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®
The SDTEST®is a simple and fun tool to uncover our unique motivational values that use mathematical psychology of varying complexity.
The SDTEST® helps us better understand ourselves and others on this lifelong path of self-discovery.
Here are reports of polls which SDTEST® makes:
1) 上個月與人員有關的公司的行動（是 /否）
2) 上個月公司與人事相關的行動（百分比）
3) 恐懼
4) 我國家面臨的最大問題
5) 建立成功的團隊時，好的領導者會使用哪些素質和能力？
6) 谷歌。影響團隊競爭力的因素
7) 求職者的主要優先事項
8) 是什麼使老闆成為偉大的領導者？
9) 是什麼使人們在工作中成功？
10) 您準備好獲得更少的薪水遠程工作嗎？
11) 是否存在年齡主義？
12) 職業中的年齡主義
13) 生活中的年齡主義
14) 年齡歧視的原因
15) 人們放棄的原因（Anna Vital）
16) 相信 (#WVS)
17) 牛津幸福調查
18) 心理健康
19) 您的下一個最激動人心的機會將在哪裡？
20) 您本週將做些什麼來照顧您的心理健康？
21) 我生活在思考我的過去，現在或將來
22) 精英制
23) 人工智能和文明的終結
24) 人們為什麼拖延？
25) 建立自信的性別差異（IFD Allensbach）
26) XING.COM文化評估
27) 帕特里克·林奇尼（Patrick Lencioni）的“團隊的五個功能障礙”
28) 移情是...
29) IT專家選擇工作機會的必不可少？
30) 為什麼人們抵制變化（SiobhánMchale作者）
31) 您如何調節情緒？ （由Nawal Mustafa M.A.）
32) 21個永遠付給您的技能（由Jeremiah Teo /趙漢昇）
33) 真正的自由是...
34) 與他人建立信任的12種方法（賈斯汀·賴特（Justin Wright））
35) 才華橫溢的員工的特徵（人才管理學院）
36) 激勵團隊的10個關鍵
37) 良心代數（弗拉基米爾·列斐伏爾）
38) 未來的三種不同的可能性（作者：Clare W. Graves 博士）
39) 建立不可動搖的自信心的行動（作者：Suren Samarchyan）
40)
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.
You can not only just create your poll in the 关税 «V.U.C.A民调设计师» (with a unique link and your logo) but also you can earn money by selling its results in the 关税 «民意测验商店», as already the authors of polls.
If you participated in VUCA polls, you can see your results and compare them with the overall polls results, which are constantly growing, in your personal account after purchasing 关税 «我的SDT»
