That every expression of language that is {true on the basis of its meaning expressed using language} must have a connection by truth preserving operations to its {meaning expressed using language} is a tautology. The accurate model of the actual world is expressed using formal language and formalized natural language.

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 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.

The notion of a simulating termination analyzer is examined at the concrete level of pairs of C functions. This is similar to AProVE: Non-Termination Witnesses for C Programs. The termination status decision is made on the basis of the dynamic behavior of the input. This paper explores what happens when a simulating termination analyzer is applied to an input that calls itself.

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)

This is an explanation of a possible new insight into the halting problem provided in the language of software engineering. Technical computer science terms are explained using software engineering terms. No knowledge of the halting problem is required. -/- It is based on fully operational software executed in the x86utm operating system. The x86utm operating system (based on an excellent open source x86 emulator) was created to study the details of the halting problem proof counter-examples at the much higher level (...) of abstraction of C/x86. (shrink)

The halting theorem counter-examples present infinitely nested simulation (non-halting) behavior to every simulating halt decider. Whenever the pure simulation of the input to simulating halt decider H(x,y) never stops running unless H aborts its simulation H correctly aborts this simulation and returns 0 for not halting.

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.

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic property of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide valid the deductive inference. Conclusions of sound arguments are derived from truth preserving finite string transformations applied to true premises.

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. ---------------------------------------------------------------------------------------------------- ---- Simulating halt decider H correctly determines that D correctly simulated by H would remain stuck in (...) recursive simulation never reaching its own final state. D cannot do the opposite of the return value from H because this return value is unreachable by every correctly simulated D. This same result is shown to be derived in the Peter Linz Turing machine based proof. (shrink)

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.

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.

Could the intersection of [formal proofs of mathematical logic] and [sound deductive inference] specify formal systems having [deductively sound formal proofs of mathematical logic]? All that we have to do to provide [deductively sound formal proofs of mathematical logic] is select the subset of conventional [formal proofs of mathematical logic] having true premises and now we have [deductively sound formal proofs of mathematical logic].

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 sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system). -- .

We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...) only because they are self-contradictory we could define them as unsound instead of defining the formal system as incomplete. (shrink)

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.

Both Tarski and Gödel “prove” that provability can diverge from Truth. When we boil their claim down to its simplest possible essence it is really claiming that valid inference from true premises might not always derive a true consequence. This is obviously impossible.

An abstract machine having a tape head that can be advanced in 0 to 0x7FFFFFFF increments an unlimited number of times specifies a model of computation that has access to unlimited memory. The technical name for memory addressing based on displacement from the current memory address is relative addressing.

When we look at 800,000 year ice core data CO2 levels since 1950 have risen at a rate of 123-fold faster than the fastest rate in 800,000 years. When we see that this rise is precisely correlated with global carbon emissions the human link to climate change seems certain and any rebuttal becomes ridiculously implausible. The 800,000 year correlation between CO2 and global temperatures seems to be predicting at least 9 degrees C of more warming based on current CO2 levels.

The fail-safe makes sure the fee is high enough to meet carbon emission reduction targets. The safeguard keeps the fee from getting any higher than needed. -/- One of the ways that we could account for the unpredictability of the price elasticity of demand for carbon would be to provide a fail-safe mechanism to ensure that we definitely stay on the carbon reduction schedule. If we keep Energy Innovation Act (HR 763) essentially as it is and scale up the annual (...) carbon fee increase by Number-of-Years-Behind-Schedule * 0.15. (shrink)

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.

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.

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)

One of the ways that we could account for the unpredictability of the price elasticity of demand for carbon would be to provide a fail-safe mechanism to ensure that we definitely stay on the carbon reduction schedule. If we kept Energy Innovation Act (HR 763) essentially as it is and scale up the annual carbon fee increase by Number-of-Years-Behind-Schedule * 0.15.

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.

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.

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)

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.

This is a transcript of a conversation between P F Strawson and Gareth Evans in 1973, filmed for The Open University. Under the title 'Truth', Strawson and Evans discuss the question as to whether the distinction between genuinely fact-stating uses of language and other uses can be grounded on a theory of truth, especially a 'thin' notion of truth in the tradition of F P Ramsey.

Modern-day societies seem to be dominated by a hedonistic approach to happiness. A less short-term and more process-based definition of happiness - eudaimonism - has been proposed by Aristotle. Can this definition of happiness exist in consumer societies as proposed by Zygmunt Bauman and how can we begin to explore such a question? This essay will provide a comparison between two ideal types: eudaimonism and consumer society. With this comparison, we hope to provide a conceptual framework for further research within (...) this subject. (shrink)

Cover songs are a familiar feature of contemporary popular music. Musicians describe their own performances as covers, and audiences use the category to organize their listening and appreciation. However, until now philosophers have not had much to say about them. This book explores how to think about covers, appreciating covers, and the metaphysics of covers and songs. Along the way, it explores a range of issues raised by covers, from the question of what precisely constitutes a cover, to the history (...) and taxonomy of the category, the various relationships that hold between songs, performances, and tracks, and the appreciation and evaluation of covers. (shrink)

P. F. Strawson; II*—Scruton and Wright on Anti-Realism Etc., Proceedings of the Aristotelian Society, Volume 77, Issue 1, 1 June 1977, Pages 15–22, https://doi.

Thomas Reid is often misread as defending common sense, if at all, only by relying on illicit premises about God or our natural faculties. On these theological or reliabilist misreadings, Reid makes common sense assertions where he cannot give arguments. This paper attempts to untangle Reid's defense of common sense by distinguishing four arguments: (a) the argument from madness, (b) the argument from natural faculties, (c) the argument from impotence, and (d) the argument from practical commitment. Of these, (a) and (...) (c) do rely on problematic premises that are no more secure than claims of common sense itself. Yet (b) and (d) do not. This conclusion can be established directly by considering the arguments informally, but one might still worry that there is an implicit premise in them. In order to address this concern, I reconstruct the arguments in the framework of subjective Bayesianism. The worry becomes this: Do the arguments rely on specific values for the prior probability of some premises? Reid's appeals to our prior cognitive and practical commitments do not. Rather than relying on specific probability assignments, they draw on things that are part of the Bayesian framework itself, such as the nature of observation and the connection between belief and action. Contra the theological or reliabilist readings, the defense of common sense does not require indefensible premises. (shrink)

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

In this paper, I reply to 18 of the essays on panpsychism in this issue. Along the way, I sketch out what a post-Galilean science of consciousness, one in which consciousness is taken to be a fundamental feature of reality, might look like.

The no-miracles argument and the pessimistic induction are arguably the main considerations for and against scientific realism. Recently these arguments have been accused of embodying a familiar, seductive fallacy. In each case, we are tricked by a base rate fallacy, one much-discussed in the psychological literature. In this paper we consider this accusation and use it as an explanation for why the two most prominent `wholesale' arguments in the literature seem irresolvable. Framed probabilistically, we can see very clearly why realists (...) and anti-realists have been talking past one another. We then formulate a dilemma for advocates of either argument, answer potential objections to our criticism, discuss what remains (if anything) of these two major arguments, and then speculate about a future philosophy of science freed from these two arguments. In so doing, we connect the point about base rates to the wholesale/retail distinction; we believe it hints at an answer of how to distinguish profitable from unprofitable realism debates. In short, we offer a probabilistic analysis of the feeling of ennui afflicting contemporary philosophy of science. (shrink)

This paper continues and extensive exploration of the QG and TOE resulting from the PF interpretation of QM. Some highlights are an exploration of symmetries of the Standard Model, outlines of testable predictions of implications for QG, that this theory can simultaneously give an account of dark matter and dark energy, probabilities and statevector collapse vs. gravity, applications of the causal interaction tensor Cαβγδ(Fi, Fj). Note the first section mentions qualia but this is not a psychological theory this is an (...) ontic theory. (shrink)

This paper appears to give a Theory of Everything.

When we ask what natural kinds are, there are two different things we might have in mind. The first, which I’ll call the taxonomy question, is what distinguishes a category which is a natural kind from an arbitrary class. The second, which I’ll call the ontology question, is what manner of stuff there is that realizes the category. Many philosophers have systematically conflated the two questions. The confusion is exhibited both by essentialists and by philosophers who pose their accounts in (...) terms of similarity. It also leads to misreading philosophers who do make the distinction. Distinguishing the questions allows for a more subtle understanding of both natural kinds and their underlying metaphysics. (shrink)

Tradução para o português do ensaio "Freedom and Resentment”, de P. F. Strawson. Publicado originalmente em Proceedings of the British Academy, v. 48, 1960. Republicado em Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 2-28]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. Editora da UFSC, 2015. ISBN: 9788532807250.

Tradução para o português do ensaio "Social Morality and Individual Ideal”. Publicado originalmente em Philosophy: The Journal of the Royal Institute of Philosophy, vol. XXXVI, n. 136, p. 1-17, Jan. 1961. Republicado em: STRAWSON, P. F. Freedom and Resentment and Other Essays. Londres: Methuen, 1974. [Routledge, 2008, p. 26-44]. ]. Publicado na coletânea: Ensaios sobre a filosofia de Strawson: com a tradução de Liberdade e ressentimento & Moralidade social e ideal individual. Organizadores: Jaimir Conte & Itamar Luís Gelain. Editora da (...) UFSC, 2015. ISBN: 9788532807250. (shrink)

Some philosophers understand natural kinds to be the categories which are constraints on enquiry. In order to elaborate the metaphysics appropriate to such an account, I consider the complicated history of scurvy, citrus, and vitamin C. It may be tempting to understand these categories in a shallow way (as mere property clusters) or in a deep way (as fundamental properties). Neither approach is adequate, and the case instead calls for middle-range ontology: starting from categories which we identify in the world (...) and elaborating their structure, but not pretending to jump ahead to a complete story about fundamental being. (shrink)

The problem of underdetermination is thought to hold important lessons for philosophy of science. Yet, as Kyle Stanford has recently argued, typical treatments of it offer only restatements of familiar philosophical problems. Following suggestions in Duhem and Sklar, Stanford calls for a New Induction from the history of science. It will provide proof, he thinks, of “the kind of underdetermination that the history of science reveals to be a distinctive and genuine threat to even our best scientific theories” (Stanford 2001, (...) p. S12). This paper examines Stanford’s New Induction and argues that it – like the other forms of underdetermination that he criticizes – merely recapitulates familiar philosophical conundra. (shrink)

Tradução para o português do livro "Ceticismo e naturalismo: algumas variedades", Strawson, P. F. . São Leopoldo, RS: Editora da Unisinos, 2008, 114 p. Coleção: Ideias. ISBN: 9788574313214. Capítulo 1 - Ceticismo, naturalismo e argumentos transcendentais 1. Notas introdutórias; 2. Ceticismo tradicional; 3. Hume: Razão e Natureza; 4. Hume e Wittgenstein; 5. “Apenas relacionar”: O papel dos argumentos transcendentais; 6. Três citações; 7. Historicismo: e o passado.