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
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
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
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. — RussellA
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
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".The question is to what extent is scientific language literal or metaphorical. — RussellA
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
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 ↪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
"This lectern" is a rigid designator. It picks out that specific individual in any possible world in which it exits. — Banno
I'll leave you to it, then.We've already explained to you why this cannot be the case. — Metaphysician Undercover
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
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