Science is about knowing what is true in the world. Philosophy is about doubting what is known to be true in the world.

A crying dog, Descartes maintained, is no different from a whining gear that needs oil — Wayfarer

If you believe that someone is acting immorally, yet they believe that they aren't, in the absence of an ultimate arbiter of morality, why should your opinion outweigh theirs ?

Personally, I believe that animals are intelligent, can reason, feel pain, experience emotions and have propositional attitudes, though not everyone agrees.

Of course heat exists in a body and moves from one object to another, quite literally — Banno

"Water is H₂O" is another unfortunate example where Kripke takes a "holiday" with language. — Richard B

I agree with @Richard B.

Kripke also wrote: “Heat is the motion of molecules.”

Wikipedia - Heat
A thermodynamic system does not contain heat.

www.britannica.com/science/heat
It is incorrect to speak of the heat in a body, because heat is restricted to energy being transferred. Energy stored in a body is not heat

www.quora.com/Does-heat-exist-or-is-it-just-another-defined-quantity-like-energy
Mark Barton - PhD physicist with University of Glasgow
"Heat" is a noun and is spoken of as a substance, even in technical language, but it's a misnomer. Strictly heat doesn't exist, it happens: it's the process of energy moving from one system to another via random microscopic interactions.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heat.html
Heat may be defined as energy in transit from a high temperature object to a lower temperature object. An object does not possess "heat"; the appropriate term for the microscopic energy in an object is internal energy. In warning teachers and students alike about the pitfalls of misusing the word "heat", Mark Zemansky advises: Don't refer to the "heat in a body", or say "this object has twice as much heat as that body".

https://van.physics.illinois.edu/ask/listing/1838
In formal scientific usage, ’heat’ refers not to the total amount of that thermal energy but only to the transfer of thermal energy caused by a temperature difference between objects.

https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/internal-energy-sal/a/heat
In thermodynamics, heat has a very specific meaning that is different from how we might use the word in everyday speech
Scientists define heat as thermal energy transferred between two systems at different temperatures that come in contact.
We don't talk about a cup of coffee containing heat, but we can talk about the heat transferred from the cup of hot coffee to your hand.
When the two systems are in contact, heat will be transferred through molecular collisions from the hotter system to the cooler system.

https://www.thermal-engineering.org/what-is-heat-in-physics-heat-definition/
While internal energy refers to the total energy of all the molecules within the object, heat is the amount of energy flowing from one body to another spontaneously due to their temperature difference. Heat is a form of energy, but it is energy in transit. Heat is not a property of a system. However, the transfer of energy as heat occurs at the molecular level as a result of a temperature difference.

Heat is a measurement, as is height, number, weight, etc. They don't exist independently of what they are measuring.

If there are two heaps of sand and we move sand from A to B, such that the height of A has decreased and the height of B increased, we don't say that height has literally moved from A to B.
If there are two piles of books and we move four books from A to B, such that the number of books in A has reduced and the number of books in B has increased, we don't say that the number four has literally moved from A to B.
If there are two buckets of water, and we move water from A to B, such that the weight of A has decreased and the weight of B has increased, we don't say that weight has literally moved from A to B.

Similarly, If there are two bodies and energy is transferred from A to B, such that the internal energy of A has decreased and the internal energy of B has increased, we cannot say that heat has literally moved from A to B.

Even if we say something like "the essential properties of this particular lectern are...", all we are doing is making "this particular lectern" into a type. That is because "essential properties" is what defines a type. — Metaphysician Undercover

If "this lectern" is a type, and as types are usually thought to be universals, who is correct, the Realist, the Nominalist or the Conceptualist ?

The Realist thinking that "this lectern" exists in a mind-independent world, the Nominalist who believes that "this lectern" only exists as one particular instantiation at one moment in time or the Conceptualist who understands "this lectern" as a concept existing in the mind only.

It seems Kripke's form of Realism was more linguistic. The reference of "this lectern" is fixed by an act of "initial baptism" which designates a very real physical object with an observable property, such as "this lectern is made of wood". However, the meaning of this expression can evolve over time and even change completely, but what establishes the reality of the expression "this lectern is made of wood" is the existence of a continuous causal chain linked to the initial baptism. Language maintains its stability, even if the meaning of the expressions it uses change with time.

IE, for Kripke's causal theory, expressions within language may start by corresponding with the world, but as time goes by, may correspond less with what initially baptised them as long as they maintain a coherence within the linguistic contexts within which they are used.

When the object "requires a new description", it is because it has changed, therefore it's not "at the same time". It's not at the same time, it's over a duration of time. A thing changes, yet continues to be the same thing, therefore it has contradicting properties, but not at the same time. — Metaphysician Undercover

It depends of which properties are essential for an object to be the same object.

It it is judged that location is an essential property of an object, then if the object changes location then by definition the object has changed. For example, a 1.5m tall piece of wood in a lecture room is a lectern, on a bonfire it is kindling.

If it is judged that location is not an essential property of an object, if the object changes location then by definition it is still the same object. For example, a euro coin in Brussels is money, in Athens it is still money.

No definition is correct, no choice of essential property is correct, as they are based on human judgement. Kripke's rigid designators are also matters of personal judgement.

The amount of heat gained or lost by a sample (q) can be calculated using the equation q = mcΔT, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change. — Khan

The heat moves from one body to the other, in a process that can be described with mathematical predictability. Nothing metaphorical about it. — Banno

The question is to what extent is scientific language literal or metaphorical. To what extent is Kripke's language literal or metaphorical.

I believe "move" is being used as a figure of speech, not that heat literally moves.

You are by-passing the question as to in what sense does heat, which doesn't exist in a body, and is a measurement, move from one body to another ?

Permit me to take a stab at that. Properties 1. Essential i.e. critical to identity e.g. the 3 sides + the 3 angles of a triangle. 2. Incidental i.e. not critical to identity e.g. the color of the triangle above. — Agent Smith

There are objects in the world and there are "objects" in the mind

Assume in the world is something that has a set of properties: being in a flat plane, three straight sides, having three angles, 10cm large, colour green, rotated at 45 degrees, located in Paris, made of paper, makes no sound, has no smell, etc

What determines that some of these properties are essential to the identity of this something and some properties are incidental ? A mind-independent world cannot make this determination, it can only be made by a person. However, in the event that one person judges that colour is an essential property whilst another person judges that colour is an incidental property, how is it determined who is correct ?

If it is a person who is judging which properties are essential and which incidental, then they are not referring to something that exists in the world as a set of properties, but they are referring to something that exists in the mind as a concept.

I agree that concepts in the mind maintain their identity even though different instantiations of the concept in the world may be associated with different properties.

When object A requires a new description (because it's properties change due to the passing of time), this does not mean that it has become a different object. That's the very reason for the law of identity, to allow us to say that a thing maintains its identity as the same thing, which it is, despite changing as time passes. — Metaphysician Undercover

A person can maintain their identity as the same thing yet at the same time have different properties.

But how can an object maintain its identity as the same thing yet at the same time have different properties ?

Are you content with this account? Is the property of having writ that post essential to your being who you are? Might you not have written it, yet have remained RussellA? — Banno

Yes. I'm not saying that I have Dissociative Identity Disorder, but there are two distinct RussellA's.

There is the RussellA that exists in the world as fundamental particles and forces, and whose identity is constantly changing. At each moment in time, RussellA's properties are both necessary and essential in order for RussellA to be identical with itself. Even if RussellA loses only one fundamental particle, then RussellA's identity would have changed

There is also the "RussellA" that exists on this Forum and whose identity stays the same over time. A "RussellA" that exists in society, exists in the mind and exists in language. "RussellA" has what Kripke calls rigid designators, ensuring that "RussellA's" identity remains the same even in all possible worlds. "RussellA" has necessary and essential properties. What these are no one knows for certain, but I believe that I have them, even if I don't know what they are. I might have had to go shopping, not had time to write this post, yet remained "RussellA". However, RussellA would inevitably have changed, gained weight, lost some more hair, etc.

If I had not written this post, I would still be "RussellA" but I wouldn't be RussellA.

The heat moves from one body to the other, in a process that can be described with mathematical predictability. — Banno

I don't see what relevance this has to the topic, unless you are claiming that the motion of molecules causes heat. — Banno

I agree that Kripke has put forward his case that true identity statements are necessary before introducing the examples of names, heat and my pain. However, if the examples he uses of true necessary identity statements are not in fact true necessary identity statements, then this casts doubt on the case he has previously made.

For example, he is using the word "heat" in two different ways, and when he writes "heat is the motion of molecules", it is unclear in what sense he is using the word "heat". "Heat" can refer to the cause and "heat" can also refer to the effect.

Specifically, Kripke gives an example of a true necessary identity statement as "heat is the motion of molecules"

Heat is the transfer of energy between objects due to a temperature difference between them. Bodies don't contain heat.

Problem one - as regards heat transfer by convection, a body having internal energy moves from location A to location B. As bodies don't contain heat, how can heat be the motion of molecules ?

Problem two - as regards heat transfer by conduction and radiation, no molecules move from hotter object A to cooler object B. How can heat move from A to B, if heat is molecules in motion, and no molecules move from A to B ?

The law of identity allows that a thing could continue to be the same thing, despite undergoing change. — Metaphysician Undercover

How can that be ?

In logic, the law of identity states that each thing is identical with itself. Gottfried Wilhelm Leibniz expressed it as "Everything is what it is". Wilhelm Wundt credits Gottfried Leibniz with the symbolic formulation, "A is A".

Object A, from the law of identity, is identical with itself.

I am taking object A as something that exists in the world, not as the name "object A". Object A and "object A" are different things. Object A exists in the world and "object A" exists in the mind. "Object A" is the name for object A.

All the properties object A has are necessary for object A to be object A, and all the properties object A has are essential for object A to be object A.

If object A changes into Object B over time, even if it has lost only one molecule, then object B cannot be the same as object A.

If the lectern before us were made of plastic instead of wood, it would be a different lectern to the wooden one that is actually before us. — Banno

Being made of wood is not essential of being a lectern.............By the law of identity all properties of a particular individual are essential properties.......... So we cannot say that it is necessarily made of wood, that might be a mistaken judgement. — Metaphysician Undercover

The law of identity
There is something in front of me. It has many properties: being made of wood, brown in colour, being in a lecture room, being 1.5m in height, not made of ice, etc. It must be true as @Metaphysician says: "By the law of identity all properties of a particular individual are essential properties". In the sense that all the properties this thing has are essential to making this thing, in that if this thing had different properties it would be a different thing. If this thing lost even one molecule, it would be a different thing. It must be true as @Banno wrote: "If the lectern before us were made of plastic instead of wood, it would be a different lectern to the wooden one that is actually before us."

We judge some properties of an object more essential than others
However, this would be inconvenient for humans in navigating their world if everything they saw in the world was continually changing. Therefore, for convenience, humans judge certain properties more essential than others. For example, one person could judge that being made of wood was more essential to being a lectern, and another person could judge that being in a lecture room was more essential to being a lectern. There is no correct judgement, it is a matter of personal judgement. It must be true as @Metaphysician wrote: "Being made of wood is not essential of being a lectern."

Kripke and Rigid Desgnators
Kripke wrote: i) "What do I mean by ‘rigid designator’? I mean a term that designates the same object in all possible worlds.", ii) "We can talk about this very object, and whether it could have had certain properties which it does not in fact have. For example, it could have been in another room from the room it in fact is in, even at this very time, but it could not have been made from the very beginning from water frozen into ice."

In order to make sense of objects in the world, those properties judged more essential than others required to maintain the identity of an object, are called by Kripke "rigid designators". Rigid designators are defined by personal judgement. For example, let a rigid designator of a lectern be "being made of wood", though it could equally well have been "being in a lecture room". As we have judged being made of wood is an essential property of a lectern, by definition, being made of wood becomes a property of a lectern.

It follows that as "being made of wood" is now part of the definition of a lectern. If I see an object that is not made of wood, then by definition it is not a lectern. It must be true as @Metaphysician wrote: "So we cannot say that it is necessarily made of wood, that might be a mistaken judgement". Because this definition of lectern doesn't include being in a lecture room, as a lectern may or may not be in a lecture room, the lectern is not necessarily in a lecture room.

Definitions are necessarily true a priori
Kripke wrote: i) "So we have to say that though we cannot know a priori whether this table was made of ice or not, given that it is not made of ice, it is necessarily not made of ice. " ii) "For example, being made of wood, and not of ice, might be an essential property of this lectern."

But what is a "lectern". What does "lectern" mean. The meaning of words cannot come empirically from observation of the world, in that, if I look at the world and see on the one hand a group of charging elephants and on the other hand a stand made of wood in a lecture room, it would be impossible to know a posteriori which of these "lectern" refers to. The meaning of "lectern" can only be determined a priori either from a dictionary or similar or from use within language. Therefore, the meaning of "lectern" is a priori and necessary.

Therefore, in Kripke's statement "being made of wood..........might be an essential property of this lectern.", "this lectern" may be replaced by "this something that is known a priori as being made of wood". This gives the statement "being made of wood..........might be an essential property of this something that is known a priori as being made of wood", which is an analytic statement, and from the law of identity, being made of wood is necessarily being made of wood.

Conclusion
Therefore, as a lectern has been defined as being made of wood, if this lectern is made of wood, then this lectern is necessarily made of wood. Such identity statements are therefore necessary and a priori.

Trouble is, we talked of heat well before we described it as the motion of molecules — Banno

Often, the cause of an effect is given the same name as the effect

Yes, I can experience a sensation in my mind such as pain. My pain as an effect in the mind may have a cause in the world. I see a thistle, and believe that the thistle is the cause of my pain. I need to know nothing about the nature of thistles in order to believe that the thistle was the cause of my pain. In Kant's terms, the thistle is a thing-in-itself.

Often, the cause of an effect is given the same name as the effect. For example, the sensation of red when looking at a red postbox. The sensation of sweet when having a sweet after dinner. The sensation of heat from a hot radiator. The sensation of a burning smell from a burning bonfire. The sensation of a bitter taste from an Angostura Bitter.

The fact that the name of an effect is the same as the name of its cause does not mean that the effect and its cause are the same thing.

whether or not the table is made of ice is always a human judgement. — Metaphysician Undercover

Yes, human judgement must come into it.

Suppose this lectern is made of wood and is in the lecture theatre

Kripke has made the judgement that being made of wood might be an essential property of this lectern, and being in a different room is a non-essential property. Someone else could have made the opposite judgement, that being made of wood is a non-essential property whilst which room this lectern is in is an essential property.

But keeping with Kripke's judgement that being made of wood might be essential property of this lectern..

Someone could say that there is a possible world where this lectern could have been made of plastic, which is highly likely. However, there can be many definitions of "possible worlds", but this is not what Kripke's means by "possible world". For Kripke, a "possible world" is a world in which this lectern keeps its essential properties.

Keeping with Kripke's understanding of "possible world" as a world where this lectern keeps its essential properties.

Therefore, this lectern, which is made of wood, has the essential property of being made of wood, meaning that in all possible worlds it is still made of wood. This lectern is necessarily made of wood in all possible worlds, because by definition, if this lectern is made of wood in the actual world it must also be made of wood in all possible worlds.

So, the statement "this lectern, which is made of wood in this actual world, must necessarily be made of wood in all possible worlds" is contingent first on Kripke's judgement that being made of wood might be an essential property of this lectern and second on Kripke's understanding of a possible world as one in which this lectern keeps its essential properties.

Sure. But not sure what your point is here. I don't see how this is a problem specific to Kripke's account, if that is what you are thinking. — Banno

How do we determine that two rigid designators refer to the same thing.

Kripke wrote: "To state the view succinctly: we use both the terms ‘heat’ and ‘the motion of molecules’ as rigid designators for a certain external phenomenon. Since heat is in fact the motion of molecules, and the designators are rigid, by the argument I have given here, it is going to be necessary that heat is the motion of molecules."

Therefore, as Kripke is saying that heat is a rigid designator, the motion of molecules is a rigid designator, and since "since heat is in fact the motion of molecules", the two rigid designators must be referring to the same thing.

As you wrote: "He provokes the difficult argument that it is necessary that heat is molecular kinetic energy, but contingent that we happen to feel this as the sensation we call heat."

When Kripke refers to "heat", is he referring to what is in the world as molecular kinetic energy, or is he referring to what is in the mind as the sensation of heat ?

As regards heat as the sensation of heat, Kripke writes:
1) "Martians, who do indeed get the very sensation that we call “the sensation of heat”"
2) "Then these creatures could be such that they were insensitive to heat; they did not feel it in the way we do; but on the other hand, they felt cold in much the same way that we feel heat."

As regards heat is the motion of molecules, Kripke writes
1) "First, imagine it inhabited by no creatures at all: then there is no one to feel any sensations of heat. But we would not say that under such circumstances it would necessarily be the case that heat did not exist; we would say that heat might have existed, for example, if there were fires that heated up the air."

If "heat" refers to the sensation of heat in the mind, then how can there be identity between something that exists in the mind and something that exists in the world, the motion of molecules.

If "heat" refers to the motion of molecules, there are two possibilities: i) heat is no more than the motion of molecules, heat is a synonym for the motion of molecules, and therefore "heat is the motion of molecules" is an analytic statement and known a priori, ii) heat exists over and above the motion of molecules, heat exists independently of the motion of molecules, and therefore heat would exist even if there were no molecules in motion, in which case heat could only be discovered a posteriori. As current scientific theory does not propose that heat exists independently of the motion of molecules, heat must be a synonym for the motion of molecules, a case of self-identity. As Kripke said "What properties, aside from trivial ones like self-identity"

Therefore, the statement "heat is the motion of molecules" is either an analytic statement known a priori or requires an understanding as to how there can be an identity between something in the mind and something in the world.

No it isn't. The heat moves from one body to the other, in a process that can be described with mathematical predictability. Nothing metaphorical about it. — Banno

Kripke said “Heat is the motion of molecules”, which is incorrect.

Heat is the energy transferred between objects due to a temperature difference between them. As you said, the amount of heat gained or lost by a sample (q) can be calculated using the equation q = mcΔT, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change. Heat is a measurement, it doesn't have an independent existence. An object does not possess heat, an object possesses internal energy.

If object A travelling at 5m/s hits a stationary object B, the speed of object A reduces to zero, and the speed of B increases to 5m/s. Something called "speed" has not literally moved from A to B. Speed is a measurement, not something that has an independent existence


If object A at 30deg C touches object B at 20deg C, the temperature of object A will reduce and the temperature of object B will increase. Something called "heat" has not literally moved from A to B. Heat is a measurement, not something that has an independent existence

The statement "The heat moves from one body to the other" is not incorrect as a figure of speech.

I wouldn't read it that way. Rather, Kripke has already made his case and is applying his account to heat. I think we can drop the heat argument without much impact on Kripke's approach to modality. He is not trying to justify his account of possible world semantics by appeal to heat. — Banno

Yes, Kripke first makes his case that if an identity statement is true, then the identity statement is necessary, and only later introduces the examples of names, heat and my pain.

But isn't his argument circular, in that if the identity statement "the Moon is made of blue cheese " is true, then he is arguing that the moon is necessarily made of blue cheese. Similarly, if the identity statement "the Moon is not made of blue cheese" is true, then the Moon is necessarily not made of blue cheese.

Kripke wrote " Identity statements..........That is to say, they are necessary if true; of course, false identity statements are not necessary." (abstract)

The problem remains in how do we determine whether an identity statement is true or not. How do we determine that two rigid designators refer to the same thing.

Kripke's case is that true identity statements are necessary
Kripke wrote: "To state finally what I think, as opposed to what seems to be the case, or what others think, I think that in both cases, the case of names and the case of the theoretical identifications, the identity statements are necessary and not contingent". (page 171)

Kripke makes a general argument
"If names are rigid designators, then there can be no question about identities being necessary, because ‘a’ and ‘b’ will be rigid designators of a certain man or thing x. Then even in every possible world, a and will both refer to this same object x, and to no other, and so there will be no situation in which a might not have been b. That would have, to be a situation in which the object which we are also now calling ‘x’ would not have been identical with itself". (page 181)

Kripke gives an example using "this lectern"
"Here is a lectern......What are its essential properties............being made of wood, and not of ice, might be an essential property of this lectern...............could this very lectern have been made from the very beginning of its existence from ice.............If one had done so, one would have made, of course, a different object. It would not have been this very lectern........The conclusion ☐P is that it is necessary that the table not be made of ice, and this conclusion is known a posteriori, since one of the premises on which it is based is a posteriori" (page 180)

Later on, Kripke refers to names, heat and my pain.
1) "If names are rigid designators, then there can be no question about identities being necessary" (page 180)
2) "We use both the terms ‘heat’ and ‘the motion of molecules’ as rigid designators for a certain external phenomenon". (page 187)
3) "In fact, it would seem that both the terms, ‘my pain’ and ‘my being in such and such a brain state’ are, first of all, both rigid designators". (page 188)

It may well be that true identity statements are necessary. The problem remains in knowing whether the identity statement is true or not. How do we know in the first place that "Cicero is Tully", "heat is the motion of molecules" and "my pain is my being in such and such a brain state" ?

Don't you think it's the word "heat" which is the most metaphorical here...Yet it maintains descriptive power by way of metaphor, so it is still used. — Metaphysician Undercover

Yes, it is a concept that exists in the mind and not the world, such as pleasure, pain, government, democracy. But as a concept, it does have great descriptive power, even if what it is describing doesn't literally exist in the world.

"Heat" is really meaningless then, because if it referred to the activity of heating or cooling, it would necessarily be in the body, in order that the body could heat up or cool down. Or is "heat" just metaphor to you? — Metaphysician Undercover

If heat is not energy, this throws a spanner in the works in Kripke's argument for a posteriori necessity.

"Heat" has meaning as a measurement.

Heat is a measurement of the change in energy of a body. Heat is not a substance. A thermodynamic system does not contain heat.

Consider two bodies, one 1,000 kJ hotter than the other. Consider two bodies, one 80 metres taller than the other.

In what sense do measurements exist. In what sense does "1,000 kJ hotter" exist. In what sense does "80 metres taller" exist.

If The Empire States Building is 80m taller than The Eiffel Tower, where does "being 80m taller" exist. Does it exist in the world independently of any object, or does it exist in the mind of an observer.

If body A is 1,000 kJ hotter than body B, where does "being 1,000kJ hotter" exist. Does it exist in the world independently of any object, or does it exist in the mind of an observer.

It can only exist in the mind of the observer as a second-order concept, as Frege and Russell argued.

If heat is the measurement "being 1,000 kJ hotter", where does "being 1,000 kJ hotter" exist. Where does heat exist?

If heat is the transfer of thermal energy, and we're using the term "heat" consistently, then in each and every instance where we use "heat", we ought be able to substitute that term with "the transfer of thermal energy", and retain all sensibility. — creativesoul

Could I be thrown off a philosophy forum for talking about the scientific nature of heat
In order to avoid being thrown off the thread for talking about the nature of heat, my reason is as follows:

Kripke concludes: "To state finally what I think, as opposed to what seems to be the case, or what others think, I think that in both cases, the case of names and the case of the theoretical identifications, the identity statements are necessary and not contingent."

One of the main planks of Kripke's justification is that “Heat is the motion of molecules will be necessary, not contingent, and one only has the illusion of contingency"

Thermal energy is due to the motion of molecules. Therefore, one of Kripke's main justifications for a posteriori necessity is his belief that heat is thermal energy.

If heat is, in fact, not thermal energy, one of Kripke's main planks disappears. This casts doubt on the other planks in his argument, which in turn casts doubt on his conclusion regarding a posteriori necessity.

The word "transfer" is being used as a metaphor
The statement "The amount of heat gained or lost by a sample (q) can be calculated using the equation q = mcΔT, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change" is being used metaphorically rather than literally. Heat is a measure of the change in energy of a body. As a thermodynamic system does not contain heat, a body cannot gain or lose heat.

Britannica writes: "heat, energy that is transferred from one body to another as the result of a difference in temperature" Again, the word "transfer" is a metaphor. Heat has not literally been transferred from one body to the other.

Language is fundamentally metaphoric
Language, both in daily and scientific use is fundamentally metaphoric. Language as we know it couldn't exist without metaphor.

When you say "The above looks suspiciously like an equivocation fallacy", "A substitution exercise shows it nicely", "If heat is the transfer of thermal energy", "perform this exercise", and "something is off" you are using language metaphorically.

George Lakoff and Mark Johnson in Metaphors We Live By argue that metaphors are not merely stylistic, but are pervasive in everyday life, not just in language, but also in thought and action.

Andrew May in his article Metaphors in Science writes: "What is a scientific theory if not a grand metaphor for the real world it aims to describe? Theories are generally formulated in mathematical terms, and it is difficult to see how it could be argued that, for example, F = ma "is" the motion of an object in any literal sense. Scientific metaphors possess uniquely powerful descriptive and predictive potential, but they are metaphors nonetheless."

The word "transfer" is being used as a metaphor. Language would not exist as we know it without the use of metaphor. The use of metaphors is unavoidable in language, and we have to depend on context to tell us whether a word is being used metaphorically or not.

You had me worried for a moment.

current principles of physics allow that the second body, the receiving body, is not necessary — Metaphysician Undercover

True, no second body is necessary for thermal radiation, in that the Sun has no "awareness" that the thermal radiation it emits will hit the Earth 8min 20sec later. The thermal radiation could continue into space without ever hitting a second body.

Radiation of heat from an object........heat can radiate — Metaphysician Undercover

Heat doesn't radiate. Heat is the transfer of thermal energy between two bodies.

There are three modes of heat transfer, conduction, convection and radiation. The transfer of heat by radiation needs no material carrier. Thermal radiation is electromagnetic radiation.

It is incorrect to speak of the heat in a body, because heat is restricted to energy being transferred.

Kirchhoff's law of thermal radiation is regarding a body at temperature T radiating electromagnetic energy. The body is not radiating heat, it is radiating electromagnetic energy.

The sun doesn't radiate heat, it radiates thermal radiation. If this thermal radiation doesn't hit a second body, as heat is the transfer of thermal energy between two bodies, no heat will be transferred.

When Theodore Parker said "Cities have always been the fireplaces of civilization, whence light and heat radiated out into the dark", he was using it as a poetic metaphor.

Well, no. Heat is measured in Joules. It is the flow of energy from place to place. I don't think we can finesse that away. — Banno

I wrote "heat is not energy". The consequence is that Kripke's statement “Heat is the motion of molecules.” is not true.

1) Heat is the transfer of thermal energy between two bodies, not the flow of thermal energy between two bodies.

Water when flowing along the Danube can exist independently of either Vienna or Budapest, however, heat cannot exist independently of the two bodies between which it is being transferred.

2) Are you saying that because heat is measured in joules and energy is measured in joules, then heat is necessarily energy ?

If so, then it would follow that because the height of the Eiffel Tower is measured in metres, and the height of the Empire States Building is measured in metres, then the Eiffel Tower is necessarily the Empire States Building.

3) Your argument is that heat, which is the transfer of energy, is energy.

From https://psiberg.com/thermal-energy-vs-heat
i) Thermal energy = It is due to the movement of particles in a system
ii) Heat = It is the transfer of thermal energy

Then it would follow that:

The banking system, which is about the transfer of money, is money.
Language, which is about the transfer of knowledge, is knowledge.
The football transfer system, which is about the transfer of football players, is the football players.

All these are true, but only metaphorically.

But given that a posteriori we know that heat = the movement of molecules, then it's the same in every possible world. Or at least, that seems to be Kripke's argument...........I don't see how molecules could exist but not their movement — Banno

Justfication three that "heat is the motion of molecules" cannot literally be true.

Relevant, as Kripke uses "heat is the motion of molecules" as evidence for necessity a posteriori.

I agree that space and time exist in the world, molecules exist in the world and the movement of molecules exists in the world.

I still don't agree that heat exists in the world in the same way that molecules and their movements exist in the world. As language transfers knowledge, heat transfers energy.

Heat
Heat can be transferred by conduction, convection or radiation. Conduction is a process in which heat is transported between parts of a continuum, through direct physical contact. Convection is the principle, wherein heat is transmitted by currents in a fluid, i.e. liquid or gas. Radiation is the heat transfer mechanism, in which the transition takes place through electromagnetic waves.

What these have in common is that heat is the process whereby energy is transferred from one body to another. Energy is due to the motion of molecules. Heat is the transfer of energy. Heat is not energy, heat is the transfer of energy. As energy is the motion of molecules, and as heat is not energy, heat is not the motion of molecules.

Heat is not a substance, it is a process
Mark Barton, PhD physicist with University of Glasgow, wrote: ""Heat" is a noun and is spoken of as a substance, even in technical language, but it's a misnomer. Strictly heat doesn't exist, it happens: it's the process of energy moving from one system to another via random microscopic interactions."

1) Heat is the transfer of energy.
2) Energy is due to the motion of molecules.
3) Heat is not energy
4) Therefore, heat is not the motion of molecules.

Heat is necessarily the motion of molecules. The sensation of heat is not......
But this does not undermine the broader case that sometimes if A=A, then ☐A=A. — Banno

The law of identity
I don't disagree that if A = A then A = ☐A. As you say "Hence, it is not that "Kripke seems to want to prove something like the law of identity.........I think he takes it as given." Yes, if heat is heat, then heat is necessarily heat. If the motion of molecules is the motion of molecules, then the motion of molecules is necessarily the motion of molecules. If the Eiffel Tower is the Eiffel Tower, then the Eiffel Tower is necessarily The Eiffel Tower.

However, the law of identity doesn't show one way or another that heat is necessarily the motion of molecules, rather than heat is the Eiffel Tower, for example.

Heat, temperature and energy are concepts and don't ontologically exist in the world
Although heat may be transferred by conduction, convection and radiation, keeping with Kripke's description of heat as the motion of molecules. I accept (for the sake of argument) that moving molecules ontologically exist in the world. Consider a body having moving molecules:

Temperature is the measure of speed of these molecules, the higher the speed the higher the temperature. However, temperature as a concept, as a measure of speed, cannot exist independently of the moving molecules. It cannot have an ontological existence in the world over and above the moving molecules themselves. If there were no moving molecules, there would be no temperature.

Energy as a concept is a measure of the number of molecules and their speed. Similarly, as a measure it cannot exist independently of the moving molecules. It cannot have an ontological existence in the world over and above the moving molecules themselves. If there were no moving molecules there would be no energy.

Heat as a concept is a measure of the transfer of momentum from one molecule to another. If a fast moving molecule hits a slow moving molecule, the fast moving molecule slows down, and heat has said to have been transferred. Heat as a measure of the change in movement cannot exist independently of the change in movement. It cannot have an ontological existence in the world over and above the moving molecules themselves. If there were no moving molecules there would be no heat.

Heat is a concept
In Bertrand Russell's terms, the existence of heat is not the first-order of an individual but the second-order of a concept. If I tell someone that the next bus will be arriving in 10 minutes, their knowledge has increased, in that my knowledge has been transferred to them. This does not literally mean that knowledge ontologically exists in the world. Similarly, if someone says that heat has been transferred from one object to another, this does not literally mean that heat ontologically exists in the world. Knowledge and heat as concepts are figures of speech.

"Heat is necessarily the motion of molecules" cannot literally be true
As heat is a concept that exists only in the mind and not ontologically in the world, and as moving molecules do ontologically exist in the world, the statement "Heat is necessarily the motion of molecules." cannot literally be true as it is comparing two fundamentally different things, though still valid as a metaphor, however.

One of the things about the thermometer definition is it explicitly states how to pick out temperature without telling you anything about temperature. I think that's a feature..........In the case of counter-factuals, when we're talking about "heat is the motion of molecules" vs. "heat is a caloric substance that goes from one object to the other", then I think both must be picking out the same things in the case of the first part, but I'm not sure about the latter part still. — Moliere

The example of the thermometer may be a key into Kripke's necessary a posteriori.

We may know an effect without needing to know its cause
I observe the number on a thermometer change. I don't know what is causing the number to change, but I name whatever is causing the number to change as heat. The number isn't heat, but what is causing the number to change is heat.

Some hypothesise that what is causing the number to change is the motion of molecules, ie, heat is the motion of molecules. Others hypothesise that what is causing the number to change is caloric, ie, heat is caloric. If one of these hypothesise becomes with time self-evidently true, it becomes an axiom. Society then accepts as given the axiom that heat is the motion of molecules.

Both the motion of molecules and caloric are referring to the same thing, heat in the world, even if we never actually know what heat in the world is. In practice, we don't need to know what is causing the numbers to change, we don't need to know what heat in the world is, all we need to know is the effect of heat in the world, the numbers changing on the thermometer.

As long as we know the effect of heat, we don't need to know what heat is.

Kripke is using the word "heat" in two very different ways
We can have a particular sensation, which we name the sensation of heat. We name the cause of this particular sensation heat. The word heat is being used in two different ways, one as a name of an effect, the sensation of heat, and the other as the name of its cause, heat. The effect is very different from the cause, though they share the same name.

Kripke refers to the sensation of heat. Page 185: "There is a certain external phenomenon which we can sense by the sense of touch, and it produces a sensation which we call “the sensation of heat.”"

Kripke also refers to heat as the motion of molecules. Page 170: “Heat is the motion of molecules.”

Heat as the sensation of heat in the mind
Kripke discusses possible connections between the sensation of heat and its cause: i) "So, it might be thought, to imagine a situation in which heat would not have been the motion of molecules" ii) "the motion of molecules but in which such motion does not give us the sensation of heat" iii) "Martians, who do indeed get the very sensation that we call “the sensation of heat” when they feel some ice which has slow molecular motion, and who do not get a sensation of heat—in fact, maybe just the reverse".

Heat as the cause in the world of the sensation of heat in the mind
Kripke discusses possible causes of our sensation of heat: i) "First, imagine it inhabited by no creatures at all: then there is no one to feel any sensations of heat" ii) "the judgment that heat is the motion of molecules would have been false."

Rigid designators
The motion of molecules in the world is a rigid designator. As this lectern is made of wood , this lectern is necessarily made of wood, similarly, as these molecules are in motion they are necessarily in motion.

A sensation of heat in the mind is a rigid designator. As this particular sensation of heat in the mind is this particular sensation, it is necessarily this particular sensation, whatever it is named, in that it could have been named "heat", "cold", "apple" or "The Eiffel Tower".

Heat in the world as the cause of a sensation of heat in the mind is a rigid designator. As this lectern is made of wood , this lectern is necessarily made of wood, similarly heat in the world as the cause of a sensation of heat in the mind is necessarily the cause of the sensation of heat in the mind, whatever it is named.

Kripke concludes that heat is necessarily the motion of molecules
He wrote: page 187: "To state the view succinctly: we use both the terms ‘heat’ and ‘the motion of molecules’ as rigid designators for a certain external phenomenon. Since heat is in fact the motion of molecules, and the designators are rigid, by the argument I have given here, it is going to be necessary that heat is the motion of molecules."

There are two possible meanings to heat is necessarily the motion of molecules
The motion of molecules in the world has one possible meaning, although heat has two possible meanings.

Meaning one: Heat in the world is necessarily the motion of molecules in the world. There may be heat in the world, and there may be molecules in motion in the world. Both the heat in the world and molecules in motion in the world are rigid designators, but it doesn't of necessity follow that there is a link between them. For example, both "Nixon" and "Caesar" are rigid designators in all possible worlds, but there is no necessary link between them.

Meaning two: Heat in the mind is necessarily the motion of molecules in the world. The sensation of heat in the mind is necessarily caused by heat in the world, but as there is no necessary link between heat in the world and the motion of molecules in the world, there is no necessary link between the sensation of heat in the mind and the motion of molecules in the world.

Conclusion
Heat is not necessarily the motion of molecules.

Exactly wrong. — Banno

True. My new understanding is:

From the SEP Rigid Designators, Kripke addresses the objection that we cannot talk about someone without first having some qualitative criterion of identity, an essence, and if we know of no such essence we cannot meaningfully talk about someone.

Kripke addresses the objection that we cannot meaningfully talk about you, with respect to another possible world, without first having some qualitative criterion of identity, some qualitatively distinguishing mark that allows us to pick you out from other objects in the world at issue, in order to assign your name to the right person, i.e., to you, as the individual that satisfies the qualitative criterion. This criterion would appeal to your essence (or be “an essence”: see Plantinga 1985, pp. 85–7; 1974, p. 98; recall, for this example, the minimal requirements of weak necessity), in the minimal respect that the criterion must be something that you and you alone have with respect to any given possible world. As an objection, the worry is that we know of no such qualitative criterion so we can not meaningfully discuss you, with respect to any merely possible world.

From Wikipedia Causal Theory of Reference, Kripke outlined a causal theory of names whereby you don't need to be able to describe what is being named, but after naming an individual in an "initial baptism" the name continues to refer through a causal chain. In fact, although the meaning of the name may change with time and use, the new meaning becomes the new "reality".

1) a name's referent is fixed by an original act of naming (also called a "dubbing" or, by Saul Kripke, an "initial baptism"), whereupon the name becomes a rigid designator of that object.
2) later uses of the name succeed in referring to the referent by being linked to that original act via a causal chain.

In lectures later published as Naming and Necessity, Kripke provided a rough outline of his causal theory of reference for names. Although he refused to explicitly endorse such a theory, he indicated that such an approach was far more promising than the then-popular descriptive theory of names introduced by Russell, according to which names are in fact disguised definite descriptions. Kripke argued that in order to use a name successfully to refer to something, you do not have to be acquainted with a uniquely identifying description of that thing. Rather, your use of the name need only be caused (in an appropriate way) by the naming of that thing.

Sure, you can use it any way you like, but if you want to maintain a distinction between knowing and believing, then I don't think loose or ambiguous usages are a good idea. — Janus

Totally agree, exactly my point.

as soon as the word 'if' appears, you are talking about a possible world, but then you doubly return us to 'this' and 'actual' world. But this actual world is necessarily the way it is, and not the way it would be if anything was different. — unenlightened

In this world, Hesperus exists. If Hesperus didn't exist in this world, it could exist in a possible world.

If Hesperus didn't exist in this world, in which world would Hesperus not exist in, this world or a possible world ?

I've suggested several times that possible worlds are a convenient way of dealing with counterfactuals. If you wish to call them a metaphor, go ahead. — Banno

Kripke wrote page 174: "All of this talk seems to me to have taken the metaphor of possible worlds much too seriously in some way."
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The salient piece for proponents of descriptions is that a proper name does not refer by making use of some description. — Banno

Within Bertrand Russell's Theory of Descriptions, a proper name refers to a set of true propositions that uniquely describe a referent.

Kripke and Donnellan rejected Descriptivism. Kripke described Descriptivism such that (1) To every name or designating expression 'X', there corresponds a cluster of properties, namely the family of those properties φ such that [speaker] A believes 'φX'

For example, to the name Aristotle there corresponds the properties Greek, a philosopher and a teacher. It is these properties that refer to the referent.

A property, such as being Greek, is also a description. As a proper name corresponds to a cluster of properties, and as properties are also descriptions, then surely doesn't Descriptivism make use of descriptions ?
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I agree the notion of removing all of an objects properties is problematic. I don't think that is mentioned anywhere in the article - is it? — Banno

Kripke wrote: "We can talk about this very object, and whether it could have had certain properties which it does not in fact have. For example, it could have been in another room from the room it in fact is in, even at this very time, but it could not have been made from the very beginning from water frozen into ice."

Kripke also wrote:"In fact, it would seem that both the terms, ‘my pain’ and ‘my being in such and such a brain state’ are, first of all, both rigid designators. That is, whenever anything is such and such a pain, it is essentially that very object, namely, such and such a pain, and wherever anything is such and such a brain state, it is essentially that very object, namely, such and such a brain state."

I agree that the possibility of removing all the properties from an object is not specifically mentioned in the article, but the problem of which properties may be removed from a rigid designator without affecting its status as a rigid designator must surely be important in understanding the article.

Objects have properties. Possible properties of this lectern are made of wood, made of ice, in another room, etc. A name is a rigid designator by virtue of having certain essential properties, whereby non-essential properties may be removed without affecting its status as a rigid designator. Kripke doesn't address the problem of how is it determined which properties are essential and which non-essential.

For example, some may believe that whether this lectern to be in this room or outside is clearly not an essential property, yet others may believe that the location of this lectern is an essential part of its identity, in that a stand made of wood outside a lecture theatre is not functioning as a lectern.

The article can only make sense to me if I can understand how is it decided which properties can be removed from a rigid designator before it no longer is a rigid designator.
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I'd also draw your attention to the difference between picking out an individual using a name and picking it out using a demonstrative. — Banno

Even Donnellan admits of description within proper names.

He wrote: "Nevertheless, so long as the user of a name can fall back on such a
description as 'the person referred to by Aristotle', the principle of identifying descriptions may be salvaged even if at expense of having to elevate one type of description to special status."

In the first case "know" is used incorrectly; you cannot know that The Red Sox will win the next game — Janus

If I am using "know" metaphorically, ironically, wryly, jokingly, humorously or sarcastically, it is not being used incorrectly.

You only have this issue if you do not distinguish between the subject and the predicate, or object and property. — Metaphysician Undercover

Yes, much of language is like that, ambiguous, in that rarely in practice if someone says "object A is object B" do they say in what sense they are using "is".

an object with no properties is beyond imagination — frank

I agree. Objects such as lecterns cannot exist in the world independently of their properties, as objects in the world are no more than the set of their properties.

I would say, that your example shows the existence of ambiguity rather than metaphor — Metaphysician Undercover

I more or less agree, but my long-term project is to show that language is fundamentally metaphorical. "Time is a thief" is a metaphor in that time is not the same as a thief. "Object A is object B" is a metaphor in that object A may be similar to object B, but object A can never be the same as object B. "Hesperus is Phosphorus" is a metaphor in that Hesperus may be similar to Phosphorus, but Hesperus can never be the same as Phosphorus.

And, Kripke supposes, this goes for any equivalence between heat and the motion of molecules. If "heat" is a rigid designator for that sensation, and "the motion of molecules" is a rigid designator for molecules in motion, then if heat is the motion of molecules, it is necessarily so. — Banno

Heat and the motion of molecules independent of any observer

Kripke wrote: "First, imagine it inhabited by no creatures at all: then there is no one to feel any sensations of heat. But we would not say that under such circumstances it would necessarily be the case that heat did not exist; we would say that heat might have existed, for example, if there were fires that heated up the air."

Beginning with this lectern, this lectern is made of wood. If it had not been made of wood it would have been a different object, so this lectern is necessarily made of wood. This sounds reasonable.

This raises the question as to whether objects such as this lectern exist over and above their properties, in that if all the properties of the lectern were removed, would this lectern remain. Would Hesperus remain if all its properties were removed. Would heat remain if there were no molecules in motion. As no example of an object existing having no properties can be found in the world, it must be concluded that an object cannot exist in the world independently of its properties.

Kripke would say heat has essential properties. These essential properties exist in all possible worlds, and as such heat is a rigid designator. Objects have properties, and for Kripke, some properties are essential and some non-essential. This can only be a human judgement. Human judgement cannot exist independently of any observer. In a mind-independent world the motion of molecules cannot be judged to be essential or non-essential, meaning that heat cannot be a rigid designator, as the world has no means of judging which properties are essential and which non-essential.

IE, heat cannot be rigid designator in a mind-independent world.

So in some possible world, Hesperus has no properties, and hence Hesperus does not exist in that world. It doesn't follow that Hesperus does not exist in some other possible world. — Banno

My next post will be about heat and the motion of molecules. One could easily become paranoid about being thrown off TPF for not sticking to the OP.

Regarding "possible worlds"
Kripke wrote: 1) What do I mean by ‘rigid designator’? I mean a term that designates the same object in all possible worlds. 2) All of this talk seems to me to have taken the metaphor of possible worlds much too seriously in some way 3) And if the phrase ‘possible worlds’ is what makes anyone think some such question applies, he should just drop this phrase and use some other expression, say ‘counterfactual situation,’ which might be less misleading.

IE, one can use the phrase "possible world", as long as one takes it metaphorically.

Existence
I proposed that if in this actual world, all the properties of Hesperus disappeared, then Hesperus would also disappear. You made the point that even if Hesperus didn't exist in one possible world, it may still exist in another possible world.

I agree that even though Hesperus no longer existed in this actual world, it could still exist in a possible world.

However, these are different kinds of existences. The first refers to something physically existing in the actual world and the second refers to a possible world existing in the mind.

And in your example, we need a similar a priori principle which states that one measurement of 12,103km is necessarily the same as another measurement of 12,103km. — Metaphysician Undercover

I know The Red Sox will win their next game, I know The Eiffel Tower is in Paris and I know that I am looking at the colour red. The word "know" is being metaphorically, in that it has degrees of certainty, because language is inherently metaphorical

Similarly, the word "same" is being used metaphorically having varying degrees of certainty.

I know a priori, before using language, that language is metaphorical. The a priori principle is that language is metaphorical. that "same" is being used metaphorically.

What do you make of this, pg 177-8: — Mww

Kripke asks on page 177: "Is everything that is necessary knowable a priori or known a priori?". He writes page on 178: "So we certainly do not know, a priori or even posteriori, that every even number is the sum of two primes”.

There is a difference between knowable a priori and known a priori.

Taking a simpler example of cardinal numbers, 1,2,3,4 etc. If numbers are invented, and only exist in the mind and not the world, it is certainly true that not every cardinal number is known a priori, because there are an infinite number of them. However, if numbers are invented, every cardinal number is certainly knowable a priori.

We may not know something that is necessary a priori, even though it is knowable a priori.

That is, what is it that the sentence quoted above is about? It seems that it is about Hesperus. If one asks what it is that you are suggesting we remove the properties from, the answer is "Hesperus", and this is so even if the properties are removed. That is, in Kripke's terms "Hesperus" is a rigid designator, while it's various properties may not be. — Banno

I agree that "Hesperus" will continue to exist in language as a rigid designator even if all the properties of Hesperus disappeared from the world.

I will use the nomenclature that "Hesperus" exists in language and Hesperus exists in the world.

"Hesperus" may exist in language even if it doesn't exist in the world
1) Hesperus as an object in the world has millions of properties, most of which are unknown, but includes properties such as being 12,103km in diameter, having a solar year of 117 Earth days, has a central iron core, has a rocky mantle and has an atmosphere 96% carbon dioxide, 3% nitrogen, etc.

2) Hesperus has been named "Hesperus". If all the properties of Hesperus disappeared from existence, Hesperus would no longer exist. There is no example of an object existing in the world that doesn't have any properties. However, "Hesperus" would still exist in language. For a word in language to have meaning, it must have a set of properties, such as "being 12,103km in diameter", "having a solar year of 117 Earth days", etc. No word in language has meaning if it has no properties, for example a word such as "xxyyxx".

Nixon may be named "Nixon".
Similarly, Richard Nixon as an object in the world has millions of properties, most of which are unknown, such as born in 1913, family home in California, attended Whittier College, had a spot on his lung, a good debater, enthusiastic, etc. There are different approaches to how Nixon is named "Nixon".

1) For Ruth Barcan Marcus, proper names are tags which refer to an object which is the bearer of the name. Tags are directly referential and without descriptive content. For example, in the morning Nixon is tagged "Nixon". The tag could be a blue cross or a sheet of paper with the word "Nixon" on it. In the evening, the person with the tag is by definition "Nixon", even though the person may in fact be George McGovern.

2) For Bertrand Russell, in the morning Nixon is described as "born in 1913", "attended Whittier College" and "a good debater", Such a description, such a cluster of properties, is judged sufficient to pick out an individual uniquely. In the evening, the person that can be described as "born in 1913", "attended Whittier College", "a good debater" is by definition "Nixon", even though in fact it could be George Elmer Outland.

3) For Kripke, from (1), page 163, x may be identical to y and x may have the property F. For "Nixon" to be a rigid designator, for "Nixon" to be "Nixon" in all possible worlds, "Nixon" must have essential properties, such as having a spot on his lung. As with the example of the lectern, a non-essential property could be being in a different room. Whether a property is essential or non-essential can only be determined by human judgement, and then codified by social institutions, either fixed in a dictionary or similar or by daily use. For "Nixon" to be "Nixon" in all possible worlds, "Nixon" must have essential properties, such as having a spot on his lungs, where the property having a spot on his lungs is one designator of "Nixon", and as fixed in all possible worlds, is a fixed designator.

"Unicorns" exist in language and may or may not exist in the world.
1) I can define a "standard weight" as having the property 12.102kg, even before ever knowing whether or not 12.102kg exists in the world. Having the property 12.102 kg is an essential property of a "standard weight", is true in all possible worlds, and is a rigid designation. If I subsequently discover 12.102kg in the world a posteriori, I know a priori that it is a "standard weight", in that having the property 12.102kg is a necessary property of a "standard weight".

2) I can define a "unicorn" as having the properties the body of a horse and a single horn in its forehead even before ever knowing that unicorns exist in the world. Having the properties the body of a horse and a single horn in its forehead are essential properties of a "unicorn", and is true in all possible worlds as a rigid designation. If I subsequently discover in the world a posteriori the body of a horse with a single horn in its forehead a posteriori, I know a priori that this is a "unicorn", as having the body of a horse with a single horn in its forehead are necessary properties of a "unicorn".

Kripke's proposition that "identity statements are necessary" is true
1) Objects are observed in the sky. By observation, as "Phosphorus" has a diameter of 12,103km, and as "Hesperus" has a diameter of 12,103km, "Phosphorus" is identical in diameter to "Hesperus". Therefore, the identity statement "Phosphorus is identical in diameter to Hesperus" is true.

2) The property being visible is a priori defined as non-essential, and the property of diameter is a priori defined as essential. As "Phosphorus" has a diameter of 12,103km, having a diameter of 12,103km is a necessary property of "Phosphorus". As "Hesperus" has a diameter of 12,103km, having a diameter of 12,103km is a necessary property of "Hesperus". As "Phosphorus" has of necessity a diameter of 12,103km, and as "Hesperus" has of necessity a diameter of 12,103km, "Phosphorus" is of necessity identical in diameter to "Hesperus". Therefore, the identity statement "Phosphorus is identical in diameter to Hesperus" is necessarily true.

So, the fact that the lectern is made of wood, and not made of ice, is supported by the empirical observations. But empirical observations do not make it necessary that the lectern is made of wood and not ice. The necessity, (that it is necessary that the lectern is wooden and not made of ice), is derived from the a priori law of identity, which states that a thing cannot be other than it is. — Metaphysician Undercover

Well, one consequence is that, that x=y may be discovered empirically - examples are given - but has necessary implications. While this may seem obvious now, it is contrary to both Kant and Quine, fir different reasons. The notion that an empirical fact implies a necessary truth is one of the novelties of this paper. — Banno

The next step, then, says that there is nothing contained in the conception of P that does not belong to the conception of H, therefore, P and H are the same thing, or, that P is H is a necessarily true statement. We don’t need the experience those conceptions represent, only that all of them are thought to co-exist equally in one object. — Mww

Kripke wrote: "To state finally what I think, as opposed to what seems to be the case, or what others think, I think that in both cases, the case of names and the case of the theoretical identifications, the identity statements are necessary and not contingent."

If "Hesperus" is "Phosphorus", then "Hesperus" is of necessity "Phosphorus", but Hesperus is not necessarily Phosphorus

I will use the practice that "Hesperus" is a name in language and either refers to or is described by its properties such as "bright", "visible", "ringless". Hesperus is an object in the world and is its set of properties bright, visible, ringless.

My belief is that Hesperus has no existence over and above its set of properties, in that, if all the properties were removed, then there would be no object, as argued by FH Bradley.

There are two identity statements to consider, "Hesperus is Phosphorus" and Hesperus is Phosphorus.

Analytic propositions
The statement "bachelors are unmarried" is an analytic proposition that is true solely by virtue of its meaning. As it is true by definition, its truth is a priori. As Kripke argues that this lectern made of wood is necessarily made of wood, a bachelor is necessarily unmarried. The meaning of words is determined by social institutions, and are codified either in dictionaries or similar or in daily use, as Wittgenstein proposed.

Empirical Observations
John and Mary observe an object first in position A and then later in position B. John believes the body moves smoothly from A to B. Mary believes the body moves in a series of jumps from A to B. It is empirically impossible to determine who is correct, as we can only infer what happens between A and B, from Hume's constant conjunction.

Axioms
If John is in the majority opinion within his society, the social institutions may codify the concept that well-behaved objects move smoothly between two points as an axiom, as the axiom of "spatio-temporal continuity". Axioms are regarded as being established, accepted or self-evidently true, as with Newton's Laws of Motion. However, it is in the nature of axioms that the axiom of "spatio-temporal continuity" may or may not be true, in the sense of corresponding with facts in the world.

In fact, if an object was observed to jump through space-time, by definition it wouldn't be a "well-behaved object". As the axiom of spatio-temporal continuity is true independent of any empirical observation, it is an analytic proposition, its truth is a priori, and well-behaved objects by definition necessarily pass smoothly through space-time.

"Phosphorus" is necessarily "Hesperus"
Phosphorus and Hesperus are objects. Phosphorus is observed as an object in the east, is named "Phosphorus". and Hesperus as an object in the west, is named "Hesperus". From the axiom of spatio-temporal continuity, and under the assumption that "Phosphorus" and "Hesperus" are well-behaved objects, moving smoothly from the east to the west, it may be concluded that "Phosphorus" and "Hesperus" is the same object, the same Planet. Note that "Phosphorus" exists in language, not in the world. For convenience this single object may be named "Venus"

If when observing the sky, what was thought to be "Hesperus" was observed not to be moving smoothly, then by definition it couldn't be "Hesperus" but must be another object.

Two possible identity statements
As the identity statement "Hesperus" is "Phosphorus is based on the assumption that both "Hesperus" and "Phosphorus" are well-behaved objects, and as well-behaved objects necessarily follow the axiom of spatio-temporal continuity, then the identity statement "Hesperus is Phosphorus" is necessarily true.

However, as it is impossible to empirically determine that when an object in the world has moved from one position to another that there have been no jumps, it cannot be proved that Hesperus is Phosphorus, meaning that the identity statement Hesperus is Phosphorus is not necessarily true.

I suppose I must stop now. All the very best to everyone in the New Year, whichever part of the world you are in. :smile:

I'd say necessity is implicit in Leibniz's law. He's just making it explicit because he's about to challenge the notion that apriori=necessary, and aposteriori=contingent. He's going to show that there can be a statement that is known aposteriori, but is necessarily true. — frank

Necessity is being used in two different ways, between objects and between an object and its property.

Necessity between objects - between a lectern and a rostrum
As regards (4), necessity is being used between objects. He writes: "For every x and y, if x equals y, then, it is necessary that x equals y."

(1), (2) and (4) make use of Leibniz's Law, where "if two objects have all the same properties, they are in fact one and the same".

It seems to me that the use of the word necessary is redundant between objects, in that what does "if two objects have all the same properties, they are in fact necessarily one and the same" add to "if two objects have all the same properties, they are in fact one and the same"

Necessity between an object and its properties - between a lectern and its property wood
As regards the lectern, necessity is being used between an object and its properties, where he writes "So we have to say that though we cannot know a priori whether this table was made of ice or not, given that it is not made of ice, it is necessarily not made of ice.

As he persuasively argues, this lectern, if made of wood, is necessarily made of wood, because if not made of wood it would have been a different object, and it wouldn't have been this lectern.

However, necessity between objects is irrelevant to the question of necessity between an object and its properties. Therefore, necessity may be removed from (1), (2) and (4) without affecting his argument about necessity between an object and its property.