Mathematical Psychology

This project investigates mathematical psychology's historical and philosophical foundations to clarify its distinguishing characteristics and relationships to adjacent fields. Through gathering primary sources, histories, and interviews with researchers, author Prof. Colin Allen - University of Pittsburgh [1, 2, 3] and his students Osman Attah, Brendan Fleig-Goldstein, Mara McGuire, and Dzintra Ullis have identified three central questions:

What makes the use of mathematics in mathematical psychology reasonably effective, in contrast to other sciences like physics-inspired mathematical biology or symbolic cognitive science?
How does the mathematical approach in mathematical psychology differ from other branches of psychology, like psychophysics and psychometrics?
What is the appropriate relationship of mathematical psychology to cognitive science, given diverging perspectives on aligning with this field?

Preliminary findings emphasize data-driven modeling, skepticism of cognitive science alignments, and early reliance on computation. They will further probe the interplay with cognitive neuroscience and contrast rational-analysis approaches. By elucidating the motivating perspectives and objectives of different eras in mathematical psychology's development, they aim to understand its past and inform constructive dialogue on its philosophical foundations and future directions. This project intends to provide a conceptual roadmap for the field through integrated history and philosophy of science.

The Project: Integrating History and Philosophy of Mathematical Psychology

This project aims to integrate historical and philosophical perspectives to elucidate the foundations of mathematical psychology. As Norwood Hanson stated, history without philosophy is blind, while philosophy without history is empty. The goal is to find a middle ground between the contextual focus of history and the conceptual focus of philosophy.

The team acknowledges that all historical accounts are imperfect, but some can provide valuable insights. The history of mathematical psychology is difficult to tell without centering on the influential Stanford group. Tracing academic lineages and key events includes part of the picture, but more context is needed to fully understand the field's development.

The project draws on diverse sources, including research interviews, retrospective articles, formal histories, and online materials. More interviews and research will further flesh out the historical and philosophical foundations. While incomplete, the current analysis aims to identify important themes, contrasts, and questions that shaped mathematical psychology's evolution. Ultimately, the goal is an integrated historical and conceptual roadmap to inform contemporary perspectives on the field's identity and future directions.

The Rise of Mathematical Psychology

The history of efforts to mathematize psychology traces back to the quantitative imperative stemming from the Galilean scientific revolution. This imprinted the notion that proper science requires mathematics, leading to "physics envy" in other disciplines like psychology.

Many early psychologists argued psychology needed to become mathematical to be scientific. However, mathematizing psychology faced complications absent in the physical sciences. Objects in psychology were not readily present as quantifiable, provoking heated debates on whether psychometric and psychophysical measurements were meaningful.

Nonetheless, the desire to develop mathematical psychology persisted. Different approaches grappled with determining the appropriate role of mathematics in relation to psychological experiments and data. For example, Herbart favored starting with mathematics to ensure accuracy, while Fechner insisted experiments must come first to ground mathematics.

Tensions remain between data-driven versus theory-driven mathematization of psychology. Contemporary perspectives range from psychometric and psychophysical stances that foreground data to measurement-theoretical and computational approaches that emphasize formal models.

Elucidating how psychologists negotiated to apply mathematical methods to an apparently resistant subject matter helps reveal the evolving role and place of mathematics in psychology. This historical interplay shaped the emergence of mathematical psychology as a field.

The Distinctive Mathematical Approach of Mathematical Psychology

What sets mathematical psychology apart from other branches of psychology in its use of mathematics?

Several key aspects stand out:

Advocating quantitative methods broadly. Mathematical psychology emerged partly to push psychology to embrace quantitative modeling and mathematics beyond basic statistics.
Drawing from diverse mathematical tools. With greater training in mathematics, mathematical psychologists utilize more advanced and varied mathematical techniques like topology and differential geometry.
Linking models and experiments. Mathematical psychologists emphasize tightly connecting experimental design and statistical analysis, with experiments created to test specific models.
Favoring theoretical models. Mathematical psychology incorporates "pure" mathematical results and prefers analytic, hand-fitted models over data-driven computer models.
Seeking general, cumulative theory. Unlike just describing data, mathematical psychology aspires to abstract, general theory supported across experiments, cumulative progress in models, and mathematical insight into psychological mechanisms.

So while not unique to mathematical psychology, these key elements help characterize how its use of mathematics diverges from adjacent fields like psychophysics and psychometrics. Mathematical psychology carved out an identity embracing quantitative methods but also theoretical depth and broad generalization.

Situating Mathematical Psychology Relative to Cognitive Science

What is the appropriate perspective on mathematical psychology's relationship to cognitive psychology and cognitive science? While connected historically and conceptually, essential distinctions exist.

Mathematical psychology draws from diverse disciplines that are also influential in cognitive science, like computer science, psychology, linguistics, and neuroscience. However, mathematical psychology appears more skeptical of alignments with cognitive science.

For example, cognitive science prominently adopted the computer as a model of the human mind, while mathematical psychology focused more narrowly on computers as modeling tools.

Additionally, mathematical psychology seems to take a more critical stance towards purely simulation-based modeling in cognitive science, instead emphasizing iterative modeling tightly linked to experimentation.

Overall, mathematical psychology exhibits significant overlap with cognitive science but strongly asserts its distinct mathematical orientation and modeling perspectives. Elucidating this complex relationship remains an ongoing project, but preliminary analysis suggests mathematical psychology intentionally diverged from cognitive science in its formative development.

This establishes mathematical psychology's separate identity while retaining connections to adjacent disciplines at the intersection of mathematics, psychology, and computation.

Looking Ahead: Open Questions and Future Research

This historical and conceptual analysis of mathematical psychology's foundations has illuminated key themes, contrasts, and questions that shaped the field's development. Further research can build on these preliminary findings.

Additional work is needed to flesh out the fuller intellectual, social, and political context driving the evolution of mathematical psychology. Examining the influences and reactions of key figures will provide a richer picture.

Ongoing investigation can probe whether the identified tensions and contrasts represent historical artifacts or still animate contemporary debates. Do mathematical psychologists today grapple with similar questions on the role of mathematics and modeling?

Further analysis should also elucidate the nature of the purported bidirectional relationship between modeling and experimentation in mathematical psychology. As well, clarifying the diversity of perspectives on goals like generality, abstraction, and cumulative theory-building would be valuable.

Finally, this research aims to spur discussion on philosophical issues such as realism, pluralism, and progress in mathematical psychology models. Is the accuracy and truth value of models an important consideration or mainly beside the point? And where is the field headed - towards greater verisimilitude or an indefinite balancing of complexity and abstraction?

By spurring reflection on this conceptual foundation, this historical and integrative analysis hopes to provide a roadmap to inform constructive dialogue on mathematical psychology's identity and future trajectory.

The SDTEST^®

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Below you can read an abridged version of the results of our VUCA poll “Fears“. The full version of the results is available for free in the FAQ section after login or registration.

Kev ntshai

kab kos Correlation

VUCA

Tseem ceeb heev tus nqi ntawm cov correlation coefficient

Kev faib tawm ib txwm, los ntawm William Seas Gosset (Tub Ntxhais Kawm) r = 0.033

Tsis tas li cas faib tawm, los ntawm Spearman r = 0.0013

Qhia tsuas yog > r = 0.033

Kev faib	Tsis li cas	Tsis li cas	Tsis li cas	Zoo li ib txwm	Zoo li ib txwm	Zoo li ib txwm	Zoo li ib txwm	Zoo li ib txwm
Txhua nqe lus nug Txhua nqe lus nug Kuv qhov kev ntshai tshaj plaws yog
Kuv qhov kev ntshai tshaj plaws yog
Answer 1	-	Tsis muaj zog zoo 0.0559	Tsis muaj zog zoo 0.0315	Tsis muaj zog tsis zoo -0.0170	Tsis muaj zog zoo 0.0920	Tsis muaj zog zoo 0.0294	Tsis muaj zog tsis zoo -0.0124	Tsis muaj zog tsis zoo -0.1539
Answer 2	-	Tsis muaj zog zoo 0.0229	Tsis muaj zog tsis zoo -0.0002	Tsis muaj zog tsis zoo -0.0448	Tsis muaj zog zoo 0.0636	Tsis muaj zog zoo 0.0445	Tsis muaj zog zoo 0.0134	Tsis muaj zog tsis zoo -0.0939
Answer 3	-	Tsis muaj zog tsis zoo -0.0032	Tsis muaj zog tsis zoo -0.0121	Tsis muaj zog tsis zoo -0.0416	Tsis muaj zog tsis zoo -0.0462	Tsis muaj zog zoo 0.0466	Tsis muaj zog zoo 0.0788	Tsis muaj zog tsis zoo -0.0195
Answer 4	-	Tsis muaj zog zoo 0.0438	Tsis muaj zog zoo 0.0348	Tsis muaj zog tsis zoo -0.0195	Tsis muaj zog zoo 0.0153	Tsis muaj zog zoo 0.0300	Tsis muaj zog zoo 0.0207	Tsis muaj zog tsis zoo -0.0980
Answer 5	-	Tsis muaj zog zoo 0.0304	Tsis muaj zog zoo 0.1282	Tsis muaj zog zoo 0.0135	Tsis muaj zog zoo 0.0734	Tsis muaj zog tsis zoo -0.0013	Tsis muaj zog tsis zoo -0.0200	Tsis muaj zog tsis zoo -0.1757
Answer 6	-	Tsis muaj zog tsis zoo -0.0002	Tsis muaj zog zoo 0.0082	Tsis muaj zog tsis zoo -0.0627	Tsis muaj zog tsis zoo -0.0083	Tsis muaj zog zoo 0.0193	Tsis muaj zog zoo 0.0831	Tsis muaj zog tsis zoo -0.0315
Answer 7	-	Tsis muaj zog zoo 0.0126	Tsis muaj zog zoo 0.0381	Tsis muaj zog tsis zoo -0.0687	Tsis muaj zog tsis zoo -0.0243	Tsis muaj zog zoo 0.0469	Tsis muaj zog zoo 0.0642	Tsis muaj zog tsis zoo -0.0515
Answer 8	-	Tsis muaj zog zoo 0.0698	Tsis muaj zog zoo 0.0848	Tsis muaj zog tsis zoo -0.0327	Tsis muaj zog zoo 0.0148	Tsis muaj zog zoo 0.0345	Tsis muaj zog zoo 0.0134	Tsis muaj zog tsis zoo -0.1365
Answer 9	-	Tsis muaj zog zoo 0.0668	Tsis muaj zog zoo 0.1676	Tsis muaj zog zoo 0.0083	Tsis muaj zog zoo 0.0693	Tsis muaj zog tsis zoo -0.0131	Tsis muaj zog tsis zoo -0.0516	Tsis muaj zog tsis zoo -0.1818
Answer 10	-	Tsis muaj zog zoo 0.0782	Tsis muaj zog zoo 0.0753	Tsis muaj zog tsis zoo -0.0204	Tsis muaj zog zoo 0.0247	Tsis muaj zog zoo 0.0342	Tsis muaj zog tsis zoo -0.0131	Tsis muaj zog tsis zoo -0.1304
Answer 11	-	Tsis muaj zog zoo 0.0578	Tsis muaj zog zoo 0.0532	Tsis muaj zog tsis zoo -0.0096	Tsis muaj zog zoo 0.0087	Tsis muaj zog zoo 0.0195	Tsis muaj zog zoo 0.0311	Tsis muaj zog tsis zoo -0.1196
Answer 12	-	Tsis muaj zog zoo 0.0390	Tsis muaj zog zoo 0.1037	Tsis muaj zog tsis zoo -0.0358	Tsis muaj zog zoo 0.0358	Tsis muaj zog zoo 0.0250	Tsis muaj zog zoo 0.0299	Tsis muaj zog tsis zoo -0.1520
Answer 13	-	Tsis muaj zog zoo 0.0644	Tsis muaj zog zoo 0.1048	Tsis muaj zog tsis zoo -0.0448	Tsis muaj zog zoo 0.0268	Tsis muaj zog zoo 0.0417	Tsis muaj zog zoo 0.0178	Tsis muaj zog tsis zoo -0.1600
Answer 14	-	Tsis muaj zog zoo 0.0712	Tsis muaj zog zoo 0.1021	Tsis muaj zog tsis zoo -0.0007	Tsis muaj zog tsis zoo -0.0088	Tsis muaj zog tsis zoo -0.0011	Tsis muaj zog zoo 0.0088	Tsis muaj zog tsis zoo -0.1169
Answer 15	-	Tsis muaj zog zoo 0.0557	Tsis muaj zog zoo 0.1365	Tsis muaj zog tsis zoo -0.0423	Tsis muaj zog zoo 0.0177	Tsis muaj zog tsis zoo -0.0162	Tsis muaj zog zoo 0.0224	Tsis muaj zog tsis zoo -0.1179
Answer 16	-	Tsis muaj zog zoo 0.0591	Tsis muaj zog zoo 0.0273	Tsis muaj zog tsis zoo -0.0386	Tsis muaj zog tsis zoo -0.0400	Tsis muaj zog zoo 0.0653	Tsis muaj zog zoo 0.0284	Tsis muaj zog tsis zoo -0.0708

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

Valerii Kosenko

Khoom Siv Khoom Saas Tsiaj Txoj Haujlwm SDTET®

Valerii tau tsim nyog raws li kev sib raug zoo-tus kws kho mob hlwb thaum xyoo 1993 thiab muaj txij xyoo thov nws kev paub hauv Project Tswj.
Valerii tau txais Master's degree thiab qhov project thiab Project Tus Thawj Coj tsim nyog rau hauv xyoo 2013. Thaum nws paub txog txoj haujlwm Geesellschaft E. V.) thiab muab kauv ntom.
Valerii tau siv ntau yam kev ntsuam xyuas muaj zog thiab siv nws txoj kev paub thiab kev paub los hloov qhov tam sim no version ntawm sdtest.
Valerii yog tus sau tshawb fawb txog qhov tsis paub tseeb ntawm V.U.c.a. Lub tswv yim siv cov kab mob muab kauv thiab cov lej lej hauv kev ua lej, ntau dua 20 cov chaw xaiv tsa thoob ntiaj teb.

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