图片来源:视频号 -流光溢彩Z 秋摄新西兰 - 提卡波 2024 (视频截图)
资料来源:Nancy J. Nersessian, Chapter 6 Creativity in Conceptual Change. In Nancy J. Nersessian, Creating Scientific Concepts. The MIT Press, 2008.
作者介绍:Nancy J. Nersessian 是佐治亚理工学院的Regents教授和认知科学教授。她的研究领域主要是科学哲学、科学史和科学心理学。
阅读难度:5 (阅读难度为5级,第5级为最难。目前等级设定完全是主观的)
语言可能成为思考者与现实之间的屏障。这就是为什么真正的创造力往往在语言结束的地方开始。——亚瑟·科斯特勒(Arthur Koestler),《创造的行为(The Act of Creation)》
一个概念不是一个孤立的、僵化的、毫无变化的形成,而是智力过程的一个活跃部分,持续参与交流、理解和解决问题。——列夫·维果茨基(Lev Vygotsky),《语言与思维(Language and Thought)》
模糊的、初步的现象理解概念是如何转变为科学概念的?本书的提议是,在许多情况下,新的概念是通过基于模型的推理构建的。因此,关于概念创新的观点是,它源于持续的、通常是渐进的建模过程——即使在这个过程中可能会出现“恍然大悟”的时刻。
毫无疑问,概念创新的方法不仅仅包括我们一直在考虑的推理类型。然而,通过研究基于模型的推理如何创造新的候选表征,我们可以在理解概念变化这一关键但被忽视的组成部分方面取得进展。尽管科学中的概念变化是一个发生在不同社区之间的现象,但主要是个别科学家创造了被研究、进一步阐述并被社区采纳的概念创新。因此,需要对个体在解决问题中的推理细节进行梳理——科学中的问题解决必须始终理解为置身于提供概念和物质资源以及对其进行限制的社会和文化背景中——以及使这种推理得以实现的认知结构。
基于模型的推理:迄今为止的论点
论证的主要结论是,基于模型的推理是真正的推理。它并不是对通过逻辑操作命题表示所进行的推理的辅助工具。推理是通过构建和操作目标现象的结构性、行为性或功能性类比模型来进行的。模型的构建是为了满足来自目标领域和源领域的约束,以及可能从模型自身产生的约束。这些约束包括空间、时间、因果、功能、类别和数学等方面的限制。约束的满足限制了可行操作的数量,而不严格规定在可能性空间内可以采取的步骤。构建的模型是动态的,能够通过模拟过程进行推理。
基于模型的推理是扩展性的,并且可以具有创造性。通过这种推理,理解得以扩大或深化,常常以导致新颖洞见甚至概念变化的方式进行。当它具有创造性时,位于普通问题解决的连续体上。它利用了普通基于模型推理背后的认知过程,包括心理建模、类比、意象化和模拟过程。同样,在科学中使用时,它也处于普通使用的连续体上。使用上的差异主要源于问题的性质和问题情境。高度创造性的使用,例如S2的例子,可能出现在无法通过已知的任何类比来源进行直接映射的问题背景下,或者是推理者无法回忆起的类比来源。科学使用,例如麦克斯韦(Maxwell)的例子,可能比普通使用更加明确和反思,因为问题情境涉及对一套方法、特定领域知识和显著问题解决经验的深入了解。
基于模型的推理涉及自引导过程,这个过程由构建、模拟、评估和调整模型的循环组成,这些模型作为目标问题的临时解释。我在这里概述了自引导过程,并在第6.2节关于概念创新中进行了详细阐述。具体过程如下:
模型构建始于对目标现象的初步理解,这种理解足以提供初始约束。这些约束以及问题解决的目标指导类比源领域的选择和相关约束的选择。选择源领域可以涉及意象化和模拟过程。通过初始模型,问题解决者尝试结合和整合来自两个领域的约束。选择和合并约束利用了抽象过程,如理想化、近似、极限情况和通用建模。
模拟通过操控模型生成新状态,使得能够检验模型中约束的相互作用、推断结果和做出预测。这些过程可以使目标、源或模型的显著约束变得突出,这些约束在之前可能未被注意或被视为显著。
评估涉及在模型的选定特征和由问题决定的目标之间进行比较。初步评估标准集中在确定模型是否表示目标的所有显著约束(即是否为同类),这需要在目标和模型之间建立初始映射。如果模型符合该标准,那么模型中的问题解决方案可以转移到目标上,并根据问题要求进行评估——例如,它提供了一个令人满意的解释机制;它使得满意的数学表示成为可能;它产生了可测试的实证假设;等等。如果模型在提供问题解决方案方面完全令人满意,过程可以在这里结束。
然而,模型在问题解决过程中经常被修改或扩展,提供了一系列构建块,朝着问题解决的方向前进。调整根据对目标、源和模型约束的增强理解进行。这可能涉及选择一个额外的源领域。
在自引导过程中,基于模型的推理涉及选择性。选择性使得能够排除(潜在)无关特征,并将注意力集中在与问题解决背景相关的特征上。需要为目标领域和源领域确定相关约束。抽象和评估过程会忽视无关因素。构建的模型可能会体现无关因素,正如我们在讨论思想实验时提到的,但要通过模型正确推理,需要将这些因素视为与认知相关因素的支架。我认为,与认知相关的因素是模型中所体现的那些因素。
显然,基于模型的推理与类比密切相关。模型的构建和评估是基于关系比较的。模型与目标之间的有效映射和转移需要满足认知科学家对类比所建立的标准。然而,在我的观点中,基于模型的推理的自引导过程超出了现有类比理论所能容纳的范围。理解基于模型的推理需要对表征构建过程以及形象化和模拟过程在推理中所起的作用进行阐述。
概念创新
第6.1节提供了关于基于模型的推理的描述,涵盖了其一般用法。现在,我回到概念变化中的创造力这一核心问题,并根据到目前为止的分析重新表述:基于模型的推理的哪些特征使其成为概念创新特别有效的手段?我对概念变化的描述不仅仅是个体认知变化的一种形式,还包括科学共同体内的一种表征变化,这通常与理论中的“革命性”变化相关联(例如,从牛顿力学中的“质量”到狭义相对论中的“质量”)。这些是由共同体成员共享的公共表征。谈论概念提供了一种在心理现象和共同体现象之间架起桥梁的方式。概念是人类表征世界的基本方式。它们对经验进行分类,并注意到它们之间的关系、差异和相互联系。对于个体而言,概念涉及一系列认知现象,包括记忆、推理、问题解决、语言理解和信念系统等。科学概念提供了系统的表征,使个人和共同体能够理解、解释和对现象进行预测。
第2章和第3章中发展出的例证为刚才概述的引导过程提供了实质内容,适用于概念创新。麦克斯韦(Maxwell)的基于模型的推理提供了表征动能和势能的方式——这是场概念的必要组成部分,而在他开始时,既没有他也没有物理学具备这种表征。他从一个相当一般的概念出发,认为电磁过程发生在物体周围的区域,并从他问题情境中的关于电和磁的实验研究与理论推导中得出一些具体约束,从而引导出场的表征。S2的基于模型的推理为均匀拉伸弹簧的机制提供了一种表征方式,这在他开始时并不存在。他显然有扭转的概念,但并未与弹簧关联。他从直观的弹簧概念和一些源于问题的具体约束出发,引导出“弹簧”的物理表征,其中包括“扭转”。每个人都经过了多次构建模型的迭代,通过利用目标领域之外的类比源领域中的表征资源。这些虚构的混合模型融合了来自目标、源和模型的约束。
我将如何通过引导过程促进概念创新的观点概述如下,并将在本章其余部分详细阐述。作为一种表征,概念指定了一系列约束,可以用于生成一类模型的成员。概念形成和变化是生成新约束或修改现有约束的过程(这涵盖了通常所称的“弱”与“强”——或“革命性”——概念变化)。基于模型的推理在科学中的概念创新中普遍存在,因为它是一种高度有效的方式,可以使现有表征系统的约束变得显而易见,并将注意力集中在这些约束上,选择性地抽象某些约束并绕过其他约束,以及促进来自多个领域的约束整合。构建的模型为引导过程提供了支架,朝着令人满意的表征发展。通过这些过程,真正新颖的约束组合可以出现,这些组合对应于迄今为止未被表征的结构和行为——在H-创造性案例中,这些组合无法在现有概念结构中被表征。
概念
在之前的研究中,我探讨了概念表征的格式问题。我反对经典的“必要和充分条件”观点,支持与关于人类分类的经验证据一致的更灵活的概念,这些概念在认知研究中正在发展,例如“图式”、“动态框架”和“理想化认知模型”。在认知科学或科学哲学中,目前尚未达成关于“概念”的共识。对正式提案和替代理论的批评通常依赖于概念在特定分析中所服务的目的。从科学变革的角度来看,经典的表征观点是不足的,因为它至多允许通过替换来实现变化,而不允许通过我所称的“后代”类型的修改来实现变化,例如从伽利略到牛顿的“惯性”概念或从法拉第到爱因斯坦的“场”概念。更复杂的是,似乎已被消除的概念特征(如“以太”)可以被视为已被其他概念吸收,在这种情况下,“场”和“时空”就是在其形成过程中历史证据表明它们发挥了作用的概念。对于当前的分析,格式问题可以通过规定无论概念的格式如何,概念都为生成一类模型的成员指定约束来绕过。
劳伦斯·巴萨洛(Lawrence Barsalou,1999)的“动态框架(dynamic frames)”概念有助于阐明概念指定约束的观点。以这种方式看待概念的一个优势在于,巴萨洛展示了他关于感知符号系统的理论如何支持这一早期的分类观念,我们在讨论心理建模时提到了这一点。第二个优势是Hanne Andersen、Peter Barker和Xiang Chen在进一步阐述托马斯·库恩(Thomas Kuhn)关于概念、不可通约性和概念变化的观点时,充分利用了这一概念。他们研究的结果在最近的一本书《科学革命的认知结构》(Andersen, Barker, and Chen 2006)中进行了总结和详细阐述。尽管并非所有科学概念都能轻易适应动态框架分析(见Nersessian和Andersen 1997, 2000),我将使用他们发展出的一个案例来说明概念指定约束(concepts specify constraints)的观点,并指出概念创新涉及改变和创建新的约束。
图6.1 雷(Ray)对鸟的概念的部分动态框架(1678)。箭头表示约束。摘自Andersen, Barker, and Chen(2006),图21,73页,经过剑桥大学出版社的许可转载
图6.1 提供了1678年J. Ray首次鸟类分类中早期鸟类概念的部分表征。鸟类被简单地分类为水鸟或陆鸟。如框架所示,喙和足的属性是相互约束的。这意味着,例如,圆形喙要求具备蹼足,而尖喙则要求具备爪足。尖叫鸟的发现带来了一个问题。尖叫鸟具有尖喙和蹼足。因此,它们违反了当时理解的鸟类概念所规定的约束。
G. Sundevall在1830年代制定的一个流行分类法通过增加相关属性的数量来容纳尖叫鸟及其他如今被归类为“涉禽”的异常情况,这改变了并增加了鸟类概念的约束(见图6.2)。安德森、巴克和向晨(2006)认为,这是一种弱形式的概念变化,因为新的表征虽然可能产生新的属性组合,但与旧分类的显著特征是一致的。特别是,它捕捉了水鸟和陆鸟之间之前的不相似关系。然而,达尔文后期的分类法需要革命性的概念变化。他们指出,H. Gadow的流行分类法不仅引入了一组不同的属性,而且属性之间的约束关系反映了新的达尔文假设,即解剖特征的相似性表明了共同起源(见图6.3)。因此,达尔文前后的鸟类概念之间存在不可通约性。我建议读者查阅他们的书以进一步阐述这一论点。
图6.2 Sundevall的鸟类概念的部分动态框架(1835)。箭头表示约束。摘自Andersen, Barker, and Chen(2006),图22,74页,经过剑桥大学出版社的许可转载。属性“羽毛”指的是第五个次级特征的存在。
以这种有限的方式思考概念可以洞察到基于模型的推理如何成为促进这种变化的有效策略。在我的观点中,概念创新涉及修改现有约束集或生成全新约束集的过程。模型的构建、评估和调整是为了满足这些约束。模型构建的目标是达到一个与目标问题的显著约束相同类型的模型。类比、视觉和模拟过程是从多个领域抽象和整合约束的有效手段。通过它们的相互作用,新的组合(H创造性或P创造性)可以涌现出来。
图6.3 Gadow的鸟类概念的部分动态框架(1893)。箭头表示约束。摘自Andersen, Barker, and Chen(2006),图35,88页,经过剑桥大学出版社的许可转载
正如我们在示例中看到的,所研究领域的已知约束不足以使问题得到解决,因此需要借助类比来源。但在这里,也无法找到直接的问题解决方案。也就是说,单独的任何一个领域都不包含足够的表征资源来解决问题。相反,类比源领域作为构建新型混合模型的约束来源——在这些情况下,模型同时是电磁学和连续介质力学的表征,或是杆和弹簧的表征。模型表征是具体的,但从中对目标现象所做的推理需要在足够广泛的层面上思考表征,以捕捉整个现象类的约束。因此,抽象过程对于约束的选择性使用和发现至关重要,类比、可视化和思维实验所带来的表征变化也是如此。我将依次考虑通过抽象过程实现的选择性和通过表征变化实现的选择性。
抽象
在科学哲学或认知科学中,不常讨论不同类型的抽象过程。正如我们在第二章和第三章中看到的,各种类型的抽象过程在模型构建中发挥着作用,特别是:理想化、近似、极限情况和一般抽象。这些提供了不同的方法,以选择性地关注与特定问题解决案例相关的特征,同时抑制可能阻碍该过程的信息。抑制和选择性突出特征提供了以认知上可处理的方式表征问题的方法。对概念创新最重要的是,它们能够整合来自不同来源的信息。
理想化(Idealization)是一种常见策略,用于将数学表征与现象相关联。从几何图形的角度来看,将三角形的边视为零宽度,或从确定运动的角度来看,将物体的质量视为集中在一个点上,这使得严格应用数学公式成为可能。一旦进行了数学化处理,理想化就提供了一个出发点,从这个点出发可以添加与问题相关的现实世界现象的信息。
极限情况的抽象(Limiting-case abstractions)涉及外推或简化到最小值。这可以包括创建一个理想化的表示,将一个值外推到零,但也包括类似于麦克斯韦(Maxwell)在考虑一个涡旋时所做的简化,或S2在将弹簧简化为一个线圈时所做的简化。在当前问题中,每个人都认为一个重复对象的一个段落具有在分析阶段与问题相关的所有必要特征。然而,在最初将棒与弹簧进行比较时,弹簧的表示必须包括多个线圈,以便S2能够表示这种伸展的差异。麦克斯韦(Maxwell)通过选择性地关注只有一个涡旋,取得了对各种磁现象进行数学表达的重大进展。然而,为了处理电与磁之间的关系,他需要考虑介质中涡旋之间的关系,这使得摩擦作为机械系统模型的问题变得突出。
近似(Approximation)提供了一种折扣差异相关性的手段。在物理学中,一个标准的近似是“一级近似(first-order approximation)”,用于应用数学表征。基本上,它假设任何高阶效应可能是无关紧要的,或者是如此复杂以至于使分析变得不可处理。例如,层流——没有水流或涡流的流动——提供了足以解决许多流体动力现象相关问题的一级近似。当麦克斯韦(Maxwell)推导涡旋与静止轮之间的数学关系时,他假设这些涡旋近似为旋转的刚性伪球体(见图2.15)。这个近似假设任何实际的偏差对于捕捉它们与静止轮之间的数学关系都是可以忽略不计的。将它们视为刚性在这个过程中是有帮助的,但处理静电现象时,他需要添加信息,即在这样的介质中,它们需要是弹性的。这对于表示介质对施加力的反应是必要的。将弹性纳入约束中最终带来了波在介质中传播近似光的洞察。S2理解多边形在边段无限小时近似为圆,使他能够折扣六边形、正方形或圆形线圈在扭转和伸展之间关系中的任何差异。多边形的表示夸大了扭转机制,这让他能够字面上看到六边形线圈的扭转,并理解这种推断可以转移到弹簧上,因为在没有边(平滑曲线)的极限情况下,扭转将均匀分布。
虽然不同类型的抽象过程往往是同时发生的,但区分它们可以引起人们对一种特别有助于合并来自多个来源的约束的抽象类型的关注,因此对于概念创新的问题具有重要意义。例如,在考虑物理系统的行为时,如弹簧,科学家们通常会描绘一个具体的实例,但随后将其作为不具体的简单谐振子进行推理,而不考虑线圈的数量和宽度。为了将其视为通用的简单谐振子,还需要抑制其弹簧状结构和行为的特征。我将其称为“通过通用建模进行的抽象(abstraction via generic modeling)”,或简单称为通用抽象(generic abstraction)。在基于模型的推理中,从不同来源提取的约束需要在足够的广泛性层面上进行理解,以便于检索、整合和转移。此外,通用抽象赋予从构建的具体模型中得出的推论以一般性。正如Berkeley所指出的,我们不能想象一个一般的三角形,而只能想象一些具体的实例。然而,在考虑它与所有三角形的共同点时,我们能够将具体的三角形视为在边长和角度上缺乏特异性。
图6.4 通过通用建模的抽象
通用抽象的概念可以通过一个例子来简单说明,参考Polya(1954)。在我构建这个例子时,读者应查看图6.4。在欧几里得几何中,理想化的三角形被理解为线条在一个点相交,围成一个空间,但没有宽度。欧几里得三角形的表示可以被理解为某种特定类型,例如等腰三角形(图6.4a),对于这种三角形,需要指定两个边和它们对面的角相等。该表示或任何其他三角形的表示(例如,图6.4b)可以被理解为一个一般的三角形(或“通用”三角形),只需指定围成角的边数为三条。要对通用三角形进行推理,需要选择性地抑制特定表示中的信息。要理解一个表示为通用多边形(图6.4c),需要理解边和角的数量是未指定的,尽管表示了特定的数量。因此,通用抽象包括选择性地抑制在表示中实例化的信息,以便进行仅与通用情况相关的推理。
我试图通过通用抽象的概念捕捉到的推理方式,与数学家所称的通过“归纳”进行推理类似,但由于这个术语可能与逻辑中的“归纳”混淆,而后者又是一种不同的推理形式,因此我使用了“通用抽象”。在逻辑中,归纳是指关注一个或几个实例的特定特征,并将这些特征应用于所有实例。使用上述例子,一个逻辑归纳的推理将是“这个等腰三角形的对角相等;因此,所有等腰三角形的对角相等。”而通用抽象则会抑制三角形实例的特定特征,得出如“欧几里得三角形的角度度数可以有多种组合,仅限于其总和为180度”的推理。通用模型与具体实例之间的关系类似于类型与实例之间的区别。通过将表示的组成部分解读为代表对象、属性、关系或行为类型,而非这些的实例,达到了表示的通用性。
在第二章和第三章中讨论了几种通用抽象的实例。在这两个例子中,问题的性质和推理的背景要求从模型得出的推理被理解为适用于现象类别的成员。S2构建了多边形线圈的具体表示——一个六边形和一个正方形——但理解到这些在被拉伸时会扭曲的推理适用于任意边数的多边形线圈。极限情况将是没有边,或一个圆形线圈。因此,S2立刻理解关于扭转的推理将适用于圆形线圈。这个推理导致了他对弹簧概念的改变,使其包括了扭转的表示。麦克斯韦(Maxwell)构建的模型的一个关键特征是,尽管它们代表了创造连续介质机械应力的具体机制,但他通过这些模型所做的推理抑制了具体的因果机制。在推理背景下,麦克斯韦(Maxwell)将模型的具体机制视为代表具有这种因果关系结构的机械系统类别的成员。从现在的角度看,我们知道,实质上,麦克斯韦(Maxwell)将机械的概念与电磁学中“力”的表示分开,从而首次为物理学提供了非机械动力系统的数学表示。麦克斯韦(Maxwell)定律所生成的模型无法在作为他用于推导方程的模型构建源领域的机械领域中表示。
一旦识别出这些概念,我们可以看到科学中的概念创新中有许多通用抽象的例子。例如,在经典力学中,牛顿可以被解读为利用通用抽象来推理行星与抛射物运动之间的共性,从而制定出它们运动的统一数学表示。他使用的模型,如图5.1所示,代表了在特定物理系统类别中成员之间的共性,这些共性是根据问题背景来观察的,在本例中是抛射物和月球。牛顿的反平方引力表示在确定运动的背景下抽象了抛射物和行星的共同点,例如,在确定运动的背景下,两者都可以被表示为点质量。在牛顿之后,反平方定律模型因此成为一种通用的作用于距离的力模型,供那些试图将所有力纳入牛顿力学范围的人使用——包括最初的电力和磁力。
我们所考虑的抽象过程提供了选择性地表示和推理模型的方法。理想化、极限情况、近似和通用抽象为将来自不同来源的约束表示和整合到模型中提供了一种手段。与问题解决无关的特征可以在模型中具体化,可能作为相关特征的支架。但通过模型进行正确推理需要识别哪些特征是相关的,哪些特征在该问题解决情境中是认知惰性的。
表征模式
可以用于解决复杂问题的信息是相当庞大的;因此,通过关注特定约束而带来的选择性表征,使推理在认知上变得可处理。在整个分析过程中,我们反复看到,如何表征某个事物的选择与要表征的内容同样重要,这直接影响到模型在推理中的有效性。如第4章所讨论的,不同的表征格式提供了不同类型的操作方式,因此,格式的选择不仅为选择所表征的信息提供了途径,也影响了支持的推理类型。
这些实例提供了关于意象表征(imagistic representations)如何在处理代表性问题时提供优势,从而导致概念创新的见解。一个可能性是,这些格式在推理时调动了感知和运动过程,例如,从图表中信息的共现推断因果关系,或通过模拟心理模型推断行为。根据我对S2协议的解读,开放的水平线圈图(图3.12)具有一个独特且关键的特征,即它是三维透视的。视觉透视的变化是显著的,因为二维杆弹簧模型无法表示弹簧行为的关键方面,即扭转机制。所有后续的多边形线圈模型渲染都采用三维透视。虽然线圈是三维的这一信息可能通过语言传达或以命题格式在内部表征,但这不太可能提供关于扭转的洞见。一方面,命题格式无法示范其背后的特征。另一方面,在S2的推理中,视觉化不仅代表了线圈的结构,还代表了其行为。他理解该图解代表了David Gooding所称的“瞬时停滞过程”(Gooding 2004, 211),即一个动态对象。三维视觉透视提供了一种心理模拟——由S2画箭头表示——其中线圈在向下拉动时扭转。从中,他通过我们讨论的步骤推断出,扭转控制弹簧的伸展。
意象表征在概念创新中可能特别有效的另一个原因是,它可以绕过现有命题或公式化表征所固有的约束(constraints inherent)。当一个人在构建和模拟心理模型时,使用意象表征可能使认知机制能够建立新的连接,而这些连接在命题或公式化表征中会受到抑制或根本不可能。麦克斯韦(Maxwell)(Maxwell)直觉到,在寻求一个新领域的数学表征时,需要将研究建立在具身表征(embodied representation)的基础上,而不是纯粹从公式化表征开始。换句话说,依赖于纯粹的数学表征存在被吸引到数学的分析可能性和细微差别,而远离现象的风险。“物理类比”提供了一种选择与目标现象相关的数学方面的方法。
早些时候讨论的麦克斯韦(Maxwell)的方法与Thomson使用形式类比之间的对比是很有启发性的。例如,直接将傅里叶(Fourier)对热的数学表征转移到静电现象中,在适当的替换下,也带来了固有于与目标现象不仅相似而且不同的现象的数学表征中的约束。如果仅仅基于公式的操作来进行推理,那么就无法捕捉和探索电磁学可能与之不同的地方,甚至是独特之处。麦克斯韦(Maxwell)从一个首先基于迄今为止对电磁学理解的要求构建的模型中推导出数学表征,这使得能够表征该领域的新特征。这些模型本身提供了约束,导致了电磁问题的新表征资源。正如我们所看到的,涡旋模型作为一个机械系统的不可行性直接通过模拟旋转的涡旋而显现出来。解决摩擦问题首先提供了一种表示电与磁之间因果关系结构的方法,然后又提供了一种表示与静电现象相关的张力和应力之间关系的方法——因此,正如我们所讨论的,场的能量成分也得以表征。
再看,回顾过去,我们可以看到,寻求与连续介质力学中已解决问题的数学表征直接的形式类比(如Thomson所做)是行不通的。连续介质力学并没有资源来表征电磁学——一个非机械的动态系统。然而,广义动力学的数学——今天我们称之为向量分析和偏微分方程——确实具有这种表征能力。也就是说,数学可以应用于比牛顿力学范围更广泛的现象。利用类比作为构建中介模型的约束来源,使麦克斯韦(Maxwell)能够以高度选择的方式使用连续介质力学知识,从而仅使用与电磁约束一致的那些部分。一旦他从模型中推导出初始数学表征,他和其他人就可以充分利用数学强大的表征能力,来推广、深化和扩展对电磁学的处理。
与抽象一样,知道在使用特定表征进行思考时该忽略什么与知道该考虑什么是相关的同样重要。在这方面,特定的可视化既可以有优势,也可以有劣势。一方面,如果推理者没有足够的目标信息来完全了解该忽略什么,模型可能会过度生成,支持与目标无关的推理。我们之前讨论的“力线”表征对法拉第(Faraday)和麦克斯韦(Maxwell)的思维产生了重要影响,这就是一个很好的例子。
在法拉第(Faraday)早期的研究中,图(图6.5)用于提供围绕磁体的铁屑图案的抽象呈现。从一开始,这个图像就旨在作为与磁体周围空间中的应力状态相关的三维过程的二维表征。法拉第假设,这种配置是由沿着这些线的张力和它们之间的压力所导致的。然而,在他场概念的发展过程中,他进一步将这个图像视为一种力的传递和相互转化的动态模型,通常通过线的应力和应变以及各种运动来实现。从这个解释来看,力线是自然界中所有力传递的物质,物质被看作是汇聚的力线的点中心(Gooding 1981;Nersessian 1984a,1985,1992a;Tweney 1985)。正如我在所引用的作品中详细讨论的那样,这种意象在法拉第的推理中是过度生成的。一般来说,他对场的最广泛概念(他称之为“物理线”,这一术语在麦克斯韦(Maxwell)1862年的论文标题中有所呼应)的动态特征源于线的运动种类,例如弯曲、曲线和波动;而不是来自连续的场过程。此外,他所制定的唯一明确的数学关系是将诱导力与“切割的线的数量”相关联,但“数量”是一个离散的度量(直接与线相关),而场过程需要一个连续的度量。
图6.5 法拉第绘制的围绕磁体的力线图
麦克斯韦(Maxwell)是完全理解法拉第(Faraday)力量概念的人之一(图6.6)。正如他在给法拉第的信中生动表达的:“你似乎看到力线绕过障碍物弯曲,直接冲向导体,在晶体中向某些方向偏转,并且在任何地方都携带着相同的吸引力,随着力线的扩展或收缩而更广或更密”(麦克斯韦(Maxwell)致法拉第,1857年11月9日,见于坎贝尔和加内特1969年附录XV)。然而,在麦克斯韦(Maxwell)的数学分析中,力线图被解释为代表以太介质中的应力和应变状态,电磁力通过该介质在与力线正交的方向上连续传播,而不是沿着力线传递。麦克斯韦(Maxwell)从法拉第的解释中获得的是张力和压力的通用约束,这些约束提供了涡旋形状的几何约束。置于磁场中的铁屑将会在草图中呈现出几何配置。
图6.6 法拉第的虚构讲座。麦克斯韦(Maxwell)在哪里?(Anne Larsen绘制)
最后,基于模型的物理系统推理的一个关键维度是所构建的模型通过心理模拟能够实现转化。我们在认知文献中看到,模拟被越来越多地假设为人类认知的组成部分,人类的概念系统建立在重演的形式之上。在推理过程中,模拟可以被理解为一种认识上的努力,其目的是通过预测模型的未来状态并检查这些状态的后果来促进洞察和推论。在创造新状态时,基于模拟的模型推理利用了嵌入在表征约束中的隐性信息。因此,心理模型模拟是一种实验形式,与全面的思想实验处于同一连续体上。正如我们所看到的,思想实验提供了选择性比较概念结构各部分的方法。概念结构系统地组织着相互关联的概念。科学强调一致性和连贯性,但概念结构是丰富而复杂的,个人或群体不太可能对其及其含义有全面的理解。思想实验的选择性示例提供了一种以特定方式揭示目标现象的表征中不一致性或矛盾的方法。思想实验被理解为代表某种情况的典型发生(通用抽象),这赋予结果以普遍性,并增强实验的影响力。也就是说,尽管思想实验者构建了一个单一模型,但其对一系列现象和情况的重要性在执行过程中得以理解。此外,思想实验的叙述形式还可以促进一个群体中的概念变化,使他人能够构建平行的心理模型,并自行推理关于现有表征的问题。
结论:基于模型的推理在概念创新中的作用
本书论证了科学中概念创新和变化记录所展现的建模实践需要被理解为一种创造性推理(creative reasoning)形式——特别是,那种为概念变化过程创造候选表征的推理。将这些视为概念创新的“方法”或“机制”要求我们扩展传统的哲学推理概念。并没有声称基于模型的推理是概念创新的唯一手段。虽然本分析集中于新颖概念表征的初始构建,但基于模型的推理同样可以在一个社区中传递新颖的表征。当然,在科学中实现概念变化,像所有科学变化一样,涉及其他广泛讨论的认知和社会文化过程。然而,本章讨论的基于模型的推理特征——并在整本书中不断发展——使其成为一种非常有效的概念创新手段。
我们已经看到,类比、形象化和模拟建模使得选择性地构建心理模型成为可能,以满足来自多个来源的约束。类比的一个重要功能是在目标领域缺乏所需资源的情况下,为模型构建提供约束。意象表征有助于感知推理,提供绕过现有命题和公式化表征的约束的方法,并促进模拟过程。在模拟中动态操控模型能够推导出显性和隐性约束相互作用的后果。当概念创新被理解为生成新约束和改变现有约束的过程时,基于模型的推理促进了概念变化,因为它包含了有效的选择性抽象、生成和整合约束的方法。各种抽象过程有助于将来自多个领域的信息整合到心理模型中,并将可能以多种格式呈现的信息纳入其中。这些过程促进了使用——并在某些情况下创造——数学来表征现象。在这些过程中,我认为通用抽象对于概念创新至关重要,因为为了实现检索、转移和整合,约束需要在足够一般的层面上被理解。它使得一种选择性成为可能,从而限制推理仅适用于某一类现象的成员,而不仅仅是特定的实例。构建、模拟和推理的循环可以导致模型的出现,这些模型表征了约束的新颖组合,包括那些超出约束所来源的特定领域的表征资源的可能性——真正的概念创新。
反思性思考:更广泛的影响
认知历史分析是一种自然主义的方法(naturalistic method),旨在进行综合分析,融合科学研究,特别是科学史和科学哲学,以及认知科学。它也是反思性的,因此在结尾时,我简要反思我对基于模型的推理的描述对这些领域的一些更广泛的影响。我选择了一些跨学科的主题,而不是逐个考虑每个学科的影响。
学习
在认知发展和科学教育中,研究人员已开始借鉴历史学家和科学哲学家对科学中概念变化的论述,以获取见解。这项研究的前提是,科学家如何构建现象的解释、学生在科学教育中如何学习概念,以及儿童在认知发展过程中掌握所需概念的方式,这些问题都是相互关联的。这一前提正证明是一个富有成效的假设,为这些领域的研究提供了框架。Susan Carey(详见Carey 2004的概述;Carey即将出版)特别指出,认知发展中的概念变化采用的引导机制与我在这里提出的基于模型的推理相似。认知发展与科学学习在儿童和青少年的教育过程中是密切交织在一起的。在“建构主义”学习观中,获得新概念(如学习科学所要求的)涉及到新表征的主动构建(概述见Duschl 1990)。连续性假设(continuum hypothesis)引出了一个推测,即科学家在创造概念时所使用的认知探究实践与如何帮助学生学习科学概念的问题是直接相关的。
从这里所阐述的基于模型的推理的论述中可以提炼出几个主要的学习教训,这些教训我在其他场合也有阐述过(参见,例如,Nersessian 1989, 1992c, 1995b),但值得重申,如下所述。首先,科学中的概念创新和变化通常是渐进的过程。也就是说,即使某个创造性洞察似乎在瞬间发生,它仍然源于之前的建模循环:构建、操控、评估和适应。科学和日常思维中的概念变化都是困难的。与科学中的引导机制一样,学习中使用的模型可以提供逐步推进的垫脚石,引导学习者逐步掌握科学概念并建立科学理解。其次,基于模型的推理依赖于领域知识、抽象领域无关原则的知识,以及如何以及何时使用抽象的知识。第三,科学家使用引导过程(bootstrapping processes)是显性的,并且具备元认知反思。而对于发展中的儿童和科学学习者来说,则并非如此。这个教训不仅没有削弱这一推测,反而可以为关于认知中元认知反思的性质和发展提出新的研究问题,并建议课程创新以促进学习者的元认知反思的发展。
目前正在进行许多基于模型的课程创新(有关样例,参见Clement和Steinberg 2002;Gilbert和Boulter 2000;Gobert和Buckley 2000;Justi和Gilbert 1999;Smith等人1997;Snir和Smith 1995;Wells、Hestenes和Swackhamer 1995;Wiser 1995)。将我们从科学实践中的基于模型的推理中学到的知识转化为在K-16教育环境中有效的学习策略并非易事,且引发了许多研究问题。其中包括:儿童具备哪些认知资源以获取参与基于模型的推理的能力?这些资源的发展轨迹是什么?我们知道,第四章提到的类比研究表明,类比的能力具有发展轨迹。那么,心理模拟的能力呢?使用图解表示的能力呢?抽象推理的能力呢?例如,在K-8课程中,有效的模型类型可能与科学家使用的模型大相径庭。关键在于推理过程应是基于模型的。“箱子中的点”可视类比模型在教授热力学概念时提供了很好的示例(参见例如,Smith、Snir和Grosslight 1992;Wiser 1995)。最后,考虑到我所说的关于问题情境对科学中基于模型的推理重要性的观点,与此相关的一个同样重要的问题是:如何将科学问题解决的情境维度转化为学习环境的情境?课堂或教学实验室的认知文化系统具有其独特的约束和支持,这些都需要纳入开发通过基于模型的推理促进学习的策略中。
类比
通过建模的视角思考类比,凸显出一些尚未在类比理论中解释的过程。如我们在第五章所见,考虑到构建模型的创造性工作对理解类比如何解决表征问题至关重要。目前的类比理论倾向于关注源问题解决方案的检索、后续的映射和转移。然而,在类比的创造性使用中,当问题不明确时(包括需要概念变化的问题),通常没有现成的源问题解决方案可以进行直接比较。相反,这种比较是间接的,要求问题解决者首先构建类比表征,通过这种表征可以解决相应的目标问题(或其部分)。在我们考虑的案例中,中介模型与目标和源领域相关,因为它们是为了满足两个领域的约束而构建的。与其直接从源领域转移映射,不如在中介模型中解决问题,这为类比映射和转移到目标领域提供了基础。实际上,模型本身被视为类比源。它是一个以特定方式与目标相关的构建对象。该模型提供了对目标的丰富理解,从而导致进一步的模型构建迭代,可能涉及来自同一或其他类比源领域的额外约束。
连续体假设,加上S2自发构建中介模型的支持,导致了这样的推测:这种表征构建的过程相当普遍,理解它对于类比推理理论至关重要。根据我所能确定的信息,目前针对问题解决者在类比推理中如何构建和修改目标和源的表征的实证研究寥寥无几。大多数研究假设存在现成的类比源解决方案,并且当匹配不精确时,存在一些相对简单的方式可以对目标或源进行适度的重新表征。我故意没有讨论类比的计算模型,因为它们都无法处理我们示例中类比使用的主要方面。人工智能文献中的主要关注点在于映射和转移。模型构建可能属于所谓的“重新表征”问题,尽管在这一领域的研究很少,但兴趣正在增长。道格拉斯·霍夫斯塔特及其同事在映射和转移过程中确实会不断对目标和源进行重新表征(French 1995; Hofstadter 1995; Mitchell 1993)。特别是,LetterSpirit程序在创造新字体类型方面促成了概念创新,但这种微观世界的方法不太可能扩大规模,以进行我们示例中展示的模型构建。
最后,我们还看到,类比利用了意象化和模拟过程(imagistic and simulative processes),一些实验发现也表明了这一点。为了适应这些过程,需要在认知科学的各个领域之间进行更深入的研究整合,而目前的情况并未达到这一点。总之,我的分析指出,需要对类比进行更丰富、更细致的解释,以涵盖所有维度。
模型与建模
最近,在科学研究中关于模型与建模的研究呈现爆炸式增长。这些实践如今被广泛认定为科学的标志性实践——无论是当代科学还是过去的科学。这些文献记录并分析了在理论发展和应用中各种模型使用的实例(例如,见Cartwright 1983;Giere 1988;Godfrey-Smith 2006;Magnani、Nersessian和Thagard 1999;Morgan和Morrison 1999)。实际上,历史与科学哲学的一个重要领域现在将模型与建模视为科学工具与实践中的重要组成部分。这一关注的转变不仅是由于科学实践随时间的变化。对过去科学的研究提供了充分证据,表明尽管现在有新工具来增强和扩展这些实践,自其诞生以来,创造和运用模型一直是科学问题解决的标准部分。相反,这一转变的原因在于许多哲学家和历史学家不再通过基于逻辑的方法来进行归纳和假设演绎推理的实证主义视角来看待科学。
我的分析为科学家更一般地使用模型提供了洞察。迄今为止,哲学文献中的研究往往过于强调“实在论”问题,而忽视了关于模型的其他重要考量;具体而言,就是通过模型能够进行的智力工作性质以及模型如何发挥作用以实现科学目标。这种关注似乎是早期关于理论实在论的担忧的延续,而模型现在被视为“在理论和现实世界之间进行中介”(Morgan和Morrison 1999,第11页)。模型确实为科学家提供了使用理论并检视其与现象关系的手段,但他们也在没有理论的情况下使用模型,作为构建理论的一种手段。本书的分析可以从另一个角度来看待模型:科学家如何在发现过程中使用模型并创造理论。从科学发现的角度来看,模型与建模是第一位的,进一步的分析则导致理论中的定律和公理的形式表达。因此,发现提供了另一个视角,用于考虑模型如何与现实世界相符合(Longino 2001),但它也突出了关于在问题解决中使用模型时推理性质的问题。特别是,由于模型是从类比源构建并作为类比源用于问题解决的,因此理解类比推理显得尤为重要。
我在这里发展出的论述综合并扩展了我对模型作为认知工具的研究,特别是科学家如何通过模型思考和推理以形成新颖的概念表征。要弄清楚模型如何以这种方式运作,需要仔细研究这些使用实例的细节,并思考创造和利用这些实践的认知性质。我在这里关于基于模型的推理所说的许多内容可以超越概念变化或物理学中特定类型建模的模型使用,但具体的细节需要通过比较研究来确定。基于模型的推理作为一种解决问题的工具在科学领域广泛应用,即使在不同领域进行时,使用的特征也有相似之处。例如,物理学中建模的类比或视觉过程与生物学中建模的类比或视觉过程的功能是相似的。这里考虑的建模类型远不止这些,还有心理学中的统计建模或物理学中的计算建模等,关于这些分析并没有涉及。我将这些留给在其他领域和使用不同类型模型的研究者来确定我的论述中哪些内容可以延续。然而,从我在体外实验和组织工程、神经工程及生物机器人领域的计算模拟模型方面进行的其他研究来看,本书中考察的建模实践似乎属于一种可以称为“通过构建进行发现”的模型使用(Nersessian 2005;Nersessian等,2003)。在构建和操作模型——无论是心理模型、物理模型还是计算模型——的过程中,科学家们对目标现象的某些方面获得了新颖的见解和暂时的理解。通过这些实践,科学在缺乏通常理解为“知识”的情况下,在某一领域取得了进展。
我对基于模型的推理实践的进一步研究正在考察生物医学工程和生物机器人实验室中的研究人员如何创建和使用体外物理模型和计算模型,以模拟他们无法直接实验的体内现象。我选择这些实验室有几个原因,这些原因都与我创建一个在创新研究的建模实践中认知与文化相互影响的叙述的目标有关。首先,众所周知,创造性成果往往源于将来自不同来源的见解结合在一起。跨学科研究实验室提供了一个环境,在这个环境中,通过迫使不同学科的概念、方法、话语、人工制品和知识论相结合,可以产生新的成就。其次,这些特定的实验室是学习的场所,旨在培养研究人员,使其成为跨学科的人,而不是作为跨学科团队的学科贡献者。第三,许多社会学家和人类学家对研究实验室的研究表明,研究实验室和团体在思考科学文化方面的研究是富有成果的,但几乎没有研究关注认知实践(参见Dunbar 1995的例外)或与整合问题相关的研究。我的研究小组从认知科学的环境视角进行实验室研究(在第1章中简要讨论),将人类认知普遍视为发生在社会、文化和物质环境中的复杂系统中。为了实现解释性的整合,关键是要创造出既不主要以认知为中心又不将文化附加其上的叙述,这需要重新思考当前的解释类别。我提供一个简要的例子。在组织工程实验室中,整体问题是创造可植入人体的活性血管替代物,研究人员构建技术性人工制品,以便对当前人类动脉体内生物过程模型进行体外模拟。这些人工制品作为他们所称的“模型系统”运作——即工程人工制品与活细胞培养相互作用的地方——在特定的解决问题过程中。这些人工制品被文化科学研究称为社区的“物质文化”,但它们也作为认知科学研究中所称的“认知人工制品”参与分布式认知系统的推理和表征过程。我的观点是,在实验室研究中,它们既是认知人工制品又是物质文化,单纯聚焦其中一方面无法理解它们如何生成知识。它们代表了当前的理解,因此在基于模型和模拟的推理中发挥了作用;它们对与社区成员身份相关的社会实践至关重要;它们是学习的场所;它们提供将一代研究人员(约五年)与另一代联系在一起的纽带;它们作为文化“棘轮”使一代人能够建立在前一代的成果之上,从而推动问题的解决。总之,它们在科学创造力得以滋养和蓬勃发展的文化-认知结构中发挥着核心作用。使用设备(模拟模型)进行问题解决要求研究人员将生物学和工程学的概念、模型和方法合并。模型系统不仅需要被理解为存在于两个或多个社区的“交易区”(Galison 1997)中的“边界对象”(Star和Griesemer 1989),并作为沟通的媒介,还需要被视为跨学科概念、模型、方法、人工制品和知识论融合的场所——在这里产生真正的新颖性。
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