will. But it tends to good only, and this is goodwill. Therefore the act of charity is nothing else than goodwill.

Reply to Objection 2. To love is indeed an act of the will tending to the good, but it adds a certain union with the beloved, which union is not denoted by goodwill. — ST II-II.27.2.ad2 - Whether to love considered as an act of charity is the same as goodwill?

Rewritten:

• Objection 2: Acts belong to the same subject as the habit. The habit of charity is in the will, therefore the act of charity is in the will. But the will tends only to good. Therefore the act of charity tends to the good and is in the will, and is therefore an act of "good-will."
• Reply to Objection 2: It is true that the act of love is an act of the will that tends to the good, but love involves a union that goodwill does not denote (i.e. love involves a sort of mutual communion, whereas we can act with goodwill towards someone with whom we have no communion or friendship). Or: Where there is love there is goodwill, but where there is goodwill there is not necessarily love.

Do you see how the objection that Aquinas presents has its own clarity and logic? That it can be followed and understood? That it possesses a coherence that allows room for a proper reply in turn? That's exactly what needs to happen when someone critiques a position, such as Aristotle's. They need to set out a clear and reasonable account of Aristotle's position, and then critique that position in turn.

Eh, well how do we view induction about math? When you say that I think of inductive mathematical proofs, which do not remind me of anything in Aristotle. So I'm at a loss again. — Leontiskos

Good point. I think Aristotle sees his categories as mathematical inductions because he empirically witnessed them.

I see them as mathematical inductions because I read Aristotle as feeling justified in writing his metaphysics because he had covered all the theories prior, showed their weaknesses and strengths, and expressed the truth given their inputs -- in light of his prior analytics I think he thought it possible to find true categories, such as the four causes, which would resemble the necessary conclusions of his prior analytics.

The categories looked real, as they do today -- but he decided, in good taste, to philosophize them. (or write down his notes so he could teach tomorrow, flip a coin)

- What do you mean when you say "mathematical induction"?

So I still want a way to characterize the difference between saying "The Eiffel Tower is tall" and "That object [pointing] is called 'the Eiffel Tower'". Yes, the first is a property and the second is not, but where do these statements fall on the syntactic/semantic spectrum? — J

Seems fair to say that in natural languages the distinction between semantic and syntactic is fluid, far more so than in a formal language.

As I understand it, Kaplan's approach is to explain the character and the content of an indexical separately. The character is a function that in a given context yields the object being pointed to. So the character of "I" yields me; the character of "that" yields what is being pointed to, and so on for different indexicals. The content is the individual involved.

So “that object [pointing]” has an indexical with character λc. demonstratum(c), and content (in c) = Eiffel Tower. There's plenty more formalism that can be dropped in here, but the idea is basically that each different indexical has a character that returns an individual as the content. "I" returns the speaker, "that" returns the thing being pointed to, "you" returns the person being addressed, and so on,

The content of "that" is a rigid designator, and so in predicate and modal logic can be an individual variable.

This is all semantics. It's about the things, not about the strings.

So "That is tall", indicating the Eiffel tower, and "The Eiffel tower is tall", are about the same thing, referring to it using a rigid designator.

But "That object [pointing] is called 'the Eiffel Tower'" has an indexical that returns a rigid designation that is then equated to a name -- hence 'the Eiffel Tower' is in quotes. Being in quotes indicates that it is part of the metalanguage, that it's about the interpretation of the language and not a sentence int he language.

Is there something here that this misses?

I don't think that's quite what he meant, but it's funny anyway! — J

More seriously, the answer is No. It's a question I remember asking as a child. I assume most people wondered at some point. But no. It's outright impossible.

Thanks. I had some vermu's and forgot!

I don't think dualism is an assumption. It's a description of a state of affairs. It's like saying gravity is an assumption. What reasonable evidence have I for disputing the tyranny of gravity?
It is everywhere confirmed that there's an internal world, and an external world - mediated by the senses. Senses that are evolved to enable us to survive; and thus, demonstrably accurate to external reality.
Not comprehensive, that thin gruel I'll gladly grant subjectivists - while denying that the external world is created by the subject.
Observation in science, is thus a valid basis for knowledge of the external world, particularly when observations are confirmed by an independent observer.
Empirical method.
What if? Could you not leave hanging what you're alluding to? The double slit experiment perhaps? Telekinesis? Or something even more mystical and weird, like subjectivism!?

It is everywhere confirmed that there's an internal world, and an external world - mediated by the senses. — karl stone

Do you mean that our experience confirms it? If not our experience, then what?
I think you will find it more helpful to think of that idea as a model, or an interpretation. The most helpful comparison is with the puzzle pictures, and the idea of a Gestalt is a more general version. There's a classic discussion of this in Wittgenstein. See Wikipedia - Rabbit-duck illusion

Gestalt psychology, gestaltism, or configurationism is a school of psychology and a theory of perception that emphasises the processing of entire patterns and configurations, and not merely individual components. It emerged in the early twentieth century in Austria and Germany as a rejection of basic principles of Wilhelm Wundt's and Edward Titchener's elementalist and structuralist psychology. — Wikipedia - Gestalt

Observation in science, is thus a valid basis for knowledge of the external world, particularly when observations are confirmed by an independent observer. — karl stone

Yes, but given the way that physics conflicts with common sense, it is important to point out that observations themselves tell us that some observations are wrong, mistaken, misleading and that observations themselves enable us to correct those mistakes - usually.