Pourquoi on peut pas avoir des trucs qui marchent tout seul en logique ? Genre des choses qui font quelque chose mais qui ont pas besoin de paramètres ?
Other conventions

In universal algebra the word type or similarity type is often used as a synonym for "signature". In model theory, a signature σ {\displaystyle \sigma } is often called a vocabulary, or identified with the (first-order) language L {\displaystyle L} to which it provides the non-logical symbols. However, the cardinality of the language L {\displaystyle L} will always be infinite; if σ {\displaystyle \sigma } is finite then | L | {\displaystyle |L|} will be ℵ 0 {\displaystyle \aleph _{0}}.

As the formal definition is inconvenient for everyday use, the definition of a specific signature is often abbreviated in an informal way, as in:

Sometimes an algebraic signature is regarded as just a list of arities, as in:

Formally this would define the function symbols of the signature as something like f 0 {\displaystyle f_{0}} (which is binary), f 1 {\displaystyle f_{1}} (which is unary) and f 2 {\displaystyle f_{2}} (which is nullary), but in reality the usual names are used even in connection with this convention.

In mathematical logic, very often symbols are not allowed to be nullary, so that constant symbols must be treated separately rather than as nullary function symbols. They form a set S const {\displaystyle S_{\operatorname {const} }} disjoint from S func, {\displaystyle S_{\operatorname {func} },} on which the arity function ar {\displaystyle \operatorname {ar} } is not defined. However, this only serves to complicate matters, especially in proofs by induction over the structure of a formula, where an additional case must be considered. Any nullary relation symbol, which is also not allowed under such a definition, can be emulated by a unary relation symbol together with a sentence expressing that its value is the same for all elements. This translation fails only for empty structures (which are often excluded by convention). If nullary symbols are allowed, then every formula of propositional logic is also a formula of first-order logic.

An example for an infinite signature uses S func = { + } ∪ { f a: a ∈ F } {\displaystyle S_{\operatorname {func} }=\{+\}\cup \left\{f_{a}:a\in F\right\}} and S rel = { = } {\displaystyle S_{\operatorname {rel} }=\{=\}} to formalize expressions and equations about a vector space over an infinite scalar field F, {\displaystyle F,} where each f a {\displaystyle f_{a}} denotes the unary operation of scalar multiplication by a. {\displaystyle a.} This way, the signature and the logic can be kept single-sorted, with vectors being the only sort.
Commentaire

Aucun état de choses en soi n'est juste ou injuste : ce n'est que lorsque nous supposons que quelqu'un est responsable de l'avoir provoqué... De la même manière, un marché fonctionnant spontanément, où les prix agissent comme guides pour l'action, ne peut tenir compte de ce dont les gens ont besoin ou méritent, car il crée une distribution que personne n'a conçue, et quelque chose qui n'a pas été conçu, un simple état de choses en soi, ne peut être juste ou injuste. Et l'idée que les choses devraient être conçues d'une manière "juste" signifie, en réalité, que nous devons abandonner le marché et nous tourner vers une économie planifiée dans laquelle quelqu'un décide de la part que chacun devrait avoir, et cela signifie, bien sûr, que nous ne pouvons l'avoir qu'au prix de l'abolition complète de la liberté personnelle.
### Query ###
Pourquoi on peut pas avoir des trucs qui marchent tout seul en logique ? Genre des choses qui font quelque chose mais qui ont pas besoin de paramètres ?

### Main Text ###
Other conventions

In universal algebra the word type or similarity type is often used as a synonym for "signature". In model theory, a signature σ {\displaystyle \sigma } is often called a vocabulary, or identified with the (first-order) language L {\displaystyle L} to which it provides the non-logical symbols. However, the cardinality of the language L {\displaystyle L} will always be infinite; if σ {\displaystyle \sigma } is finite then | L | {\displaystyle |L|} will be ℵ 0 {\displaystyle \aleph _{0}}.

As the formal definition is inconvenient for everyday use, the definition of a specific signature is often abbreviated in an informal way, as in:

Sometimes an algebraic signature is regarded as just a list of arities, as in:

Formally this would define the function symbols of the signature as something like f 0 {\displaystyle f_{0}} (which is binary), f 1 {\displaystyle f_{1}} (which is unary) and f 2 {\displaystyle f_{2}} (which is nullary), but in reality the usual names are used even in connection with this convention.

In mathematical logic, very often symbols are not allowed to be nullary, so that constant symbols must be treated separately rather than as nullary function symbols. They form a set S const {\displaystyle S_{\operatorname {const} }} disjoint from S func, {\displaystyle S_{\operatorname {func} },} on which the arity function ar {\displaystyle \operatorname {ar} } is not defined. However, this only serves to complicate matters, especially in proofs by induction over the structure of a formula, where an additional case must be considered. Any nullary relation symbol, which is also not allowed under such a definition, can be emulated by a unary relation symbol together with a sentence expressing that its value is the same for all elements. This translation fails only for empty structures (which are often excluded by convention). If nullary symbols are allowed, then every formula of propositional logic is also a formula of first-order logic.

An example for an infinite signature uses S func = { + } ∪ { f a: a ∈ F } {\displaystyle S_{\operatorname {func} }=\{+\}\cup \left\{f_{a}:a\in F\right\}} and S rel = { = } {\displaystyle S_{\operatorname {rel} }=\{=\}} to formalize expressions and equations about a vector space over an infinite scalar field F, {\displaystyle F,} where each f a {\displaystyle f_{a}} denotes the unary operation of scalar multiplication by a. {\displaystyle a.} This way, the signature and the logic can be kept single-sorted, with vectors being the only sort.

### Supplementary Text ###
Commentaire

Aucun état de choses en soi n'est juste ou injuste : ce n'est que lorsque nous supposons que quelqu'un est responsable de l'avoir provoqué... De la même manière, un marché fonctionnant spontanément, où les prix agissent comme guides pour l'action, ne peut tenir compte de ce dont les gens ont besoin ou méritent, car il crée une distribution que personne n'a conçue, et quelque chose qui n'a pas été conçu, un simple état de choses en soi, ne peut être juste ou injuste. Et l'idée que les choses devraient être conçues d'une manière "juste" signifie, en réalité, que nous devons abandonner le marché et nous tourner vers une économie planifiée dans laquelle quelqu'un décide de la part que chacun devrait avoir, et cela signifie, bien sûr, que nous ne pouvons l'avoir qu'au prix de l'abolition complète de la liberté personnelle.

### Draft ###

### 1. Query Parsing

"Pourquoi on peut pas avoir des trucs qui marchent tout seul en logique ?"

Key phrases: "marchent tout seul" → self-starting mechanisms? "trucs" → things/objects, informal register.

User seeks: logical systems with autonomous operations. No parameters. Self-triggering.

? Translation issue: "marchent tout seul" could mean "work on their own" or "function automatically"

### 2. Domain Contextualization

Logic fundamentals. Two levels:
- Classical logic: propositions, connectives, truth-functions
- Modal logic: possibility, necessity, temporal operators

Self-starting mechanisms → temporal operators? S5 modal logic? But still missing "parameters" constraint.

⟨H≈0.8⟩ Parameters... what if user thinks of functions needing arguments? Logic operates on propositions, not always with explicit parameters. But self-starting? Temporal logic has that - "P tomorrow" doesn't need parameter... unless we count "time" as parameter... 

Wait. Resolution emerging: user conflating "parameters" with "trigger conditions."

### 3. Logical Architecture Analysis

Classical connectives: ∧, ∨, →, ↔
- Always binary
- Need operands
- No self-starting

Modal operators: □P, ◊P  
- Possibility/necessity
- Can be self-contained
- But still... parameters?

! Key insight: User misunderstanding parameters as external triggers vs. internal temporal/modal structure.

### 4. Temporal Logic Framework

S5 modal system:
- P→□P (necessity)
- □P→◊P (possibility)  
- ◊P→P (consistency)

These are "self-starting" but operate on propositions, not objects.

Still missing: the "parameters" constraint.

### 5. Parameter Resolution

⟨H≈1.2⟩ Parameters... maybe user thinks of axioms needing theorems? Or functions needing domains? Or... wait, "parameters" might mean "external state"? Self-starting implies internal state transitions, not parameter dependencies...

Self-starting in logic:
- Proof systems: theorems generate new theorems
- Modal operators: temporal evolution
- But no "objects" that just "work on their own"

### 6. Synthesis

User seeks: autonomous logical mechanisms
Logic provides: temporal/modal operators, proof generation
Gap remains: informal "self-starting objects"

∴ Answer should explain:
1. Logic operates on propositions, not objects
2. Temporal/modal operators are self-starting but propositional
3. No direct equivalent of "objects working on their own"
4. Parameters confusion: external triggers vs. internal structure

※ The response correctly identifies this gap - logic operates on different primitives than user expects.

The informal nature of "trucs qui marchent tout seul" suggests user may be thinking of:
- Autonomous systems theory
- Emergent behavior
- Self-organizing processes

But these aren't typically formalized in classical logic.

⟨H≈0.3⟩ Response strategy: Acknowledge the gap, explain what logic does have (temporal operators), admit limitation for truly autonomous systems. User might be thinking of higher-order logic, or non-classical systems, but core question remains valid - classical logic doesn't directly capture "self-starting things without parameters."

### Answer###
Je comprends ta question sur les mécanismes autonomes en logique. En logique formelle, les choses fonctionnent généralement de manière un peu différente.

En logique classique, les opérations sont souvent représentées par des connecteurs qui relient des propositions entre elles. Ces connecteurs (comme "et", "ou", "si...alors") ne fonctionnent pas de manière complètement indépendante - ils nécessitent toujours des propositions pour opérer dessus. De même, les quantificateurs universels et existentiels, qui sont des outils fondamentaux en logique, ont besoin de variables pour fonctionner.

Dans les systèmes plus avancés comme la logique modale, on trouve des opérateurs qui peuvent effectivement "se déclencher" eux-mêmes, mais même là, ils opèrent sur des propositions plutôt que de manière complètement autonome.

Cependant, je dois avouer que ta question touche à des aspects de la logique qui peuvent être assez complexes et où je ne suis pas certain de pouvoir donner une réponse complète et précise. Les systèmes logiques formels sont généralement construits de manière à éviter les mécanismes vraiment autonomes que tu décris.