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.

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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 0.0532	Tsis muaj zog zoo 0.0292	Tsis muaj zog tsis zoo -0.0175	Tsis muaj zog zoo 0.0919	Tsis muaj zog zoo 0.0301	Tsis muaj zog tsis zoo -0.0114	Tsis muaj zog tsis zoo -0.1523
Answer 2	-	Tsis muaj zog zoo 0.0208	Tsis muaj zog tsis zoo -0.0014	Tsis muaj zog tsis zoo -0.0431	Tsis muaj zog zoo 0.0641	Tsis muaj zog zoo 0.0449	Tsis muaj zog zoo 0.0130	Tsis muaj zog tsis zoo -0.0931
Answer 3	-	Tsis muaj zog tsis zoo -0.0053	Tsis muaj zog tsis zoo -0.0130	Tsis muaj zog tsis zoo -0.0406	Tsis muaj zog tsis zoo -0.0456	Tsis muaj zog zoo 0.0474	Tsis muaj zog zoo 0.0793	Tsis muaj zog tsis zoo -0.0204
Answer 4	-	Tsis muaj zog zoo 0.0427	Tsis muaj zog zoo 0.0328	Tsis muaj zog tsis zoo -0.0200	Tsis muaj zog zoo 0.0158	Tsis muaj zog zoo 0.0306	Tsis muaj zog zoo 0.0217	Tsis muaj zog tsis zoo -0.0980
Answer 5	-	Tsis muaj zog zoo 0.0255	Tsis muaj zog zoo 0.1255	Tsis muaj zog zoo 0.0143	Tsis muaj zog zoo 0.0732	Tsis muaj zog tsis zoo -0.0019	Tsis muaj zog tsis zoo -0.0196	Tsis muaj zog tsis zoo -0.1747
Answer 6	-	Tsis muaj zog tsis zoo -0.0027	Tsis muaj zog zoo 0.0074	Tsis muaj zog tsis zoo -0.0629	Tsis muaj zog tsis zoo -0.0074	Tsis muaj zog zoo 0.0199	Tsis muaj zog zoo 0.0835	Tsis muaj zog tsis zoo -0.0324
Answer 7	-	Tsis muaj zog zoo 0.0110	Tsis muaj zog zoo 0.0371	Tsis muaj zog tsis zoo -0.0688	Tsis muaj zog tsis zoo -0.0227	Tsis muaj zog zoo 0.0471	Tsis muaj zog zoo 0.0650	Tsis muaj zog tsis zoo -0.0523
Answer 8	-	Tsis muaj zog zoo 0.0693	Tsis muaj zog zoo 0.0825	Tsis muaj zog tsis zoo -0.0321	Tsis muaj zog zoo 0.0139	Tsis muaj zog zoo 0.0351	Tsis muaj zog zoo 0.0147	Tsis muaj zog tsis zoo -0.1369
Answer 9	-	Tsis muaj zog zoo 0.0643	Tsis muaj zog zoo 0.1659	Tsis muaj zog zoo 0.0082	Tsis muaj zog zoo 0.0699	Tsis muaj zog tsis zoo -0.0136	Tsis muaj zog tsis zoo -0.0513	Tsis muaj zog tsis zoo -0.1826
Answer 10	-	Tsis muaj zog zoo 0.0760	Tsis muaj zog zoo 0.0730	Tsis muaj zog tsis zoo -0.0219	Tsis muaj zog zoo 0.0254	Tsis muaj zog zoo 0.0318	Tsis muaj zog tsis zoo -0.0138	Tsis muaj zog tsis zoo -0.1318
Answer 11	-	Tsis muaj zog zoo 0.0571	Tsis muaj zog zoo 0.0514	Tsis muaj zog tsis zoo -0.0099	Tsis muaj zog zoo 0.0077	Tsis muaj zog zoo 0.0206	Tsis muaj zog zoo 0.0308	Tsis muaj zog tsis zoo -0.1211
Answer 12	-	Tsis muaj zog zoo 0.0373	Tsis muaj zog zoo 0.1013	Tsis muaj zog tsis zoo -0.0357	Tsis muaj zog zoo 0.0357	Tsis muaj zog zoo 0.0243	Tsis muaj zog zoo 0.0296	Tsis muaj zog tsis zoo -0.1524
Answer 13	-	Tsis muaj zog zoo 0.0621	Tsis muaj zog zoo 0.1036	Tsis muaj zog tsis zoo -0.0438	Tsis muaj zog zoo 0.0273	Tsis muaj zog zoo 0.0414	Tsis muaj zog zoo 0.0176	Tsis muaj zog tsis zoo -0.1608
Answer 14	-	Tsis muaj zog zoo 0.0703	Tsis muaj zog zoo 0.1007	Tsis muaj zog zoo 9.54E-5	Tsis muaj zog tsis zoo -0.0088	Tsis muaj zog tsis zoo -0.0011	Tsis muaj zog zoo 0.0084	Tsis muaj zog tsis zoo -0.1174
Answer 15	-	Tsis muaj zog zoo 0.0554	Tsis muaj zog zoo 0.1349	Tsis muaj zog tsis zoo -0.0418	Tsis muaj zog zoo 0.0179	Tsis muaj zog tsis zoo -0.0165	Tsis muaj zog zoo 0.0219	Tsis muaj zog tsis zoo -0.1181
Answer 16	-	Tsis muaj zog zoo 0.0581	Tsis muaj zog zoo 0.0255	Tsis muaj zog tsis zoo -0.0388	Tsis muaj zog tsis zoo -0.0407	Tsis muaj zog zoo 0.0654	Tsis muaj zog zoo 0.0283	Tsis muaj zog tsis zoo -0.0714

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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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