Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.

Within the (Haskell Curry) notion of a formal system we complete Tarski's formal correctness: ∀x True(x) ↔ ⊢ x and use this finally formalized notion of Truth to refute his own Undefinability Theorem (based on the Liar Paradox), the Liar Paradox, and the (Panu Raatikainen) essence of the conclusion of the 1931 Incompleteness Theorem.

Hypothesis: WFF(x) can be applied syntactically to the semantics of formalized declarative sentences such that: WFF(x) ↔ (x ↦ True) ∨ (x ↦ False) (see proof sketch below) For clarity we focus on simple propositions without binary logical connectives.

We begin with the hypothetical assumption that Tarski’s 1933 formula ∀ True(x) φ(x) has been defined such that ∀x Tarski:True(x) ↔ Boolean-True. On the basis of this logical premise we formalize the Truth Teller Paradox: "This sentence is true." showing syntactically how self-reference paradox is semantically ungrounded.

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to true conclusions without any need for other representations such as model theory.

If the conclusion of the Tarski Undefinability Theorem was that some artificially constrained limited notions of a formal system necessarily have undecidable sentences, then Tarski made no mistake within his assumptions. When we expand the scope of his investigation to other notions of formal systems we reach an entirely different conclusion showing that Tarski's assumptions were wrong.

If there truly is a proof that shows that no universal halt decider exists on the basis that certain tuples: (H, Wm, W) are undecidable, then this very same proof (implemented as a Turing machine) could be used by H to reject some of its inputs. When-so-ever the hypothetical halt decider cannot derive a formal proof from its input strings and initial state to final states corresponding the mathematical logic functions of Halts(Wm, W) or Loops(Wm, W), halting undecidability has been (...) decided. (shrink)

To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.

This paper decomposes the Liar Paradox into its semantic atoms using Meaning Postulates (1952) provided by Rudolf Carnap. Formalizing truth values of propositions as Boolean properties of these propositions is a key new insight. This new insight divides the translation of a declarative sentence into its equivalent mathematical proposition into three separate steps. When each of these steps are separately examined the logical error of the Liar Paradox is unequivocally shown.

For any natural (human) or formal (mathematical) language L we know that an expression X of language L is true if and only if there are expressions Γ of language L that connect X to known facts. -/- By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that evaluate to neither True nor False.

Tarski "proved" that there cannot possibly be any correct formalization of the notion of truth entirely on the basis of an insufficiently expressive formal system that was incapable of recognizing and rejecting semantically incorrect expressions of language. -/- The only thing required to eliminate incompleteness, undecidability and inconsistency from formal systems is transforming the formal proofs of symbolic logic to use the sound deductive inference model.

When we understand that every potential halt decider must derive a formal mathematical proof from its inputs to its final states previously undiscovered semantic details emerge. -/- When-so-ever the potential halt decider cannot derive a formal proof from its input strings to its final states of Halts or Loops, undecidability has been decided. -/- The formal proof involves tracing the sequence of state transitions of the input TMD as syntactic logical consequence inference steps in the formal language of Turing Machine (...) Descriptions. (shrink)

This is the formal YACC BNF specification for Minimal Type Theory (MTT). MTT was created by augmenting the syntax of First Order Logic (FOL) to specify Higher Order Logic (HOL) expressions using FOL syntax. Syntax is provided to enable quantifiers to specify type. FOL is a subset of MTT. The ASSIGN_ALIAS operator := enables FOL expressions to be chained together to form HOL expressions.

Minimal Type Theory (MTT) shows exactly how all of the constituent parts of an expression relate to each other (in 2D space) when this expression is formalized using a directed acyclic graph (DAG). This provides substantially greater expressiveness than the 1D space of FOPL syntax. -/- The increase in expressiveness over other formal systems of logic shows the Pathological Self-Reference Error of expressions previously considered to be sentences of formal systems. MTT shows that these expressions were never truth bearers, thus (...) never sentences of any formal logic system. (shrink)

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to deductive conclusions without any need for other representations.

By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be (...) semantically incorrect. (shrink)

The generalized conclusion of the Tarski and Gödel proofs: All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences. Is not the immutable truth that Tarski made it out to be it is only based on his starting assumptions. -/- When we reexamine these starting assumptions from the perspective of the philosophy of logic we find that there are alternative ways that formal systems can be defined that make undecidability inexpressible in all of these formal systems.

Abstract In this paper I embrace what Brian Keeley calls in “Of Conspiracy Theories” the absurdist horn of the dilemma for philosophers who criticize such theories. I thus defend the view that there is indeed something deeply epistemically wrong with conspiracy theorizing. My complaint is that conspiracy theories apply intentional explanations to situations that give rise to special problems concerning the elimination of competing intentional explanations.

Realism about consciousness conjoins a claim that consciousness exists with a claim that the existence is independent in some interesting sense. Consciousness realism so conceived may thus be opposed by a variety of anti-realisms, distinguished from each other by denying the first, the second, or both of the realist’s defining claims. I argue that Dennett’s view of consciousness is best read as an anti-realism that affirms the existence of consciousness while denying an important independence claim.

This chapter argues that mental fictionalism can only be a successful account of our ordinary folk-psychological practices if it can in some way preserve its original function, namely its explanatory aspect. A too strong commitment to the explanatory role moves fictionalism unacceptably close to the realist or eliminativist interpretation of folk psychology. To avoid this, fictionalists must degrade or dispense with this explanatory role. This motivation behind the fictionalist movement seems to be rather similar to that of Sellars when he (...) came up with the Myth of Jones, his proto-theory of mental concepts. He was faced with the problem of preserving the explanatory status of mental concepts without turning them into proper theoretical entities. By introducing the Sellarsian proto-theory of concepts related to the mental and outlining its main points, this chapter aims to provide a critique of the two versions of mental fictionalism that are arguably the strongest: Adam Toon’s prop-oriented pretence theory and Tamás Demeter’s expressive storyism. (shrink)

Many so-called problems in contemporary philosophy of mind depend for their expression on a collection of inter-defined technical terms, a few of which are qualia, phenomenal property, and what-it’s-like-ness. I express my scepticism about Keith Frankish’s illusionism, the view that people are generally subject to a systematic illusion that any properties are phenomenal, and scout the relative merits of two alternatives to Frankish’s illusionism. The first is phenomenal meta-illusionism, the view that illusionists such as Frankish, in holding their view, are (...) themselves thereby under an illusion. The second is qualia quietism, the view that nothing worth saying is said by employing any of the aforementioned inter-defined technical terms. (shrink)

The goal of the present paper is to defend against a certain line of attack the view that conscious experience of color is no more fine-grained that the repertoire of non- demonstrative concepts that a perceiver is able to bring to bear in perception. The line of attack in question is an alleged empirical argument - the Diachronic Indistinguishability Argument - based on pairs of colors so similar that they can be discriminated when simultaneously presented but not when presented across (...) a memory delay. My aim here is to show that this argument fails. (shrink)

Often, sensory input underdetermines perception. One such example is the perception of illusory contours. In illusory contour perception, the content of the percept includes the presence of a contour that is absent from the informational content of the sensation. (By “sensation” I mean merely information-bearing events at the transducer level. I intend no further commitment such as the identification of sensations with qualia.) I call instances of perception underdetermined by sensation “underdetermined perception.” The perception of illusory contours is just one (...) kind of underdetermined perception. The focus of this chapter is another kind of underdetermined perception: what I shall call "active perception". Active perception occurs in cases in which the percept, while underdetermined by sensation, is determined by a combination of sensation and action. The phenomenon of active perception has been used by several to argue against the positing of representations in explanations of sensory experience, either by arguing that no representations need be posited or that far fewer than previously thought need be posited. Such views include, but are not limited to those of Gibson (1966, 1986), Churchland. (shrink)

Among our conscious states are conscious thoughts. The question at the center of the recent growing literature on cognitive phenomenology is this: In consciously thinking P, is there thereby any phenomenology—is there something it’s like? One way of clarifying the question is to say that it concerns whether there is any proprietary phenomenology associated with conscious thought. Is there any phenomenology due to thinking, as opposed to phenomenology that is due to some co-occurring sensation or mental image? In this paper (...) we will present two arguments that a “yes” answer to this question of cognitive phenomenology can be obtained via appeal to the HOT theory of consciousness, especially the version articulated and defended by David Rosenthal. (shrink)

'Sliders' are a speculative introspection-enhancing future technology allowing humans with cybernetic brain implants to precisely and voluntarily modulate moods and other mental states that vary along a one-dimensional scale. Such future humans may, for example, use the Sliders interface to temporarily present a COWARDLY–COURAGEOUS 'slider' in their visual field, and with a mere act of will change their level of courage from a 60 to a 65 on the 100-point scale. The present article discusses the implications of such a technology (...) in the form of an epistolary fiction in which the author's future persona warns the reader of the dire consequences and hardearned insights arising from widespread Slider use and abuse. (shrink)

s Gibson (1982) correctly points out, despite Quine’s brief flirtation with a “mitigated phenomenalism” (Gibson’s phrase) in the late 1940’s and early 1950’s, Quine’s ontology of 1953 (“On Mental Entities”) and beyond left no room for non-physical sensory objects or qualities. Anyone familiar with the contemporary neo-dualist qualia-freak-fest might wonder why Quinean lessons were insufficiently transmitted to the current generation.

According to representionalists, qualia-the introspectible properties of sensory experience-are exhausted by the representational contents of experience. Representationalists typically advocate an informational psychosemantics whereby a brain state represents one of its causal antecedents in evolutionarily determined optimal circumstances. I argue that such a psychosemantics may not apply to certain aspects of our experience, namely, our experience of space in vision, hearing, and touch. I offer that these cases can be handled by supplementing informational psychosemantics with a procedural psychosemantics whereby a representation (...) is about its effects instead of its causes. I discuss conceptual and empirical points that favor a procedural representationalism for our experience of space. (shrink)

Control consciousness is the awareness or experience of seeming to be in control of one’s actions. One view, which I will be arguing against in the present paper, is that control consciousness is a form of sensory consciousness. In such a view, control consciousness is exhausted by sensory elements such as tactile and proprioceptive information. An opposing view, which I will be arguing for, is that sensory elements cannot be the whole story and must be supplemented by direct contributions of (...) nonsensory, motor elements. More specifically, I will be arguing for the view that the neural basis of control consciousness is constituted by states of recurrent activation in relatively intermediate levels of the motor hierarchy. (shrink)

Many have urged that the biggest obstacles to a physicalistic understanding of consciousness are the problems raised in connection with the subjectivity of consciousness. These problems are most acutely expressed in consideration of the knowledge argument against physicalism. I develop a novel account of the subjectivity of consciousness by explicating the ways in which mental representations may be perspectival. Crucial features of my account involve analogies between the representations involved in sensory experience and the ways in which pictorial representations exhibit (...) perspectives or points of view. I argue that the resultant account of subjectivity provides a basis for the strongest response physicalists can give to the knowledge argument. (shrink)

Higher-Order Representational theories of consciousness — HORs — primarily seek to explain a mental state’s being conscious in terms of the mental state’s being represented by another mental state. First-Order Representational theories of consciousness — FORs — primarily seek to explain a property’s being phenomenal in terms of the property being represented in experience. Despite differences in both explanans and explananda, HORs and FORs share a reliance on there being such a property as being represented. In this paper I develop (...) an argument — the Unicorn Argument — against both HORs and FORs. The core of the Unicorn is that since there are mental rep- resentations of things that do not exist, there cannot be any such prop- erty as being represented, and thus no such property with which to identify either being conscious or being phenomenal. (shrink)

I develop an argument that believing in the survivability of a mind uploading procedure conveys value to its believers that is assessable independently of assessing the truth of the belief. Regardless of whether the first-order metaphysical belief is true, believing it conveys a kind of Darwinian fitness to the believer. Of course, a further question remains of whether having that Darwinian property can be a basis—in a rational sense of being a basis—for one’s holding the belief. I’ll also make some (...) remarks in the present article toward answering that latter question. (shrink)

Deviant phenomenal knowledge is knowing what it’s like to have experiences of, e.g., red without actually having had experiences of red. Such a knower is a deviant. Some physicalists have argued and some anti-physicalists have denied that the possibility of deviants undermines anti-physicalism and the Knowledge Argument. The current paper presents new arguments defending the deviant-based attacks on anti-physicalism. Central to my arguments are considerations concerning the psychosemantic underpinnings of deviant phenomenal knowledge. I argue that physicalists are in a superior (...) position to account for the conditions in virtue of which states of deviants constitute representations of phenomenal facts. (shrink)

I argue against a class of philosophical views of color perception, especially insofar as such views posit the existence of color sensations. I argue against the need to posit such nonconceptual mental intermediaries between the stimulus and the eventual conceptualized perceptual judgment. Central to my arguments are considerations of certain color illusions. Such illusions are best explained by reference to high-level, conceptualized knowledge concerning, for example, object identity, likely lighting conditions, and material composition of the distal stimulus. Such explanations obviate (...) the need to appeal to nonconceputal mental links in the causal chains eventuating in conceptualized color discriminations. (shrink)

In this paper I discuss one of the key issuesin the philosophy of neuroscience:neurosemantics. The project of neurosemanticsinvolves explaining what it means for states ofneurons and neural systems to haverepresentational contents. Neurosemantics thusinvolves issues of common concern between thephilosophy of neuroscience and philosophy ofmind. I discuss a problem that arises foraccounts of representational content that Icall ``the economy problem'': the problem ofshowing that a candidate theory of mentalrepresentation can bear the work requiredwithin in the causal economy of a mind and (...) anorganism. My approach in the current paper isto explore this and other key themes inneurosemantics through the use of computermodels of neural networks embodied and evolvedin virtual organisms. The models allow for thelaying bare of the causal economies of entireyet simple artificial organisms so that therelations between the neural bases of, forinstance, representation in perception andmemory can be regarded in the context of anentire organism. On the basis of thesesimulations, I argue for an account ofneurosemantics adequate for the solution of theeconomy problem. (shrink)

The neurophilosophy of consciousness brings neuroscience to bear on philosophical issues concerning phenomenal consciousness, especially issues concerning what makes mental states conscious, what it is that we are conscious of, and the nature of the phenomenal character of conscious states. Here attention is given largely to phenomenal consciousness as it arises in vision. The relevant neuroscience concerns not only neurophysiological and neuroanatomical data, but also computational models of neural networks. The neurophilosophical theories that bring such data to bear on the (...) core philosophical issues of phenomenal conscious construe consciousness largely in terms of representations in neural networks associated with certain processes of attention and memory. (shrink)

The philosophical technical term "supervenience" is frequently used in the philosophy of mind as a concise way of characterizing the core idea of physicalism in a manner that is neutral with respect to debates between reductive physicalists and nonreductive physicalists. I argue against this alleged neutrality and side with reductive physicalists. I am especially interested here in debates between psychoneural reductionists and nonreductive functionalist physicalists. Central to my arguments will be considerations concerning how best to articulate the spirit of the (...) idea of supervenience. I argue for a version of supervenience, "fine-grained supervenience," which is the claim that if, at a given time, a single entity instantiates two distinct mental properties, it must do so in virtue of instantiating two distinct physical properties. I argue further that despite initial appearances to the contrary, such a construal of supervenience can be embraced only by reductive physicalists. (shrink)

I have laid out what seem to me to be the most promising arguments on opposing sides of the question of whether what humans regard as the first-person accessible aspects of pain could also be implemented in robots. I have emphasized the ways in which the thought experiments in the respective arguments attempt to marshal hypothetical first- person accessible evidence concerning how one’s own mental life appears to oneself. In the Chinese room argument, a crucial premise involves the thesis that (...) from a lack of it seeming that one is in pain, one can conclude that one is not in pain. There’s a counterpart thesis playing a crucial role in the prosthetic neurons argument, one asserting an entailment from its seeming that one is in pain to one’s being in pain. I further suggested that by adopting a HOT theory of consciousness, of the sort reviewed in Pereplyotchik’s chapter in the present volume, one is thereby in a better position to endorse the prosthetic neurons argument over the Chinese room argument than to make the opposite appraisal. (shrink)

Is the Introspection Thesis true? It certainly isn’t obvious. Introspection is the faculty by which each of us has access to his or her own mental states. Even if we were to suppose that mental states are identical to brain states, it doesn’t follow immediately from this supposition that we can introspect our mental states as brain states. This point is analogous to the following. It doesn’t follow immediately from the mere fact that some distant object is identical to a (...) horse that we can perceive it as a horse. Further, it isn’t obvious that any amount of education would suffice to make some distant speck on the horizon seem like a horse. It may very well be the case that no matter how well we know that some distant speck is a horse; as long as we are sufficiently distant from it we will only be able to see it as a speck. Analogously then, it may very well be the case that no matter how well we know that our mental states are brain states, we will only be able to introspect them as irreducibly mental. (shrink)

Hehner and Stoddart agree that the halting problem has an inconsistent, unsatisfiable specification. Hehner and Macias agree that a key issue with the halting problem is that it requires a: subjective specification(Hehner) / context dependent function(Macias). When a problem has an unsatisfiable specification because this specification is inconsistent then the unsatisfiability of the specification is anchored in its error thus does not actually limit computation.

The most promising approaches to understanding phenomenal consciousness are what I’ll call cognitive approaches, the most notable exemplars of which are the theories of consciousness articulated by David Rosenthal and Daniel Dennett. The aim of the present contribution is to review the core similarities and differences of these exemplars, as well as to outline the main strengths and remaining challenges to this general sort of approach.

A movement dedicated to applying neuroscience to traditional philosophical problems and using philosophical methods to illuminate issues in neuroscience began about twenty-five years ago. Results in neuroscience have affected how we see traditional areas of philosophical concern such as perception, belief-formation, and consciousness. There is an interesting interaction between some of the distinctive features of neuroscience and important general issues in the philosophy of science. And recent neuroscience has thrown up a few conceptual issues that philosophers are perhaps best trained (...) to deal with. After sketching the history of the movement, we explore the relationships between neuroscience and philosophy and introduce some of the specific issues that have arisen. (shrink)

Though the following problem is not explicitly raised by her, it seems sufficiently similar to an issue of pertinence to Akins's "Black and White and Color" (this volume) to merit the moniker, Akins's Problem : Can there be a visual experience devoid of both color phenomenology and black-and-white phenomenology? The point of the present paper is to draw from Akins's paper the materials needed to sketch a case for a positive answer to Akins's Problem. I am unsure about how much (...) of what follows Akins will want to endorse, but I hope this helps move us forward in our collective pursuit of a theory of visual consciousness. (shrink)

Many philosophical issues concern questions of objectivity and subjectivity. Of these questions, there are two kinds. The first considers whether something is objective or subjective; the second what it _means_ for something to be objective or subjective.

A pair of C functions are defined such that D has the halting problem proof's pathological relationship to simulating termination analyzer H. When D correctly simulated by H must be aborted to prevent its own infinite execution then H is necessarily correct to reject D as specifying non-halting behavior. This exact same reasoning is applied to the Peter Linz Turing machine based halting problem proof.

A simulating halt decider correctly predicts what the behavior of its input would be if this simulated input never had its simulation aborted. It does this by correctly recognizing several non-halting behavior patterns in a finite number of steps of correct simulation. -/- When simulating halt decider H correctly predicts that directly executed D(D) would remain stuck in recursive simulation (run forever) unless H aborts its simulation of D this directly applies to the halting theorem.

A simulating halt decider correctly predicts whether or not its correctly simulated input can possibly reach its own final state and halt. It does this by correctly recognizing several non-halting behavior patterns in a finite number of steps of correct simulation. Inputs that do terminate are simply simulated until they complete.

The object of realist metaphysics is generally thought to be to describe the structure of the world as it is in itself, or, alternatively, to determine precisely what is real. The purpose of this essay is to suggest that, although there have been many attempts to achieve this goal, they all fall down, not simply because they have misconstrued the nature of the in-itself or precisely what is real, but because, more fundamentally, they are not clear about what it is (...) to talk about the in-itself or the real. In short, contemporary realism, both continental and analytic, does not have an adequate concept of reality. (shrink)

The novel concept of a simulating halt decider enables halt decider H to to correctly determine the halt status of the conventional “impossible” input D that does the opposite of whatever H decides. This works equally well for Turing machines and “C” functions. The algorithm is demonstrated using “C” functions because all of the details can be shown at this high level of abstraction.

MIT Professor Michael Sipser has agreed that the following verbatim paragraph is correct (he has not agreed to anything else in this paper) -------> -/- If simulating halt decider H correctly simulates its input D until H correctly determines that its simulated D would never stop running unless aborted then H can abort its simulation of D and correctly report that D specifies a non-halting sequence of configurations.