Papers by Christopher S Gifford
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A Kripke-style aoristic semantics is presented, the guiding idea of which is that an indeterminat... more A Kripke-style aoristic semantics is presented, the guiding idea of which is that an indeterminate proposition results in the indeterminate identification of worlds, which in turn, results in indeterminate satisfaction. One interpretation of the conditional is that it expresses determinate preservation of truth.
Both Weak and Strong Kleene truth tables include entries with indeterminacy for a logical equivalence if there is indeterminacy on one side of a logical equivalence. Accordingly, the Kripke-style conditions can be taken in a Weak/Strong Kleene spirit.
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The subject of this thesis is the problem of the many - a problem which presents the challenge of... more The subject of this thesis is the problem of the many - a problem which presents the challenge of there being many objects in situations in which we putatively take there to be one. The problem demands attention since it is paradoxical, ubiquitous in its extent, prompts a revision of the concepts it invokes (identity, distinctness, vagueness, and indeterminacy), and promises a revelation of the relation between it and other philosophical problems. Chapters 2-3 establish what the problem of the many is and establishes its relationship to other problems and paradoxes. Chapters 3-9 consider the most standard responses to the problem and chapter 10 presents a new response called role theory. There are three main original contributions:
1. The introduction of a new delegic and aoristic modality which models theoretical commitment and indeterminacy (respect.). It is claimed that the modality is more appropriate to model indeterminacy than current methods of modeling indeterminacy
which are based on alethic modality, such as those supplied by the
supervaluationist and the ontic indeterminist.
2. The introduction of a new theory called role theory which is an axiomatic ontology that quantifies over roles and the objects that fill them. The theory is defended against presented responses to the problem of the many.
3. The demonstration of a significant difference between the sorites paradox and the problem of the many. This is achieved by contrasting the necessary conditions for the problems and by diagnosing the former as an instance of underdeterminacy and the latter as an instance of overdeterminacy. The difference gives us cause to revise the putative suitability of theories of vagueness as responses to the problem of the many especially due to a demonstrated inability of the theories to cope with situations in which there are instances of both problems.
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This article is an exercise in the transposition of certain approaches in analytic philosoph... more This article is an exercise in the transposition of certain approaches in analytic philosophy to issues concerning business value and identity in business. We examine the notion of business value and several accounts of value that have been offered in the literature. Luciano Floridi’s formal logical account of a business is introduced and applied as a first step towards a logical framework of business value. Peter Peverelli has claimed that Chinese business identity is accounted for in terms of competitors, administration levels, hierarchical structures, and those government agencies with jurisdiction over enterprises (viz. regulators). It is argued that this quadripartite method of identification cannot be fully generalized to all businesses in any geographical location since distinct businesses can exist which have the same competitors, administration levels, hierarchical structures, and governed by the same government agencies. In such a case the distinguishing features of the businesses are the job descriptions or duties of the employees. Hence job descriptions or duties play an important role in the identification of businesses. It turns out that the identification of business according to the job descriptions of employees has less in common with Peverelli's approach and more in common with Bang, Cleemann, and Drucker's notion of business value understood in terms of the technical and the social "as processes and as outputs of production”.
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We present some teaching materials for metaphysics which use the method of introducing issues via... more We present some teaching materials for metaphysics which use the method of introducing issues via puzzles, paradoxes, problems, and conundrums in metaphysics. The method is motivated by the aim to increase student participation and engagement in metaphysical issues so that the student considers and understands philosophical theories based on specific metaphysical concepts. These materials are a result of distilling first and second year undergraduate academic materials into simple presentations that retain the core focus on salient concepts. The presented teaching methods share the same approach as Raymond Smullyan's puzzle-first approach to teaching. Potential goals for the material are numerous; one main goal is the development of the individual student's independent, original, and creative philosophical thinking and analysis as applied to the area of metaphysics. Other goals include the appreciation of overlap between different subareas within metaphysics - overlaps that we note. The article finishes with a further consideration of the importance and utilization of the emotions elicited from materials of philosophical problems and how these can be best incorporated into the teaching methods.
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The relationship between alethic modality and indeterminacy is yet to be clarified. A modal argum... more The relationship between alethic modality and indeterminacy is yet to be clarified. A modal argument—an argument that appeals to alethic modality—against vague objects given by Joseph Moore offers a potential clarification of the relationship; it is proposed that there are cases for which the following holds: if it is indeterminate whether A = B then it is possible that it is determinate that A = B. However, the argument faces three problems. The problems remove the argument’s threat against vague objects and prompt a fuller scrutiny of Moore’s proposed relationship between alethic modality and indeterminacy. Such a scrutiny offers valuable lessons concerning the justification for claims of indeterminate identity, appeals to identity principles in contexts involving both alethic modality and indeterminacy, and how to identify the form of Gareth Evans’s argument against vague objects in other arguments.
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Teaching Documents by Christopher S Gifford
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Three students attending, though this constitutes the whole class. One late. The atmosphere is ve... more Three students attending, though this constitutes the whole class. One late. The atmosphere is very relaxed right from the start, with all the students talking very quickly, and then regularly from then on. They are very friendly with each other and CG, and quick to laugh, particularly at CG's dry humor. It is obvious that an excellent rapport between students and tutor has been built up over the term. Two of the students more or less reported at the beginning that they had been up all night writing essays and had planned to take things easy; nevertheless they are prepared, and rise to the occasion admirably. I got the impression that they were keen for CG's review to go well, and put in the effort, which shows they like him. The students seem of mixed ability, but all are involved and trying their best to get to grips with the subject matter. They are entirely comfortable asking questions and expressing puzzlement, and seem to have no fear at all of looking foolish. There is plenty of interaction between the students as well as between individuals and CG. And they are all awake and following the discussion, throughout as far as I could tell; for instance, they catch him in a slip of the tongue, misattributing a position, which quietly confused or unengaged students would have just let pass. All this very much seems to be out of genuine unforced interest and desire to understand the topic. CG has been blessed with good students in this group, but his excellent handling of the seminar (and no doubt previous seminars) contributed substantially to the success of the session. He opens with a useful recap of relevant previous issues, then quickly starts engaging them, getting statements of the positions from them and so on. CG has an extremely friendly and laid-back style, but one which conceals how effectively he is directing the proceedings; the session is very well-structured, for instance, and his clock control is unobtrusive but effective. He also politely brings them back to the point when they wander from the central issues, and whilst he allows them to raise and outline examples they have thought of themselves, he always then presses them to connect them to the theories under discussion. Throughout they are pressed to develop their points, sometimes with humor but always with quiet encouragement, and at an unhurried pace; the result is that a thoughtful atmosphere pervades the meeting. He frequently checks that they are understanding, asking them to briefly outline a point to prove it when they've said that they have, but he is suspicious they haven't; it should be said that the positions usually are appropriately grasped. When they are not, CG skillfully connects their mistaken statements/intuitions to the genuine positions. He is also good at getting them to understand points by framing them from a different angle, and he connects later developments to earlier points raised by students in a very helpful way. Although he does not blithely assume that the students will remember theories and definitions from earlier in the course, he seems confident that they will, and that confidence seemed warranted for at least the most part. This attests to the way their understanding has developed as the course has progressed.
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Drafts by Christopher S Gifford
Are there instances of indeterminacy expressed in extensions of the language of mathematics that ... more Are there instances of indeterminacy expressed in extensions of the language of mathematics that contain the appropriate vocabulary to express indeterminacy? On one hand, the language of mathematics is a paradigm example of a precise language so there are no instances of indeterminacy expressed in such extensions of the language of mathematics. Hence the claim that there are instances of indeterminacy expressed in such extensions of the language of mathematics is unpalatable. On the other hand, there are putative examples of indeterminacy such as the Continuum Hypothesis and Goldbach's Conjecture in the language of mathematics so there are instances of indeterminacy expressed in such extensions of the language of mathematics. Hence the claim that there are instances of indeterminacy expressed in extensions of the language of mathematics is palatable. If there is indeterminacy expressed extensions of the language of mathematics then one straightforward method to account for the indeterminacy expressed in the language of mathematics is by the same method of treatment of the sorites paradox. According to such a method the source of indeterminacy is either our knowledge (the theory of epistemicism), ontology/metaphysics (the theory of ontic vagueness or metaphysical vagueness), an incorrect conception of truth-values (the theory of fuzzy logic or many-valued logic), context equivocation (contextualism), or semantics (the theory of super-/sub-/pluri-valuationism). Since there exists no instance of the sorites paradox in the language of mathematics, whether theories of vagueness are applicable to putative instances of indeterminacy expressed in the language of mathematics warrants argument. One Constructivist argument runs as follows. Take an example of putative indeterminacy expressed in the language of mathematics – for example, consider Goldbach's Conjecture – the statement 'It is indeterminate whether every even integer greater than 2 can be expressed as the sum of two primes'. Goldbach's Conjecture is not provable in a theory of mathematics and the negation of Goldbach's Conjecture is not provable in a theory of mathematics. If Goldbach's conjecture is not provable in a theory of mathematics then there is no fact that every even integer greater than 2 can be expressed as the sum of two primes. And if the negation of Goldbach's conjecture is not provable in a theory of mathematics then there is no fact that not every even integer greater than 2 can be expressed as the sum of two primes. Hence it is indeterminate whether every even integer greater than 2 can be expressed as the sum of two primes and so Goldbach's Conjecture is indeterminate. Crispin Wright (2003) has claimed that Golbach's Conjecture is subject to the Evidential Constraint that: if P then it is feasible to know that P and claimed that the conjecture is not undecidable on pain of contradiction. (Whereby undecidability is construed as: T knows that it is impossible to know whether or not P). I argue that the contraposition of the Evidential Constraint is false and so that the contradiction can be obviated. If the previous Constructivist argument is sound and generalizable to all instances of undecidability expressed in the language of mathematics then there are statements that are both undecidable and indeterminate expressed in the language of mathematics. And if there are instances of both undeciability and indeterminacy expressed in the language of mathematics then it will turn out that it is the case that it is indeterminate whether such instances are undecidable and it will turn out that it is the case that it is undecidable whether such instances are indeterminate. For a modal operator can be introduced to express 'It is undecidable whether' and a modal operator can be introduced to express 'It is indeterminate whether'. And if a statement is undecidable then it is true that it is undecidable whether that statement is true and if a statement is indeterminate then it will be true that it is indeterminate whether that statement is true (under the assumption of the Tarskian T-Schema). Hence, for example, it is both true that it is indeterminate whether it is undecidable whether every even integer greater than 2 can be expressed as the sum of two primes and that it is undecidable whether it is indeterminate whether every even integer greater than 2 can be expressed as the sum of two primes.
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Papers by Christopher S Gifford
Both Weak and Strong Kleene truth tables include entries with indeterminacy for a logical equivalence if there is indeterminacy on one side of a logical equivalence. Accordingly, the Kripke-style conditions can be taken in a Weak/Strong Kleene spirit.
1. The introduction of a new delegic and aoristic modality which models theoretical commitment and indeterminacy (respect.). It is claimed that the modality is more appropriate to model indeterminacy than current methods of modeling indeterminacy
which are based on alethic modality, such as those supplied by the
supervaluationist and the ontic indeterminist.
2. The introduction of a new theory called role theory which is an axiomatic ontology that quantifies over roles and the objects that fill them. The theory is defended against presented responses to the problem of the many.
3. The demonstration of a significant difference between the sorites paradox and the problem of the many. This is achieved by contrasting the necessary conditions for the problems and by diagnosing the former as an instance of underdeterminacy and the latter as an instance of overdeterminacy. The difference gives us cause to revise the putative suitability of theories of vagueness as responses to the problem of the many especially due to a demonstrated inability of the theories to cope with situations in which there are instances of both problems.
Teaching Documents by Christopher S Gifford
Drafts by Christopher S Gifford
Both Weak and Strong Kleene truth tables include entries with indeterminacy for a logical equivalence if there is indeterminacy on one side of a logical equivalence. Accordingly, the Kripke-style conditions can be taken in a Weak/Strong Kleene spirit.
1. The introduction of a new delegic and aoristic modality which models theoretical commitment and indeterminacy (respect.). It is claimed that the modality is more appropriate to model indeterminacy than current methods of modeling indeterminacy
which are based on alethic modality, such as those supplied by the
supervaluationist and the ontic indeterminist.
2. The introduction of a new theory called role theory which is an axiomatic ontology that quantifies over roles and the objects that fill them. The theory is defended against presented responses to the problem of the many.
3. The demonstration of a significant difference between the sorites paradox and the problem of the many. This is achieved by contrasting the necessary conditions for the problems and by diagnosing the former as an instance of underdeterminacy and the latter as an instance of overdeterminacy. The difference gives us cause to revise the putative suitability of theories of vagueness as responses to the problem of the many especially due to a demonstrated inability of the theories to cope with situations in which there are instances of both problems.