1. The document discusses three computational modes of the mind: ordinary thought (conscious classical computation and unconscious quantum computation), and meta-thought (unconscious and non-algorithmic). 2. It proposes a quantum meta-language (QML) and probabilistic identity axiom to describe aspects of human reasoning and the disintegration of the self in conditions like schizophrenia. 3. The document introduces the concept of quantum coherent states of the mind, drawing an analogy to coherent states in quantum field theory which are eigenstates of the annihilation operator.

1. 1
INCOHERENT QUANTUM META-LANGUAGE AND SCHIZOPHRENIA
Paola Zizzi
“Paolo Sotgiu” Institute for research in Quantitative & Quantum Psychiatry & Cardiology
L.U.de.S. of Lugano, Switzerland
paola.zizzi@uniludes.ch
A Long Shadow over the Soul:
Molecular and Quantum Approaches to Psychopathology An Interdisciplinary Dialog with
Psychiatrists
FANO - March 2012

2. 2
CONTENTS:
1. Three computational modes of the mind
2. The logic of human reasoning
3. Quantum Meta-Language
4. The probabilistic identity axiom and disintegration of the Self
5. Quantum coherent states of the mind
Conclusions
References

3. 3
1. Three computational modes of the mind
(Zizzi, 2012)
We make the formal distinction between ordinary thought and meta-thought:
Ordinary thought: i) conscious – classical computation, classical formal language
ii) unconscious -quantum computation, quantum formal language
Meta-thought: unconscious, non-algorithmic, Quantum Meta-Language (QML)
(Zizzi 2010).
We call the MIND items i) and ii). MIND ii) is the Quantum Mind
a) The quantum mode
b) The classical mode
c) The non-algorithmic mode

4. 4
a) The quantum mode
The unconscious ordinary thought: driven by mental processes which are extremely fast,
much more than those concerning the conscious thought.
This already suggests that the above processes are quantum-computational
(a quantum computer is exponentially faster than its classical counterpart).
The sudden decision-makings or understandings, creativity, imagination and discoveries
Arising from an unconscious state of the mind, are just the results of a
quantum mental process, whose intermediate steps, however, remain unknowable.
In quantum computing: one can get the result of a computation
with a given probability, but the intermediate steps are not available.
Then, these two features seem to indicate that the unconscious mind is indeed quantum-
computational. The Quantum Mind.
b) The classical mode

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The unconscious mind computes in the quantum mode, and it “prepares”,
at highest speed, what we then recognize as a conscious thought.
The conscious thought derives from a choice (a projective measurement)
made on the quantum computational state, and thereafter uses a classical mode.
.We don’t have much time to re-elaborate the outputs of the unconscious mind
(half a second) then, our conscious thought looks more like a succession of flashes of
consciousness rather than a proper classical computation.
We use the partial information obtained from quantum measurements.
But in effect, we do not compute anything new.
In fact, most of the time, humans compute in a quantum mode.
.
c) The non-algorithmic mode

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Meta-thought is the process of thinking about our own thought.
It has no computational mode, neither classical, nor quantum.
Quantum meta-thought, which thinks about the quantum, unconscious thought,
can be viewed as the roots of the unconscious mind (or Quantum Mind)
It is the aspect of thought most closely related to matter
(physical processes in the brain).
The latter are supposed to be described by a Dissipative Quantum Field Theories
(DQFT) of the brain (Vitiello 2001).
Quantum Meta-thought co-ordinates intuition, intentions, and (quantum) control.
Meta-thought processes could be interpreted as aiming to keep some sort of coherence in
ordinary thought (coherent states in DQFT).
2. The logic of human reasoning

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The study of the “natural” logic of mental processes is very important in the
context of a constructivist approach to logic.
Constructivism: logic is not pre-existent in the Platonic “world of ideas”,
but instead is a by-product of the mind.
In this regard, one can adopt either the microscopic or the macroscopic point of view.
Macroscopic point of view: Phenomenology of “thought processes” (Cognitive Science)
Philosophy of Mind
Dynamical constructivism (Sambin, 2002),
cognitive/social interpretation of mental processes.
Microscopic point of view: focuses on the quantum processes
occurring in the brain, and can be formalized by Quantum Theory.
Classical laws of thought :
Law of identity: A→ A ( states that an object is the same as itself)

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Law of excluded middle: ( A ∨ ¬ A) = 1 (A or non A is true)
Law of non-contradiction: ( A ∧¬ A) = 0 ( A and non A is false)
The law of identity partitions the Universe into two parts: the Self and the Other
Universe
The
Other
The Self
It is a dichotomy: a partition of the whole into two parts that are:
Mutually exhaustive S ∪O =U → (excluded middle)
Mutually exclusive S IO = Ø → (non-contradiction)
The Other is the complement of the Self in U.
However, we claim that human logic is not Aristotelian classical logic.
The latter is in fact: i) too abstract
(the resources-the premises-can be used as many times as one likes).
ii) too much structured

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(has structural rules-contraction-weakening-exchange)
In sequent calculus notation: − turnstile (or yelds) , Γ,∆... contexts A,B...propositions
Γ , AA − ∆
Contraction: Γ , A − ∆ (data can be copied)
Γ−∆
Weakening: Γ, A − ∆ (data can be deleted)
Γ , A, B , Γ ' − ∆
Exchange: Γ , B , A, Γ ' − ∆
Instead the mind operates in a very simple way at the fundamental level.
Then the mind must be described by a weaker (that is, with fewer structural rules)
and less abstract logic than classical logic, which should, nevertheless, have extensions
(among which, classical logic).
Macroscopic point of view: Basic Logic (Sambin et al., 2000) is the best choice for
the logic of the conscious, classical MIND.
Basic Logic: Substructural (lacks the structural rules of weakening and contraction)

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Symmetry: (every connective has its dual)
The law of identity hold: A −A
Γ − A A−∆
The cut rule holds: Γ −∆ (this is a meta-rule)
The principle of the excluded middle does not hold
(As in Intuitionist logic, proving the excluded middle would require producing proof for
the truth or falsity of all possible statements, which is impossible)
By symmetry, the principle of non-contradiction does not hold as well
Visibility: all active formula are isolated from the context
Reflection: metalinguistic links between assertions of the metalanguage
are reflected into logical connectives between propositions of the
object-language through the definitional equation
The BL Metalanguage consists of:
Metalinguistic links: − (yelds or entails), and
Atomic assertions: −A (proposition A “is”),

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Compound assertions. Example: − A and − B
Object-language consists of:
Propositions A, B,….
Logical connectives &, ,→ ←⊗,℘
∨ , , (and, or, implies, counter-implies, times, par).
The connectives ⊗,℘ , borrowed from Linear logic, are the multiplicative conjunction and disjunction
respectively.
The negation ¬ A is an abbreviation for: A →⊥ (A implies the false)
The double negation can be introduced: A → ¬¬ A
But the elimination ¬¬ A → A does not hold.
Definitional equation for the connective &:
Γ − A& B iff Γ −A and Γ −B
Microscopic point of view: Logic Lq (Zizzi, 2010)
Symmetry, as in BL
Visibility, as in BL
Reflection principle, as in BL

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The law of the excluded middle does not hold
The law of non-contradiction does not hold
Is many-valued (fuzzy) and probabilistic
The law of identity holds probabilistically
None of the structural rules holds
The (quantum) cut rule holds
Two new connectives: Quantum superposition λ0 &λ1
Quantum entanglement @ = f (℘,&)
Fuzzy probabilistic propositions in Lq
There is a relation between the probability p and the fuzzy notion probably
(H’ajek et al, 1995).
In fact, the latter can be axiomatized as a fuzzy modality.
Having a probability p on Boolean formulas, define for each such formula p i

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a new formula P( pi ) , read “probably p i ”, and define the truth value of
P ( p i ) to be the probability of p i :
v( P( pi )) = p( pi ) ∈ [0,1] .
Then, it holds:
n
∑ v( P( p )) = 1
i =1
i
where n is the number of atomic propositions p i
3. Quantum Metalanguage
Metalinguistic sequents with no antecedent −A

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are assertions in the (classical) metalanguage ML.
There is a close relation between assertions, the truth values of propositions in the OL and the truth
predicate of Tarski, T, which is formulated in ML (Tarski (1944)).
Tarski Convention T:
By Tarski Convention T, every sentence p of OL must satisfy:
(T): ‘p’ is true iff p
‘p’ stands for the name of the proposition p, which is the translation in the metalanguage ML,
of the corresponding proposition in the OL
or:
(T): −p iff p
T-schema (inductive definition of truth):
a sentence of the form "A and B" is true if and only if A is true and B is true
In the formalism of sequent calculus:
− A & B iff − A and − B
which is nothing else than the definitional eq. of & in BL

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Convention PT
When the certitude in the assertion is not full, also the truth values of the propositions are
partial, and Convention T must be modified as Convention PT:
(PT): ‘p’ is probably true iff P( p)
In sequent notation:
λ
(PT): − p iff P( p)
The proposition ' p ' is asserted with assertion degree λ if and only if
“probably” p, with probability λ ∈ [0,1] , and the partial truth value of P ( p )
2
is just the probability of p :
v ( P ( p )) = p ( p ) = λ
2
Given p 0 , p1 of the QOL:
λ0
(PT): − p0 iff P( p 0 )
λ1
(PT): − p1 iff P( p1 )
with: v ( P ( p 0 )) = p ( p 0 ) = λ0 , v ( P ( p1 )) = p ( p1 ) = λ1
2 2

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Apply T-schema:
P( p 0 ) & P( p1 ) is true iff P( p 0 ) is true and P( p1 ) is true.
Define: P( p 0 ) & P( p1 ) ≡ p0 λ &λ p1
0 1
In the sequent formalism:
− p0 λ0 & λ1 p1 iff −
λ0
p0 and −
λ1
p1
Definitional equation for the connective λ0 & λ1 “quantum superposition”
The QML consists of the same metalinguistic links of the classical ML, but quantum assertions are
asserted with an assertion degree, which is a complex number, λ interpreted as a probability
amplitude.
λ
We physically interpret the atomic quantum assertions − pi
i
as quantum field states of the
DQFT of the brain.

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4. The probabilistic identity axiom and the disintegration of the Self
In the classical case:
−A proposition A is true
( − A) ⊥ = A − proposition A is false ( ⊥ Sambin-Girard duality ).
The identity axiom:
A − A stays for: ( − A ) − ( − A )
In the quantum case:
λ
− A A is (probably) true for λ = 1 it reduce sto the classical case − A
(− A )
λ ⊥'
= A−
λ*
A is (probably) false ( λ is the complex coniugate of
*
λ)
gluing operator o:

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λ* λ
A− o − A gives:
λ
2
A− A Probabilistic identity axiom
States that an object is probabilistically the same of itself.
In particular: The Self is probabilistically the same of itself.
(Disintegration of the Self in schizophrenia).
Truth-value of the “Probably” Self:
vS = 1 − vO where vO is the truth of the Other
In the classical case, it was:
A in S, ¬ A in O
now we have A ∧ ¬ A true in S ∩ O
.
The non validity of the law of non-contradiction here

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is not just a philosophical choice as in Intuitionist logic and in BL,
but follows from the probabilistic nature of the identity axiom.
As the dichotomy is lost, A and its negation are no more mutually exclusive.
This is a feature of para-consistent logic.
In the logic of the quantum mind, a para-consistent logic
allows for quantum superpositions of bits 0 and 1, and then, for quantum computation.
5. Quantum coherent states of the mind
Consider:
A set S of N atomic Boolean propositions:
ψi ( i =1, 2 ,...... N )
and

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pi ( i =1, 2....... n ) with n < N , propositions of a subset S'⊂ S ,
n
to which it is possible to assign a probability p such that ∑ p( p ) = 1 .
i
i =1
Then, it holds:
n
∑ v( P( p )) = 1
i =1
i
Call: ϕ i ( i = n +1,........ n + r = N ) the remaining r = N − n Boolean propositions
to which it was not assigned a probability.
Assuming the propositions ϕi true, with full truth value1, it holds:
N =n+r
∑ v(ϕ ) = r
i = n +1
i
It follows:
N
∑ v(ψ
i =1
i ) = 1+ r
In the limit case where all the propositions had the same truth value
v ⋅ N = 1+ r
Uncertainty relation for quantum logical propositions: (Zizzi, 2012)

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“It is impossible to fully determine both the truth values of the propositions
belonging to a set S, and the power of S”:
∆v ⋅ ∆N ≥ 1
For r = 0, N = n :
The uncertainty relation is saturated:
∆v ⋅ ∆n = 1
v= λ
2
As it is: , the uncertainty of the truth value ∆v can be expressed
in terms of the uncertainty of the assertion degree ∆λ as:
∆v = 2 λ ∆λ ,
The uncertainty relation:
k
∆λ ⋅ ∆N ≥
2

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k 1
∆λ ⋅ ∆ n = with: k=
2 λ .
reminds of the uncertainty relation phase-number of quantum optics,
which is saturated by coherent Glauber states (Glauber, 1963).
Definition:
“Quantum-coherent atomic propositions are those fuzzy- probabilistic
atomic propositions whose partial truth values are all equal and sum up to1”.
Physical interpretation
Quantum coherence in QFT is a property of some particular quantum field states, the coherent
states α , which are eigenvectors of
the annihilation operator a , with eigenvalues α:
aα =α α .
As the operator a is non-hermitian, the eigenvalue α is in general a complex number.
A coherent state α is itself a superposition of states, in the Fock basis { n }:

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Coherent states are the “most classical” among quantum states, and are very robust against
decoherence.
In quantum optics, Glauber coherent states minimize the phase-number uncertainty
1
relation:
∆ϕ ⋅ ∆n =
2
The metalogical equivalent of a coherent state is the ensemble of sequents:
α
− pi with: α ∈C , i = 1,………n
Notice:

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The superposition of two coherent states α α +β β is not, in general a coherent state,
1
unless α = β = .
2
The resulting coherent state:
1
( α + −α )
2
is called the “cat” coherent state in quantum optics.
Cat states are very fragile against decoherence.
Compound quantum-coherent propositions
The identification
p 0 λ0 & λ1 p1 = P( p 0 & p1 )
1
can be made only in the particular case with λ0 = λ1 = 2 :
P( p 0 & p1 ) ≡ p0 1 & 1 p1
2 2

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In this particular case, we can apply Convention PT :
1
λ=
− 2 ( p0 & p1 ) iff P ( p0 & p1 )
A compound quantum-coherent proposition is a “cat state” proposition.
A general, incoherent state is, in the Fock basis:
ψ = ∑ λn n
n
This corresponds to the n-ple of incoherent atomic assertions:
λi
− pi i = 1,….n
Two kinds of quantum metalanguages
Coherent QML Incoherent QML
α λi
− pi − pi

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1 1 λ0 λ1
− p0
2
and − p1
2 − p0 and
− p1
Conclusions
It is a fact that an healthy mind is capable of a rational abstract thought,
which is coherent and logical.
Then, such a mind process should come from a coherent metalanguage,
which should also provide a logic.
Such a metalanguage has coherent “cat” assertions.
In the physical model, such coherent cat states are very fragile against decoherence,
which means that the passage to the classical mode of consciousness is very fast,

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as it should be.
Otherwise, the mind would remain for too long trapped in the quantum mode
(the inconscious).
On the other side, an healthy mind should also be capable of a creative,
unpredictable, fuzzy thought.
This kind of thought would be incoherent, perhaps disorganized,
but nevertheless would be ruled by a particular kind of logic.
It correspond to an incoherent quantum metalanguage.
This metalanguage provides the logic of quantum information Lq which is
the logic of the quantum mode of the mind, the unconscious.
For some reasons, in schizophrenia, the incoherent QML is dominant
on the coherent QML (work in progress).

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Schizophrenia
The healthy mind
The Double
IQML= The
Double
IQML
CQML
CQML
Hallucinations
References:

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P. Zizzi, “When Humans Do Compute Quantum”,
in: A Computable Universe, Hector Zenil (Ed), Word Scientific Publishing (2012).
P. Zizzi, “From Quantum Metalanguage to the Logic of Qubits”.
PhD Thesis, arXiv:1003.5976 (2010).
G. Sambin , G. Battilotti, C. Faggian, “Basic logic: reflection, symmetry, visibility”.
The Journal of Symbolic Logic, 65, 979-1013 (2000).
G. Sambin, “Steps towards a dynamical constructivism”. In the scope of Logic, Methodology and Philosophy of Science, Vol.
1, 263-289. Kluwer, Dordrecht (2002).
G. Vitiello. My double unveiled. Amsterdam: Benjamins (2001).
H´ajek P., Godo L., Esteva F., Probability and Fuzzy Logic.
In Proc. Of Uncertainty in Artificial Intelligence UAI’95, (Besnard and Hanks, Eds.)
Morgan Kaufmann. San Francisco, 237–244 (1995).
A. Tarski, “The semantic conception of truth”.
Philosophy and Phenomenological Research, 4, 13-47 (1944).
R. J. Glauber, “Coherent and incoherent states of radiation field”,
Phys. Rev. 131, 2766-2788 (1963).
P. Zizzi, “The Uncertainty Relation for quantum Propositions”,
arXiv:1112.2923 (2012), submitted to IJTP.