## Jacques Lacan (Encyclopædia Britannica Online)

## The revolution … Another Gödel’s that does not exist!

#### Completeness, incompleteness, consistency, inconsistency, decidable and undecidable are concepts of meta logic which can be attributed to certain features of the formal logical systems, more precisely axiomatic systems. These are concepts that are attributed to K Gödel from their theorems from the beginning of the previous century. They emerge in a very particular context of mathematics as opposed to the ideal of David Hilbert who believed that everything in that area could be proof.

#### Kurt Gödel was born on April 28, 1906 in Brünn, Moravia. It became part of the Vienna Circle, and from that moment they begin to develop their most important theories on the completeness of the formal systems from two publications: his doctoral thesis written in 1929, and the theorem (formally on propositions undecidable in the Principia Mathematica and related systems) published in 1931.In 1931, Gödel published About propositions …, article that called into question the agenda D Hilbert, because not only showed that the system Russel and Whitehead had cracks, but the entire system would be axiomatic.

#### An axiomatic system consists of a set of formulas set forth or allowed without demonstration-axioms-from which all others are derived assertions theory called theorems. The set of axioms over the definition of phrasing or formula System (definition preceding statement of the axioms) and the set of rules for obtaining theorems from the axioms (transformation rules) are the basis of the primitive system.

#### K. Gödel proved that it is impossible to establish consistency internal logic of a broad class of deductive systems, unless it is taken early so complex reasoning that its internal consistency remains as subject to the doubt as to the systems themselves, putting at stake the impossibility proofing certain propositions. Consistency, inconsistency, completeness and incompleteness.What is a system, which means that it is consistently inconsistent, complete or incomplete, which is a proposition, etc.?

A system is a set of axioms and rules of inference, a claim that a proposition can be true or false. When a system is complete? Once inside it can be determined by the value of truth or falsity of any proposition

The completeness assures us that there is no truth in our system that we will not be able to find But we can only be sure of being able to reach the whole truth if our system is complete.Change is incomplete when it contains proposals on which we are unable to determine their truth or falsity. Moreover, a system is consistent when no contradictions of any kind nor does it have any paradox, and is inconsistent when we run into contradictions and paradoxes. A system is consistent if it is clean of paradoxes and contradictions and complete if any proposition can be proved or disproved sign him. Gödel believed that if it is consistent is incomplete and if it is completely inconsistent.In that sense, consistency means that it is not possible to deduce from the same set of axioms, two theorems which are contradictory. When it comes to contradiction semantics, the system is inconsistent.
#### The principle of inconsistency then assumed that the truth-value of a system can not be determined from a set of axioms, but only from a foreign axiom. That is a system that is inconsistent when it can not get rid of its internal contradictions semantic.

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#### The article’s complete translation from Spanish Language is:

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Tuesday October 2, 2007

LACAN’s LOGIC

What is the consistency? (*)- Uses Lacan of the concepts of consistency, inconsistency, completeness and incompletenessReferences

At its annual course Witz is in the symptom that dictates in the Association of Psychoanalysis of La Plata, Enrique Acuña introduced the notions of inconsistency, consistency, and completeness and incompleteness to mention that Lacan over his teaching. In his last part in the seminar sinthome The 23, in relation to the Borromean knot defined by the imaginary consistency, as symbolic of the inconsistency in relation to significant misunderstanding, and what is real by the former existence. Consistency or inconsistency of the other incompletud Another, logical consistency of purpose, consistency of the imaginary, are different enunciated over the teaching of Lacan gaining different ways.

#### José Ferrater Mora in his Dictionary of Philosophy, stresses that the concept of consistency appears in three different contexts: a use which describes the “actual subsistence in terms of consistency,” a metaphysical sense in which the term is linked essence, by declaring that the essence of what something is that this “something” is – with some referral to the notion of substance, and finally a logical starting expressions as evidence of consistency by which it is tested whether a calculation is consistent or not.

####
Tuesday October 2, 2007

LACAN’s LOGIC

What is the consistency? (*)- Uses Lacan of the concepts of consistency, inconsistency, completeness and incompletenessReferences

At its annual course Witz is in the symptom that dictates in the Association of Psychoanalysis of La Plata, Enrique Acuña introduced the notions of inconsistency, consistency, and completeness and incompleteness to mention that Lacan over his teaching. In his last part in the seminar sinthome The 23, in relation to the Borromean knot defined by the imaginary consistency, as symbolic of the inconsistency in relation to significant misunderstanding, and what is real by the former existence. Consistency or inconsistency of the other incompletud Another, logical consistency of purpose, consistency of the imaginary, are different enunciated over the teaching of Lacan gaining different ways.

LACAN’s LOGIC

What is the consistency? (*)- Uses Lacan of the concepts of consistency, inconsistency, completeness and incompletenessReferences

At its annual course Witz is in the symptom that dictates in the Association of Psychoanalysis of La Plata, Enrique Acuña introduced the notions of inconsistency, consistency, and completeness and incompleteness to mention that Lacan over his teaching. In his last part in the seminar sinthome The 23, in relation to the Borromean knot defined by the imaginary consistency, as symbolic of the inconsistency in relation to significant misunderstanding, and what is real by the former existence. Consistency or inconsistency of the other incompletud Another, logical consistency of purpose, consistency of the imaginary, are different enunciated over the teaching of Lacan gaining different ways.

#### José Ferrater Mora in his Dictionary of Philosophy, stresses that the concept of consistency appears in three different contexts: a use which describes the “actual subsistence in terms of consistency,” a metaphysical sense in which the term is linked essence, by declaring that the essence of what something is that this “something” is – with some referral to the notion of substance, and finally a logical starting expressions as evidence of consistency by which it is tested whether a calculation is consistent or not.

#### The revolution … Another Gödel’s that does not exist.

Completeness, incompleteness, consistency, inconsistency, decidable and undecidable are concepts of meta logic which can be attributed to certain features of the formal logical systems, more precisely axiomatic systems. These are concepts that are attributed to K Gödel from their theorems from the beginning of the previous century. They emerge in a very particular context of mathematics as opposed to the ideal of David Hilbert who believed that everything in that area could be proof.

Kurt Gödel was born on April 28, 1906 in Brünn, Moravia. It became part of the Vienna Circle, and from that moment they begin to develop their most important theories on the completeness of the formal systems from two publications: his doctoral thesis written in 1929, and the theorem (formally on propositions undecidable in the Principia Mathematica and related systems) published in 1931.
In 1931, Gödel published About propositions …, article that called into question the agenda D Hilbert, because not only showed that the system Russel and Whitehead had cracks, but the entire system would be axiomatic.

An axiomatic system consists of a set of formulas set forth or allowed without demonstration-axioms-from which all others are derived assertions theory called theorems. The set of axioms over the definition of phrasing or formula System (definition preceding statement of the axioms) and the set of rules for obtaining theorems from the axioms (transformation rules) are the basis of the primitive system.

K. Gödel proved that it is impossible to establish consistency internal logic of a broad class of deductive systems, unless it is taken early so complex reasoning that its internal consistency remains as subject to the doubt as to the systems themselves, putting at stake the impossibility proofing certain propositions

Consistency, inconsistency, completeness and incompleteness

What is a system, which means that it is consistently inconsistent, complete or incomplete, which is a proposition, etc.?

A system is a set of axioms and rules of inference, a claim that a proposition can be true or false. When a system is complete? Once inside it can be determined by the value of truth or falsity of any proposition

The completeness assures us that there is no truth in our system that we will not be able to find But we can only be sure of being able to reach the whole truth if our system is complete.

. Change is incomplete when it contains proposals on which we are unable to determine their truth or falsity. Moreover, a system is consistent when no contradictions of any kind nor does it have any paradox, and is inconsistent when we run into contradictions and paradoxes. A system is consistent if it is clean of paradoxes and contradictions and complete if any proposition can be proved or disproved sign him. Gödel believed that if it is consistent is incomplete and if it is completely inconsistent.

In that sense, consistency means that it is not possible to deduce from the same set of axioms, two theorems which are contradictory. When it comes to a contradiction semantics, the system is inconsistent.

The principle of inconsistency then assumed that the truth-value of a system can not be determined from a set of axioms, but only from a foreign axiom. That is a system that is inconsistent when it can not get rid of its internal contradictions semantic.

– Variations concepts: consistency real and imaginary symbolic.

Another Consistency, consistency of purpose, consistency of the imaginary, inconsistency and incompleteness of the Other … what meaning acquire these concepts in these statements Lacan over their teaching?

Initially, more precisely before the construction of the graph of desire, without mark Another appears, that is complete and consistent. This is a symbolic while suffering from semantic contradiction, and a quantum completud as no significant fault. Another is a belief that the neurotic builds.

The inconsistency of this other – introduced by misleading significant that reveals that not everything can be known-is revealed with more force in the workshop of The Anxiety builds when the scheme of dual causation of the subject and the object from the castration of the Other .

The seminar From Another one to the other, the expression appears logical consistency in relation to the new version of the object being constructed linked to the release of more than enjoy. There consistency is not linked to the version of a symbolic logic that represents an axiomatic system free of contradiction, but rather the version of a “real consistency linked to the substance.” Real subsistence in terms of consistency linked to the substance, since it is something. This version is opposed to drift significant chain in which we were unable to find any consistency as defined in these terms. This object “substance” comes to take the place empty Another That is the consistency of the object takes its weight from the inconsistency the Other. The object in its consistency, cover the inconsistency of the Other. Opposes well to the inconsistency of the results from the chain, the consistency of the object substantial a.

As for the registration imaginary, comprehensiveness is at stake in the stadium at the beginning of the mirror with respect to that image that comes to ensuring actual fragmentation of the body. Image complete in itself full of joy to the baby.

On the other hand consistency in relation to the imaginary Lacan the shows at the seminar The sinthome when opposed to the inability of the real and the symbolic semantic inconsistency introduced by misleading significant. There defines consistency imaginary “which holds together” (1)

Enrique Acuña, class of 12 September from its current annual Witz is on the symptom in the APLP, referred to the version of the Borromean knot that Lacan introduces The Third whereby this function “which keeps together “meets the object a.

It is an “a” that gives stability. He raised hence the need to follow the path that leads to Lacan towards formulating the sinthome since his father’s name through the object to the horizon with the question why Lacan replaced in the role of “what holds together” in order “” by the sinthome?.

It is the uses that Lacan makes the concepts drawn from other disciplines-in this case of mathematics, logic and topology-to try to say every time a new way, that he called his symptoms, the real.

#### An the original document is:

http://microscopia2007.blogspot.com/2007/10/logicas-lacanianas.html

¿Qué es un sistema, qué significa que sea consistente, **inconsistente**, completo o incompleto, qué es una proposición, etcétera?

Un sistema es un conjunto de axiomas y reglas de inferencia, una proposición una afirmación que puede ser cierta o falsa. ¿Cuándo un sistema es completo? Cuando dentro de él puede determinarse el valor de verdad o falsedad de toda proposición

La completud nos asegura que no hay ninguna verdad en nuestro sistema que nosotros no seamos capaces de encontrar Pero solo podremos estar seguros de poder alcanzar toda la verdad si nuestro sistema es completo.

.En cambio es incompleto cuando contiene proposiciones sobre las que no podemos decidir su verdad o falsedad. Por otra parte, un sistema es coherente cuando no hay contradicciones de ningún tipo ni tiene ninguna paradoja; y es incoherente cuando nos encontramos con contradicciones y paradojas. Un sistema es consistente si está limpio de paradojas y contradicciones y completo si toda proposición puede ser demostrada o refutada entro de él. Gödel considera que si es consistente es incompleto y si es completo es **inconsistente**.

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An axiomatic system consists of a set of formulas set forth or allowed without demonstration-axioms-from which all others are derived assertions theory called theorems. The set of axioms over the definition of phrasing or formula System (definition preceding statement of the axioms) and the set of rules for obtaining theorems from the axioms (transformation rules) are the basis of the primitive system.

K. Gödel proved that it is impossible to establish consistency internal logic of a broad class of deductive systems, unless it is taken early so complex reasoning that its internal consistency remains as subject to the doubt as to the systems themselves, putting at stake the impossibility proofing certain propositions

A system is a set of axioms and rules of inference, a claim that a proposition can be true or false. When a system is complete? Once inside it can be determined by the value of truth or falsity of any proposition

The completeness assures us that there is no truth in our system that we will not be able to find But we can only be sure of being able to reach the whole truth if our system is complete.

The principle of inconsistency then assumed that the truth-value of a system can not be determined from a set of axioms, but only from a foreign axiom. That is a system that is inconsistent when it can not get rid of its internal contradictions semantic.

Another Consistency, consistency of purpose, consistency of the imaginary, inconsistency and incompleteness of the Other … what meaning acquire these concepts in these statements Lacan over their teaching?

Initially, more precisely before the construction of the graph of desire, without mark Another appears, that is complete and consistent. This is a symbolic while suffering from semantic contradiction, and a quantum completud as no significant fault. Another is a belief that the neurotic builds.

On the other hand consistency in relation to the imaginary Lacan the shows at the seminar The sinthome when opposed to the inability of the real and the symbolic semantic inconsistency introduced by misleading significant. There defines consistency imaginary “which holds together” (1)

It is an “a” that gives stability. He raised hence the need to follow the path that leads to Lacan towards formulating the sinthome since his father’s name through the object to the horizon with the question why Lacan replaced in the role of “what holds together” in order “” by the sinthome?.

¿Qué es un sistema, qué significa que sea consistente, **inconsistente**, completo o incompleto, qué es una proposición, etcétera?

Un sistema es un conjunto de axiomas y reglas de inferencia, una proposición una afirmación que puede ser cierta o falsa. ¿Cuándo un sistema es completo? Cuando dentro de él puede determinarse el valor de verdad o falsedad de toda proposición

La completud nos asegura que no hay ninguna verdad en nuestro sistema que nosotros no seamos capaces de encontrar Pero solo podremos estar seguros de poder alcanzar toda la verdad si nuestro sistema es completo.

.En cambio es incompleto cuando contiene proposiciones sobre las que no podemos decidir su verdad o falsedad. Por otra parte, un sistema es coherente cuando no hay contradicciones de ningún tipo ni tiene ninguna paradoja; y es incoherente cuando nos encontramos con contradicciones y paradojas. Un sistema es consistente si está limpio de paradojas y contradicciones y completo si toda proposición puede ser demostrada o refutada entro de él. Gödel considera que si es consistente es incompleto y si es completo es **inconsistente**.