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This is a list of lowercase nonhyphenated single words found in the 200805 issue of Erkenntnis which did not have English entries in the English Wiktionary when this list was created. More info...
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Contents
44582 tokens ‧ 37823 valid lowercase tokens ‧ 4235 types ‧ 77 (~ 1.818%) words before cleaning ‧
200805[edit]
 acausal

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 According to the traditional philosophical analysis, mathematical theorems are a priori truths about acausal, nonspatiotemporal objects.

 approximatively

2008 April 17, Kajsa Bråting and Johanna Pejlare, “Visualizations in Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891043:_{add}  _{notemp}
 He considered the function strip as a collection of functions that are approximatively equal to each other and he considered a function to represent a strip if all its values belongs to the strip.

 argumentations

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 The first historical case study presented pertains to the criticism and the eventual decline of visualization in mathematics triggered by geometrical and analytical argumentations drifting apart in the course of the rigourization of analysis in the 19th century.

 axiomatics

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 In his “The role of axioms in mathematics”, Kenny Easwaran wants to correct another aspect that received wisdom has to offer on axiomatics.

 axiomatizations

2008 April 11, Dirk Schlimm, “On Abstraction and the Importance of Asking the Right Research Questions: Could Jordan have Proved the JordanHölder Theorem?”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089108z:_{add}  _{notemp}
 The subsequent spread of the abstract notion involved the transfer of particular theorems for substitution groups to the abstract case, the acknowledgment of the notion of group as a fundamental structure in algebra, and detailed investigations of different axiomatizations.

 calculational

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 Correspondingly, computers can be thought of as augmenting a mathematician’s calculational powers.

 checkability

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 The ideal of uncontroversial checkability of mathematical arguments, however, seems to be related to formal derivations rather than scribblings on napkins.

 contextualism

2008 March 21, Brendan Larvor, “What can the Philosophy of Mathematics Learn from the History of Mathematics?”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891070:_{add}  _{notemp}
 If contextualism is true, then change ramifies through all the contextual connections.

 decomposability

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 11 Next to this quest for a formal proof however, since about the middle of the eighteenth century, substantial efforts have been done to check an increasing amount of specific numbers upon this particular way of decomposability.

 deductivists

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 Although, in mathematics, one is not supposed to settle for anything short of absolute proof, even staunch deductivists might appreciate the potential value of this way of proceeding.

 dehistoricize

2008 March 21, Brendan Larvor, “What can the Philosophy of Mathematics Learn from the History of Mathematics?”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891070:_{add}  _{notemp}
 They think they are doing a thing honour when they dehistoricize it, sub specie aeterni —when they make a mummy of it.

 digitalization

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 Topics that have been found to become philosophically informing in this respect include digitalization, complexity, feasibility, and induction.

 disjunctiveness

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 3 was that computer proofs may tend to be less explanatory than traditional proofs because they are more disjunctive, and disjunctiveness reduces explanatoriness.

 explanatoriness

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 3 was that computer proofs may tend to be less explanatory than traditional proofs because they are more disjunctive, and disjunctiveness reduces explanatoriness.

 fictionalists

2008 March 21, Kenny Easwaran, “The Role of Axioms in Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891061:_{add}  _{notemp}
 With foundational axioms, realists about abstract numbers can share the theorems of Peano arithmetic with fictionalists, while with structural axioms, group theorists can share theorems about topological spaces with set theorists.

 formalizability

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 In Wilhelmus ( 2007 ), the author investigated the philosophical question “Is formalizability of an argument a necessary condition for mathematical knowledge?

 foundationalism

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 A radical denial of foundationalism is offered by social constructivism (Ernest 1998 ), an approach that many researchers in mathematics education embrace.

 foundationalist

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 These innerscientific episodes, as witnessed by their public reflection, suggest that one should consider a revision of the foundationalist epistemology of mathematics.

 foundationally

2008 March 21, Kenny Easwaran, “The Role of Axioms in Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891061:_{add}  _{notemp}
 If there is no room for philosophical disagreement, then the axioms must be treated structurally rather than foundationally.

 gapless

2008 March 21, Brendan Larvor, “What can the Philosophy of Mathematics Learn from the History of Mathematics?”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891070:_{add}  _{notemp}
 Turning to the case of mathematics, even if there are mathematical objects or truths laid up in a Platonic heaven, or gapless proofs that an ideal mathematician could give ‘in principle’, such ideal items are no more historically effective than the contents of scripture.

 historiographic

2008 March 21, Brendan Larvor, “What can the Philosophy of Mathematics Learn from the History of Mathematics?”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891070:_{add}  _{notemp}
 The historian of philosophy (in Williams’ sense) uses historiographic techniques to place texts and actors in their proper contexts and understand them in their proper times, but only insofar as this serves the philosophical goals of the enquiry.

 incomputability

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 The informal dimension inherent to these fields of inquiry is captured by notorious notions such as unpredictability, nonlinearity, chaos, emergence, or incomputability.

 indispensible

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 However, whereas Van Bendegem and Van Kerkhove conclude by saying that experimental methods and an empirical basis form an indispensible backdrop for mathematical practice, Baker goes the other way and says that the fact that mathematicians use experiments in the context of discovery is “compatible with the view that mathematics is a priori and deductive at its core”.

 inductiveness

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 The main difficulty with (I) stems from an ambiguity over how to understand the core condition concerning inductiveness.

 logicist

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 Their solution was to adopt Russell’s logicist thesis that every mathematical concept can be defined in the language of logic and that every mathematical proof can be replaced by a purely logical derivation using the logical definitions of the concepts involved; hence the label “ Logical Empiricism”.

 monotonicity

2008 April 17, Kajsa Bråting and Johanna Pejlare, “Visualizations in Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891043:_{add}  _{notemp}
 The ‘intuitively evident’ fact that a function that varies continuously must be piecewise monotonic was used, and differentiability and monotonicity were linked together.

 nondeductive

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 At no point in this process need the computations be offered as providing nondeductive support for the conjecture.

 nonrigorous

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 Most likely we will wind up abandoning the task of keeping track of price altogether and complete the metamorphosis to nonrigorous mathematics.

 piecewise

2008 April 17, Kajsa Bråting and Johanna Pejlare, “Visualizations in Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891043:_{add}  _{notemp}
 The ‘intuitively evident’ fact that a function that varies continuously must be piecewise monotonic was used, and differentiability and monotonicity were linked together.

 platonism

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 Among those interested in this question are philosophers trying to strengthen the QuinePutnam indispensability argument for mathematical platonism.

 primehood

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 Because it involves the addition of numbers defined in terms of multiplication, this problem is as hard to tackle as it is easy to phrase and grasp (as for the latter, it only takes one to master the concepts of evenness and primehood).

 prover

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 The prover belongs to a family of checking devices, Turing machines or sequences of these, that are capable of establishing the probable correctness of solutions for very large classes of problems.

 reconceptualize

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 But perhaps it does have the right form if we reconceptualize what is going on.

 reducibility

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 This reducibility part of the work was independently double checked with different programs and computers.

 rigourization

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 The first historical case study presented pertains to the criticism and the eventual decline of visualization in mathematics triggered by geometrical and analytical argumentations drifting apart in the course of the rigourization of analysis in the 19th century.

 spacetimes

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 In the second scenario, they employ Malament–Hogarth spacetimes, a theory that recently gained a lot of attention in the computability community as these solutions to the Einstein equations of General Relativity allowing for an infinite amount of time to pass in what is a finite amount of time for an observer.

 supertasks

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 One might object that this scenario is truly a fiction, but the recent literature on supertasks shows that, although their reality is definitely still not established, at least its plausibility can be argued for.

 surveyability

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 The fourth topic, induction, touches upon the alleged experimental and other nondeductive dimensions to mathematical activity, involving such techniques as the brute manipulation of numbers, probability arguments, or visual proofs, and putting to the test the epistemic principles of surveyability and understanding.

 surveyable

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 For example, this criticism also applies to deductive proofs so long or complex that they are not globally surveyable by any one individual, however intellectually supreme.

 tenseless

2008 March 21, Brendan Larvor, “What can the Philosophy of Mathematics Learn from the History of Mathematics?”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891070:_{add}  _{notemp}
 We began with history and philosophy as opposite poles (one temporal and particular, the other tenseless and universal).

 ultrafinitism

2008 March 21, Kenny Easwaran, “The Role of Axioms in Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891061:_{add}  _{notemp}
 And philosophers may continue debates about types of ultrafinitism and constructivism that are largely considered dead in the mathematical community.

 ultrafinitists

2008 March 21, Kenny Easwaran, “The Role of Axioms in Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891061:_{add}  _{notemp}
 (Though some philosophical argument against ultrafinitists and the like must have occurred.

 unexplanatory

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 If explanation is indeed tied closely to unification then it is not hard to see how the disjunctiveness characteristic of computer proof tends to yield proofs that are also considered relatively unexplanatory by mathematicians.

 unfeasibly

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 The most common reason for resorting to computers to help with proving a given result is because we are faced with an unfeasibly large number of particular cases that need to be worked through in order to verify a general claim.

 unilluminating

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 There is a widespread view that computer proofs are unilluminating, that they offer little insight into why a given result is true.

 unproblematically

2008 May 30, Alan Baker, “Experimental Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s106700089109y:_{add}  _{notemp}
 More serious, perhaps, for the computational characterization is that many uses of computation fall unproblematically under traditional mathematical methodology and seem to have nothing to do with experimental mathematics.

 usurpatory

2008 March 21, Bernd Buldt, Benedikt Löwe and Thomas Müller, “Towards a New Epistemology of Mathematics”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891016:_{add}  _{notemp}
 Kant was concerned about certain metaphysical notions, but we think that usurpatory concepts reflect a general phenomenon of language as it evolves over time.

Sequestered[edit]
 persistance  typo only?

2008 January 31, Bart Van Kerkhove and Jean Paul Van Bendegem, “Pi on Earth, or Mathematics in the Real World”, Erkenntnis, volume 68, number 3, DOI:10.1007/s1067000891025:_{add}  _{notemp}
 We can only aim at part of the answer here, contending that, at the very least, this persistance has to do somehow with the hope of increasing insight in problems at hand, more particularly by exploring the mathematical realm surrounding them.
