Survey Results

Foundations of mathematics: constructivism/intuitionism, set-theoretic, logicism, structuralism, or formalism?


600 respondents
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What the percentages mean: "Accept or lean toward P: 50% (40%)" means that 50% of respondents endorsed this answer inclusively (including multiple-answer endorsements) and 40% endorsed this answer exclusively (excluding multiple-answer endorsements).

These results should not be used for comparison to 2009 results due to different populations and parameters. For meaningful longitudinal comparisons, see the longitudinal analysis section.

Accept or lean towards:
constructivism/intuitionism
15.33% (13.67%)
Reject or lean against:
constructivism/intuitionism
3.33% (0.00%)
Accept or lean towards:
formalism
6.17% (5.17%)
Reject or lean against:
formalism
3.50% (0.00%)
Accept or lean towards:
logicism
11.83% (10.33%)
Reject or lean against:
logicism
2.50% (0.00%)
Accept or lean towards:
structuralism
21.17% (17.83%)
Reject or lean against:
structuralism
1.17% (0.00%)
Accept or lean towards:
set-theoretic
15.33% (13.00%)
Reject or lean against:
set-theoretic
2.00% (0.00%)
Accept a combination of views
5.67%
Accept an alternative view
7.33%
The question is too unclear to answer
1.17%
There is no fact of the matter
2.00%
Agnostic/undecided
23.33%
Other
0.50%
N = 600, excluding skipped & insufficiently familiar (522 respondents)
Alternative Views

58 target respondents indicated that they accept or lean toward an alternative view. The words used in their responses cluster as follows. These results are not filtered by AOS, region, etc.

  • PLAT (15): platonism (13) platonis (1) platonic (1)
  • REAL (5): realism (5)
  • FICT (3): fictionalism (3)
  • WITT (3): wittgenstein (3)
  • ARIS (3): aristotelian (3)

Longitudinal comparison to 2009 survey

This question was not in the 2009 survey

Strongest correlations with main questions (target population)

r: 0.35
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 24 33
Reject 29 258
n: 344
p < 0.0001
r: 0.27
Foundations of mathematics: formalism Accept Reject
Accept 5 21
Reject 23 355
n: 404
p < 0.0001
r: -0.25
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 57 21
Reject 376 46
n: 500
p < 0.0001
r: 0.24
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 25 45
Reject 39 324
n: 433
p < 0.0001
r: -0.24
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 29 41
Reject 291 72
n: 433
p < 0.0001
r: 0.24
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 16 44
Reject 21 316
n: 397
p < 0.0001
r: 0.23
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 18 56
Reject 35 361
n: 470
p < 0.0001
r: -0.21
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 10 48
Reject 141 147
n: 346
p < 0.0001
r: 0.21
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 28 33
Reject 62 253
n: 376
p < 0.0001
r: 0.21
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 11 67
Reject 21 402
n: 501
p < 0.0001
r: 0.21
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 11 67
Reject 22 401
n: 501
p < 0.0001
r: -0.21
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 21 57
Reject 202 175
n: 455
p < 0.0001
r: -0.2
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 34 42
Reject 240 116
n: 432
p < 0.0001
r: -0.19
Foundations of mathematics: structuralism Accept Reject
Accept 16 85
Reject 100 234
n: 435
p < 0.0001
r: -0.18
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 49 37
Reject 314 109
n: 509
p < 0.0001
r: 0.18
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 11 64
Reject 24 339
n: 438
p < 0.0001
r: 0.18
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 9 52
Reject 23 320
n: 404
p: 0.0003
r: 0.18
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 6 77
Reject 12 399
n: 494
p < 0.0001
r: 0.18
Foundations of mathematics: set-theoretic Accept Reject
Accept 39 27
Reject 84 158
n: 308
p: 0.0018
r: 0.18
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 32 33
Reject 104 215
n: 384
p: 0.0005
r: 0.17
Foundations of mathematics: logicism Accept Reject
Accept 23 18
Reject 91 144
n: 276
p: 0.0036
r: 0.17
Foundations of mathematics: structuralism Accept Reject
Accept 21 75
Reject 35 262
n: 393
p: 0.0005
r: 0.17
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 45 30
Reject 122 224
n: 421
p: 0.0004
r: 0.17
Foundations of mathematics: formalism Accept Reject
Accept 24 3
Reject 197 177
n: 401
p: 0.0006
r: 0.17
Foundations of mathematics: logicism Accept Reject
Accept 14 27
Reject 58 208
n: 307
p: 0.0027
r: -0.17
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 12 61
Reject 125 212
n: 410
p: 0.0005
r: 0.17
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 35 34
Reject 64 284
n: 417
p: 0.0005
r: 0.17
Foundations of mathematics: formalism Accept Reject
Accept 6 16
Reject 51 234
n: 307
p: 0.0029
r: -0.17
Foundations of mathematics: logicism Accept Reject
Accept 10 48
Reject 86 270
n: 414
p: 0.0006
r: 0.17
Foundations of mathematics: logicism Accept Reject
Accept 6 44
Reject 26 327
n: 403
p: 0.0007
r: 0.17
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 11 37
Reject 21 239
n: 308
p: 0.0032
r: 0.17
Foundations of mathematics: set-theoretic Accept Reject
Accept 25 23
Reject 80 183
n: 311
p: 0.0031
r: 0.17
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 7 59
Reject 14 315
n: 395
p: 0.001
r: -0.16
Foundations of mathematics: structuralism Accept Reject
Accept 25 59
Reject 98 128
n: 310
p: 0.0039
r: 0.16
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 7 63
Reject 17 346
n: 433
p: 0.0007
r: -0.16
Foundations of mathematics: structuralism Accept Reject
Accept 9 89
Reject 55 281
n: 434
p: 0.0008
r: 0.16
Foundations of mathematics: set-theoretic Accept Reject
Accept 54 13
Reject 216 113
n: 396
p: 0.0014
r: 0.16
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 17 51
Reject 42 307
n: 417
p: 0.0011
r: 0.16
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 27 25
Reject 116 190
n: 358
p: 0.0026
r: 0.16
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 11 44
Reject 50 263
n: 368
p: 0.0024
r: 0.16
Foundations of mathematics: formalism Accept Reject
Accept 5 16
Reject 25 297
n: 343
p: 0.0036
r: 0.16
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 7 28
Reject 15 220
n: 270
p: 0.01
r: 0.15
Foundations of mathematics: structuralism Accept Reject
Accept 14 78
Reject 25 253
n: 370
p: 0.0029
r: -0.15
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 31 36
Reject 162 170
n: 399
p: 0.0021
r: -0.15
Foundations of mathematics: set-theoretic Accept Reject
Accept 36 44
Reject 204 172
n: 456
p: 0.001
r: 0.15
Foundations of mathematics: set-theoretic Accept Reject
Accept 18 53
Reject 66 269
n: 406
p: 0.0022
r: 0.15
Foundations of mathematics: structuralism Accept Reject
Accept 54 47
Reject 92 241
n: 434
p: 0.0017
r: -0.15
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 74 1
Reject 361 2
n: 438
p: 0.0016
r: 0.15
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 9 51
Reject 38 282
n: 380
p: 0.0035
r: 0.15
Foundations of mathematics: set-theoretic Accept Reject
Accept 13 47
Reject 41 241
n: 342
p: 0.0065
r: 0.15
Foundations of mathematics: logicism Accept Reject
Accept 39 11
Reject 230 115
n: 395
p: 0.0035
r: 0.15
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 24 44
Reject 56 267
n: 391
p: 0.0037
r: -0.15
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 53 27
Reject 340 66
n: 486
p: 0.0012
r: 0.15
Foundations of mathematics: logicism Accept Reject
Accept 24 20
Reject 97 165
n: 306
p: 0.0109
r: -0.14
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 20 50
Reject 190 176
n: 436
p: 0.0025
r: 0.14
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 43 33
Reject 154 180
n: 410
p: 0.0034
r: 0.14
Foundations of mathematics: logicism Accept Reject
Accept 29 21
Reject 128 176
n: 354
p: 0.0069
r: 0.14
Foundations of mathematics: structuralism Accept Reject
Accept 10 86
Reject 30 268
n: 394
p: 0.0058
r: 0.14
Foundations of mathematics: structuralism Accept Reject
Accept 27 65
Reject 57 221
n: 370
p: 0.0075
r: 0.14
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 31 38
Reject 69 243
n: 381
p: 0.0067
r: 0.14
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 16 38
Reject 45 256
n: 355
p: 0.0102
r: 0.14
Foundations of mathematics: set-theoretic Accept Reject
Accept 71 11
Reject 249 103
n: 434
p: 0.0045
r: 0.14
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 37 17
Reject 127 150
n: 331
p: 0.0139
r: 0.13
Foundations of mathematics: formalism Accept Reject
Accept 5 20
Reject 60 310
n: 395
p: 0.0075
r: 0.13
Foundations of mathematics: set-theoretic Accept Reject
Accept 21 47
Reject 63 238
n: 369
p: 0.0098
r: 0.13
Foundations of mathematics: logicism Accept Reject
Accept 6 51
Reject 26 312
n: 395
p: 0.0081
r: 0.13
Foundations of mathematics: set-theoretic Accept Reject
Accept 35 34
Reject 110 223
n: 402
p: 0.0078
r: 0.13
Foundations of mathematics: formalism Accept Reject
Accept 6 17
Reject 89 244
n: 356
p: 0.0128
r: 0.13
Foundations of mathematics: logicism Accept Reject
Accept 14 53
Reject 75 348
n: 490
p: 0.0036
r: -0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 41 45
Reject 237 171
n: 494
p: 0.0035
r: 0.13
Foundations of mathematics: structuralism Accept Reject
Accept 40 42
Reject 83 167
n: 332
p: 0.0171
r: 0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 7 49
Reject 27 245
n: 328
p: 0.0178
r: -0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 42 34
Reject 236 124
n: 436
p: 0.0066
r: 0.13
Foundations of mathematics: formalism Accept Reject
Accept 21 10
Reject 155 227
n: 413
p: 0.0082
r: 0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 30 35
Reject 61 271
n: 397
p: 0.0097
r: 0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 32 43
Reject 109 269
n: 453
p: 0.0059
r: 0.13
Foundations of mathematics: logicism Accept Reject
Accept 51 14
Reject 263 149
n: 477
p: 0.0048
r: -0.13
Foundations of mathematics: structuralism Accept Reject
Accept 19 75
Reject 55 209
n: 358
p: 0.0147
r: 0.13
Foundations of mathematics: formalism Accept Reject
Accept 11 9
Reject 104 152
n: 276
p: 0.0328
r: -0.13
Foundations of mathematics: structuralism Accept Reject
Accept 21 76
Reject 110 208
n: 415
p: 0.0088
r: 0.13
Foundations of mathematics: set-theoretic Accept Reject
Accept 34 46
Reject 122 253
n: 455
p: 0.0061
r: 0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 8 68
Reject 13 346
n: 435
p: 0.0076
r: 0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 19 54
Reject 75 321
n: 469
p: 0.0057
r: 0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 11 38
Reject 84 223
n: 356
p: 0.0164
r: 0.13
Foundations of mathematics: formalism Accept Reject
Accept 9 21
Reject 63 301
n: 394
p: 0.0116
r: 0.13
Foundations of mathematics: set-theoretic Accept Reject
Accept 70 6
Reject 334 28
n: 438
p: 0.0079
r: -0.13
Foundations of mathematics: formalism Accept Reject
Accept 12 21
Reject 280 128
n: 441
p: 0.0078
r: 0.13
Foundations of mathematics: structuralism Accept Reject
Accept 82 16
Reject 239 97
n: 434
p: 0.0086
r: 0.13
Foundations of mathematics: set-theoretic Accept Reject
Accept 46 31
Reject 178 201
n: 456
p: 0.0071
r: -0.13
Foundations of mathematics: structuralism Accept Reject
Accept 32 83
Reject 134 231
n: 480
p: 0.0059
r: 0.13
Foundations of mathematics: logicism Accept Reject
Accept 17 39
Reject 82 297
n: 435
p: 0.0089
r: 0.13
Foundations of mathematics: set-theoretic Accept Reject
Accept 13 55
Reject 37 263
n: 368
p: 0.0162
r: 0.13
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 27 48
Reject 80 283
n: 438
p: 0.0087
r: 0.12
Foundations of mathematics: set-theoretic Accept Reject
Accept 43 22
Reject 155 166
n: 386
p: 0.0143
r: -0.12
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 21 44
Reject 157 193
n: 415
p: 0.0114
r: 0.12
Foundations of mathematics: structuralism Accept Reject
Accept 28 68
Reject 81 218
n: 395
p: 0.0139
r: -0.12
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 28 47
Reject 241 155
n: 471
p: 0.0072
r: -0.12
Foundations of mathematics: logicism Accept Reject
Accept 11 28
Reject 85 173
n: 297
p: 0.0346
r: 0.12
Foundations of mathematics: logicism Accept Reject
Accept 32 25
Reject 104 246
n: 407
p: 0.0135
r: 0.12
Foundations of mathematics: constructivism/intuitionism Accept Reject
Accept 7 56
Reject 21 293
n: 377
p: 0.0176

Strongest correlations with demographic questions (target population)

r: -0.17
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 5 87
Reject 28 397
n: 517
p < 0.0001
r: 0.16
Foundations of mathematics: logicism Yes No
Accept 30 38
Reject 189 238
n: 495
p: 0.0005
r: -0.15
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 13 79
Reject 121 304
n: 517
p: 0.0007
r: 0.14
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 11 76
Reject 10 418
n: 515
p: 0.001
r: -0.14
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 69 21
Reject 381 46
n: 517
p: 0.0011
r: 0.14
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 21 69
Reject 45 382
n: 517
p: 0.0012
r: 0.14
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 7 69
Reject 5 338
n: 419
p: 0.004
r: 0.14
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 5 71
Reject 6 337
n: 419
p: 0.0044
r: 0.14
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 5 87
Reject 3 422
n: 517
p: 0.0018
r: 0.13
Foundations of mathematics: structuralism Yes No
Accept 48 73
Reject 111 286
n: 518
p: 0.0027
r: 0.13
Foundations of mathematics: set-theoretic Yes No
Accept 82 6
Reject 375 53
n: 516
p: 0.0031
r: -0.13
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 15 77
Reject 143 282
n: 517
p: 0.0032
r: -0.12
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 64 23
Reject 392 36
n: 515
p: 0.0052
r: 0.12
Foundations of mathematics: formalism Yes No
Accept 5 30
Reject 39 441
n: 515
p: 0.0065
r: 0.12
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 12 80
Reject 13 412
n: 517
p: 0.0075
r: 0.12
Foundations of mathematics: structuralism Yes No
Accept 50 70
Reject 170 209
n: 499
p: 0.0088
r: 0.12
Foundations of mathematics: logicism Yes No
Accept 15 53
Reject 47 399
n: 514
p: 0.008
r: 0.12
Foundations of mathematics: structuralism Yes No
Accept 12 109
Reject 14 383
n: 518
p: 0.0082
r: 0.12
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 10 82
Reject 14 411
n: 517
p: 0.0087
r: -0.11
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 16 76
Reject 76 349
n: 517
p: 0.0101
r: 0.11
Foundations of mathematics: logicism Yes No
Accept 11 56
Reject 31 392
n: 490
p: 0.0125
r: 0.11
Foundations of mathematics: logicism Yes No
Accept 16 41
Reject 40 320
n: 417
p: 0.0291
r: 0.11
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 16 60
Reject 35 308
n: 419
p: 0.0289
r: -0.1
Foundations of mathematics: set-theoretic Yes No
Accept 6 63
Reject 40 309
n: 418
p: 0.0343
r: 0.1
Foundations of mathematics: formalism Yes No
Accept 10 25
Reject 69 411
n: 515
p: 0.0205
r: 0.1
Foundations of mathematics: structuralism Yes No
Accept 69 29
Reject 187 98
n: 383
p: 0.0481
r: 0.1
Foundations of mathematics: structuralism Yes No
Accept 18 103
Reject 16 381
n: 518
p: 0.0225
r: -0.1
Foundations of mathematics: formalism Yes No
Accept 7 28
Reject 83 397
n: 515
p: 0.0285
r: -0.09
Foundations of mathematics: structuralism Yes No
Accept 7 114
Reject 32 365
n: 518
p: 0.0315
r: 0.09
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 12 77
Reject 21 414
n: 524
p: 0.0309
r: 0.09
Foundations of mathematics: formalism Yes No
Accept 5 30
Reject 18 462
n: 515
p: 0.0325
r: 0.09
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 15 77
Reject 35 390
n: 517
p: 0.0335
r: 0.09
Foundations of mathematics: set-theoretic Yes No
Accept 34 49
Reject 188 228
n: 499
p: 0.0371
r: 0.09
Foundations of mathematics: constructivism/intuitionism Yes No
Accept 8 84
Reject 10 415
n: 517
p: 0.0375
r: 0.09
Foundations of mathematics: logicism Yes No
Accept 62 6
Reject 391 53
n: 512
p: 0.0402
r: 0.09
Foundations of mathematics: logicism Yes No
Accept 11 60
Reject 34 416
n: 521
p: 0.0423
r: 0.09
Foundations of mathematics: formalism Yes No
Accept 16 20
Reject 204 256
n: 496
p: 0.048
r: 0.09
Foundations of mathematics: logicism Yes No
Accept 7 61
Reject 15 431
n: 514
p: 0.0485