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

SEP lists four theories. I favour the third, although the second and fourth have merit. The first is subject to the criticisms mentioned in this thread.

Like you keep reminding us, logic is grammar i.e. syntax (rules) are its stock-in-trade; the semantics is either ignored or is secondary e.g. I believe the implication as defined truth functionally is counterintuitive e.g. $the ~ moon ~ is ~ made ~ of ~ green ~ cheese \to 2 + 2 = 4$ is true despite the antecedent being false and there being no discernible semantic connection between it and the consequent.

Not just syntax; possible world semantics is about more than mere syntax. The semantics can be defined extensionally in terms of satisfaction.

So let v be a valuation that assigns either T or F to the the propositional variables of predicate calculus ( the set of formulas Γ ), then

7.6 Semantic Notions
We define the following semantic notions:
Definition 7.19. 1. A formula φ is satisfiable if for some v, v ⊨ φ; it is unsat-
isfiable if for no v, v ⊨ φ;
2. A formula φ is a tautology if v ⊨ φ for all valuations v;
3. A formula φ is contingent if it is satisfiable but not a tautology;
4. If Γ is a set of formulas, Γ ⊨ φ (“Γ entails φ”) if and only if v ⊨ φ for every valuation v for which v ⊨ Γ.
5. If Γ is a set of formulas, Γ is satisfiable if there is a valuation v for which v ⊨ Γ, and Γ is unsatisfiable otherwise. — Open Logic

There are variations that attempt to deal with non-extensional contexts. One might seem the aim here as sorting out what can be said without contradiction.

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 ? — RussellA

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.

Downloaded the file. Gracias. True that determining/assuming the truth value of a proposition requires semantics - only after having understood the meaning of a proposition can we say it's true ... or false.

However we can write a short piece of code for a run-of-the-mill PC, e.g. it can just include a modus ponens subroutine, and it'll churn out truths like nobody's business; all that with zero semantics ability (computers allegedly don't have semantic understanding though they're annoying grammar Nazis). I believe that was the whole point of logic.

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 ?

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.

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

The need for this judgement, as to which properties are essential and which are accidental, is what is eliminated by the law of identity. This law puts the identity of the thing within the thing itself, therefore the thing's identity is not based in any human judgement of essential properties.

This forms the difference between the identity of a thing, and the identity of a type. A type is identified by essential properties, " a lectern must be... in order to be a lectern", for example. A statement of essential properties is a statement of the necessary criteria for a type. It cannot be a statement of the necessary criteria for a particular thing, because it's a human judgement, and human judgements are fallible. 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.

So the best we can do as human beings is to set the criteria for a type, by naming essential properties, and judge the particular as to whether it fulfills the conditions of that type. If we desire to set the conditions for a particular, we need to name also the accidentals because a particular consists not only of essential properties (of its type), bit also the accidentals (of that particular). But the accidentals change at every passing moment, and we cannot know them all, so our attempts to identify a particular in this way, are not a true identity.

That is why we must insist that any claim to know the identity of a particular, made by human beings, is mere sophistry. All these human beings are doing is naming a type (essential properties), and claiming that there is only one of this type. But that is not really an instance of producing the identity of an individual. To produce the identity of an individual would require naming all the accidentals.

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.

S4 Modal logic (which lacks logical quantifiers) is best thought of as a weakening of first-order logic:

Instead of having the particular comonad known as 'universal quantification' and the particular monad known as' existential quantification' which already give first order logic a canonical and a priori definition of "necessity" and "possibility", S4 has a weakly defined arbitrary comonad called "necessity" and an arbitrary monad called "possibility", making it weaker than first order logic.

But gven that modern type theories permit arbitrary definitions of monadic structure in addition to explicitly possessing quantifiers whose use is optional, what justifies philosophers continuing the study of modal logic with it's antiquated and impoverished syntax and weaker modes of justification that ironically encourage misleading over-interpretation by philosophers?

In my understanding, what gives Modal logic continued relevance is the usefulness of Kripke Semantics, i.e. the intuitive and useful concept of an accessibility graph of possible worlds together with propositions that pick out subsets of those worlds, a semantics which the syntax of Modal logic succinctly describes.

But if the semantics of modal logic are merely regarded as the predetermined outcome of 'real' modal operators of an underlying modal logic, as seems to be indicated when philosophers attempt to justify their abstract modal reasoning with respect to an assumed definition of the modal operators, then i think Modal logic is either obsolete, and misleading.

Ironically, I think where Kripke Semantics shines is when it is used descriptively in a data-driven fashion to chart one's present knowledge of possible worlds, without appealing to the necessary implications of a dubious modal operator. For modern logic handles reasoning from dubious assumptions in a much clearer, richer and flexible fashion.

The question is to what extent is scientific language literal or metaphorical. — RussellA

The question is whether molecules moving is the very same as heat. Of course heat exists in a body and moves from one object to another, quite literally, as the movement of the molecules involved averages out. Reframing this in terms of metaphor is "by-passing the question".

If "this lectern" is a type, — RussellA

"This lectern" is a demonstrative, not a type. "Lectern" would be a type.

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 ? — RussellA

What I said, is that if "this lectern" is identified by essential properties, then "this lectern refers to a type rather than a particular. That is because types are identified by essential properties, not particulars. Each accidental property is essential to the identity of a particular.

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". — RussellA

The problem is that "this" is demonstrative, as says. It does not serve as an identity. And when when that demonstrative refers to "lectern" it only identifies a type. So if Kripke points to an object and says "this lectern", he has said that the object pointed to, is that type.

The identity of the thing is within the thing itself, as indicated by the law of identity. So identifying an object as a type does not provide the object's true identity. And, if someone moved to identity all the essential properties of the named thing (the properties which make the thing the very thing which it is), they would have to name all the accidentals. The accidentals are what make a particular particular. Naming essentials always results only in a defined type, not a particular. Therefore we cannot produce the identity of a particular lectern by naming essentials, we would only produce a type of lectern.

The problem is that "this" is demonstrative, as ↪Banno says. It does not serve as an identity. And when when that demonstrative refers to "lectern" it only identifies a type. So if Kripke points to an object and says "this lectern", he has said that the object pointed to, is that type. — Metaphysician Undercover

Your capacity to misunderstand continues to astonish.

"This lectern" is a rigid designator. It picks out that specific individual in any possible world in which it exits.

"Lecterns such as this" might pick out a type.

"This lectern" is a rigid designator. It picks out that specific individual in any possible world in which it exits. — Banno

We've already explained to you why this cannot be the case. It is a false premise. Now I've moved on from that, to describe the difference between a particular and a type, which follows from proper employment of the law of identity.

We've already explained to you why this cannot be the case. — Metaphysician Undercover

I'll leave you to it, then.

"Water is H₂O" is another unfortunate example where Kripke takes a "holiday" with language. Consider the following quote from N&N, "Let's consider how this applies to the type of identity statements expressing scientific discoveries that talked about before - say, that water is H₂O. It certainly represents a discovery that water is H₂O. We identified water originally by its characteristic feel, appearance and perhaps, (though the taste may usually be due to impurities). If there were a substance, even actually, which had completely different atomic structure from that of water, but resembled water in these respects, would we say that some water wasn't H₂O? I think not."

In fact, the scientific discovery is not "water is H₂O", but that the substance (whether liquid, solid or gas) we often call "water" we often detect H₂O molecules. Additionally, that substance we call water is not just H₂O molecules, but made up of multitude of compounds, mineral, ion, etc. Not only it is made up of a multitude of different molecules, but that composition can change from thing to thing we call or refer to as "water". So, when any one refers "water", am I referring to only H₂O, or all of molecules that make up any given thing called "water"? Due to multiple uses of "water", and multiple things we use "water" to refer to or could refer to, it is an error to say "water is H₂O" is discover scientically. Lastly, could we say that "some water wasn't H₂O". Yes, in fact we can and do say this, D₂O is called "heavy water" is the scientific community.

So, what is Kripke's error in this example? I believe he ignores the common uses of the word of "water" along with what actually science discovers about "water". What use he has in mind for "water" is how we use the word(symbol) "H₂O"; thus, what he is expressing is "H₂O is H₂O" which is not an a posteriori necessity.

Does this throw some doubt on Kripke's philosophical theory, or just show what he is saying is just trivial, or both?

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.