id sid tid token lemma pos s7526973f4w 1 1 mathematical mathematical ADJ s7526973f4w 1 2 explanation explanation NOUN s7526973f4w 1 3 has have AUX s7526973f4w 1 4 become become VERB s7526973f4w 1 5 a a DET s7526973f4w 1 6 topic topic NOUN s7526973f4w 1 7 central central ADJ s7526973f4w 1 8 to to ADP s7526973f4w 1 9 the the DET s7526973f4w 1 10 philosophy philosophy NOUN s7526973f4w 1 11 of of ADP s7526973f4w 1 12 mathematics mathematic NOUN s7526973f4w 1 13 and and CCONJ s7526973f4w 1 14 category category NOUN s7526973f4w 1 15 theory theory NOUN s7526973f4w 1 16 is be AUX s7526973f4w 1 17 an an DET s7526973f4w 1 18 area area NOUN s7526973f4w 1 19 of of ADP s7526973f4w 1 20 mathematics mathematic NOUN s7526973f4w 1 21 that that PRON s7526973f4w 1 22 has have AUX s7526973f4w 1 23 become become VERB s7526973f4w 1 24 increasingly increasingly ADV s7526973f4w 1 25 applicable applicable ADJ s7526973f4w 1 26 across across ADP s7526973f4w 1 27 mathematics mathematic NOUN s7526973f4w 1 28 . . PUNCT s7526973f4w 2 1 this this DET s7526973f4w 2 2 dissertation dissertation NOUN s7526973f4w 2 3 bridges bridge VERB s7526973f4w 2 4 these these DET s7526973f4w 2 5 two two NUM s7526973f4w 2 6 topics topic NOUN s7526973f4w 2 7 by by ADP s7526973f4w 2 8 arguing argue VERB s7526973f4w 2 9 that that SCONJ s7526973f4w 2 10 category category NOUN s7526973f4w 2 11 theory theory NOUN s7526973f4w 2 12 has have VERB s7526973f4w 2 13 explanatory explanatory ADJ s7526973f4w 2 14 value value NOUN s7526973f4w 2 15 . . PUNCT s7526973f4w 3 1 category category NOUN s7526973f4w 3 2 theory theory NOUN s7526973f4w 3 3 has have AUX s7526973f4w 3 4 proven prove VERB s7526973f4w 3 5 to to PART s7526973f4w 3 6 be be AUX s7526973f4w 3 7 useful useful ADJ s7526973f4w 3 8 in in ADP s7526973f4w 3 9 many many ADJ s7526973f4w 3 10 distinct distinct ADJ s7526973f4w 3 11 areas area NOUN s7526973f4w 3 12 of of ADP s7526973f4w 3 13 mathematics mathematic NOUN s7526973f4w 3 14 and and CCONJ s7526973f4w 3 15 the the DET s7526973f4w 3 16 usefulness usefulness NOUN s7526973f4w 3 17 of of ADP s7526973f4w 3 18 this this DET s7526973f4w 3 19 applicability applicability NOUN s7526973f4w 3 20 is be AUX s7526973f4w 3 21 often often ADV s7526973f4w 3 22 a a DET s7526973f4w 3 23 result result NOUN s7526973f4w 3 24 of of ADP s7526973f4w 3 25 the the DET s7526973f4w 3 26 fact fact NOUN s7526973f4w 3 27 that that SCONJ s7526973f4w 3 28 the the DET s7526973f4w 3 29 category category ADJ s7526973f4w 3 30 theoretic theoretic ADJ s7526973f4w 3 31 approach approach NOUN s7526973f4w 3 32 produces produce VERB s7526973f4w 3 33 explanation explanation NOUN s7526973f4w 3 34 . . PUNCT s7526973f4w 4 1 first first ADV s7526973f4w 4 2 , , PUNCT s7526973f4w 4 3 i i PRON s7526973f4w 4 4 demonstrate demonstrate VERB s7526973f4w 4 5 that that SCONJ s7526973f4w 4 6 existing exist VERB s7526973f4w 4 7 accounts account NOUN s7526973f4w 4 8 of of ADP s7526973f4w 4 9 mathematical mathematical ADJ s7526973f4w 4 10 explanation explanation NOUN s7526973f4w 4 11 fall fall VERB s7526973f4w 4 12 short short ADJ s7526973f4w 4 13 and and CCONJ s7526973f4w 4 14 that that SCONJ s7526973f4w 4 15 these these DET s7526973f4w 4 16 accounts account NOUN s7526973f4w 4 17 can can AUX s7526973f4w 4 18 be be AUX s7526973f4w 4 19 improved improve VERB s7526973f4w 4 20 by by ADP s7526973f4w 4 21 more more ADV s7526973f4w 4 22 closely closely ADV s7526973f4w 4 23 considering consider VERB s7526973f4w 4 24 features feature NOUN s7526973f4w 4 25 of of ADP s7526973f4w 4 26 mathematical mathematical ADJ s7526973f4w 4 27 practice practice NOUN s7526973f4w 4 28 . . PUNCT s7526973f4w 5 1 second second ADV s7526973f4w 5 2 , , PUNCT s7526973f4w 5 3 i i PRON s7526973f4w 5 4 characterize characterize VERB s7526973f4w 5 5 the the DET s7526973f4w 5 6 kind kind NOUN s7526973f4w 5 7 of of ADP s7526973f4w 5 8 structure structure NOUN s7526973f4w 5 9 inherent inherent ADJ s7526973f4w 5 10 in in ADP s7526973f4w 5 11 category category NOUN s7526973f4w 5 12 theory theory NOUN s7526973f4w 5 13 and and CCONJ s7526973f4w 5 14 illustrate illustrate VERB s7526973f4w 5 15 that that SCONJ s7526973f4w 5 16 this this DET s7526973f4w 5 17 structure structure NOUN s7526973f4w 5 18 often often ADV s7526973f4w 5 19 gives give VERB s7526973f4w 5 20 rise rise NOUN s7526973f4w 5 21 to to ADP s7526973f4w 5 22 explanatory explanatory ADJ s7526973f4w 5 23 generalizations generalization NOUN s7526973f4w 5 24 and and CCONJ s7526973f4w 5 25 analogies analogy NOUN s7526973f4w 5 26 . . PUNCT s7526973f4w 6 1 i i PRON s7526973f4w 6 2 then then ADV s7526973f4w 6 3 expand expand VERB s7526973f4w 6 4 upon upon SCONJ s7526973f4w 6 5 this this DET s7526973f4w 6 6 point point NOUN s7526973f4w 6 7 by by ADP s7526973f4w 6 8 considering consider VERB s7526973f4w 6 9 a a DET s7526973f4w 6 10 specific specific ADJ s7526973f4w 6 11 case case NOUN s7526973f4w 6 12 study study NOUN s7526973f4w 6 13 : : PUNCT s7526973f4w 6 14 the the DET s7526973f4w 6 15 van van PROPN s7526973f4w 6 16 kampen kampen PROPN s7526973f4w 6 17 theorem theorem PROPN s7526973f4w 6 18 . . PUNCT s7526973f4w 7 1 this this DET s7526973f4w 7 2 theorem theorem NOUN s7526973f4w 7 3 serves serve VERB s7526973f4w 7 4 as as ADP s7526973f4w 7 5 an an DET s7526973f4w 7 6 illuminating illuminating ADJ s7526973f4w 7 7 example example NOUN s7526973f4w 7 8 because because SCONJ s7526973f4w 7 9 it it PRON s7526973f4w 7 10 can can AUX s7526973f4w 7 11 formulated formulate VERB s7526973f4w 7 12 both both DET s7526973f4w 7 13 category category NOUN s7526973f4w 7 14 theoretically theoretically ADV s7526973f4w 7 15 and and CCONJ s7526973f4w 7 16 non non ADJ s7526973f4w 7 17 - - ADJ s7526973f4w 7 18 category category ADJ s7526973f4w 7 19 theoretically theoretically ADV s7526973f4w 7 20 . . PUNCT s7526973f4w 8 1 the the DET s7526973f4w 8 2 comparison comparison NOUN s7526973f4w 8 3 of of ADP s7526973f4w 8 4 these these DET s7526973f4w 8 5 two two NUM s7526973f4w 8 6 approaches approach NOUN s7526973f4w 8 7 highlights highlight VERB s7526973f4w 8 8 the the DET s7526973f4w 8 9 explanatoriness explanatoriness NOUN s7526973f4w 8 10 of of ADP s7526973f4w 8 11 category category NOUN s7526973f4w 8 12 theory theory NOUN s7526973f4w 8 13 . . PUNCT s7526973f4w 9 1 in in ADP s7526973f4w 9 2 total total ADJ s7526973f4w 9 3 , , PUNCT s7526973f4w 9 4 these these DET s7526973f4w 9 5 three three NUM s7526973f4w 9 6 chapters chapter NOUN s7526973f4w 9 7 clarify clarify VERB s7526973f4w 9 8 some some DET s7526973f4w 9 9 important important ADJ s7526973f4w 9 10 features feature NOUN s7526973f4w 9 11 of of ADP s7526973f4w 9 12 mathematical mathematical ADJ s7526973f4w 9 13 explanation explanation NOUN s7526973f4w 9 14 and and CCONJ s7526973f4w 9 15 shed shed VERB s7526973f4w 9 16 philosophical philosophical ADJ s7526973f4w 9 17 light light NOUN s7526973f4w 9 18 on on ADP s7526973f4w 9 19 the the DET s7526973f4w 9 20 success success NOUN s7526973f4w 9 21 of of ADP s7526973f4w 9 22 category category NOUN s7526973f4w 9 23 theory theory NOUN s7526973f4w 9 24 within within ADP s7526973f4w 9 25 mathematics mathematic NOUN s7526973f4w 9 26 . . PUNCT