Can formal reasoning capture this? In 2000, Eekels published a paper  that among other things discussed a type of inference called in...
|Can formal reasoning capture this?|
There are three commonly used kinds of logical inference. Deduction was the earliest formalized form of inferring new facts from old ones. It's defined by the classic modus ponens rule: p, p ⇒ q; q. It's read as "If p is true, and p implies q, then q is true also." This is the kind of inference mechanism made famous by Mr. Spock and Sherlock Holmes.
Induction was developed later, largely to capture the style of reasoning of science. Its main inference rule can be written as: p1 ⇒ q1, p2 ⇒ q2, p3 ⇒ q3,...; p ⇒ q. It's meant to capture the notion that a sufficiently large number of instances of specific inferences allows one to deduce a general rule about any such instances. It relates to science in that the development of general scientific laws and theories follow from repeated specific experiments. There's been a lot of work on expanding inductive reasoning in the last few decades, because it seems to mirror so well how humans develop abstract knowledge from specific experiences. Induction is also foundational to evidentialism, a philosophical stance that maintains knowledge is derived from evidence, and that the "stronger" the evidence, the more robust the knowledge.
A third type of inference is abduction. It's only about 100 years old. In abduction, the deductive modus ponens rule is mucked about with, yielding: q, p ⇒ q; p. An example of abductive reasoning could be: (a) there is blood on the floor; (b) if someone were attacked with a knife, there would be blood on the floor; therefore (c) someone was attacked with a knife. Abduction is often used as a model of scientific explanation. It can also be used to model design reasoning; in this case, q are the requirements and p is a design. The biggest difference between deduction and abduction is that while a deductive conclusion is definite and singular, an abductive conclusion only captures one of many possible alternatives. That is, if we abduce p ⇒ q, q; p, there is no reason to also abduce r ⇒ q, q; r. In science, this means that any one explanation does not necessarily preclude other explanations; in design, this means that one design does not necessarily preclude other designs.
And then there's innoduction. Eekels proposed innoduction to model innovation and creativity in design. In this kind of inference, the basic rule is written: q; p ⇒ q, p. That is, we start with a single premise, q, and infer from that both p ⇒ q and p. The reason for this, as explained by Roozenburg , is that abduction assumes that the proposed design, p, must exist as a premise of the rule. If it must exist, then it cannot be new. If this is so, then abduction cannot capture any sense of "new designs" or "innovative designs."
This is not an unreasonable reading of the rule for abductive inference. In making an inference, all the premises must be true for the inference to hold; therefore, the design (idea) must be known before abductive inference can be performed.
However, I think there are two significant problems with this interpretation.
First, Eekels's and Roozenburg's arguments against abduction assume that no other reasoning occurs except the abductive inference. If the only reasoning step we can take is the abductive inference, then they are correct, the design must be known before the inference is carried out. However, that's not how design happens. All other kinds of reasoning can happen, interwoven with the abduction. Indeed, the entire act of designing happens largely between when q (the requirements) is known and p is proposed. The statement p ⇒ q can be read as "the design implies the requirements are met;" it's essentially the verification step of any design process. Once we have verified that a design satisfies the requirements, then we can claim the design (p) as an abductive conclusion. How exactly the design process is modelled is another question entirely, and is irrelevant to establishing whether abduction makes sense or not.
Second - and this one is quite controversial - is the assumption that there is such a thing as a "new idea." Innoduction is motivated by the need to capture new ideas, which it is claimed is not the case in abduction. Strictly speaking, though, it is only an assumption that new ideas exist. While at first blush it seems rather obvious that such a thing as a new idea can be developed, it depends on how "new" is defined.
One sense of "new" is that of a creation completely novel, having arisen spontaneously out of nothing from a person's mind. I disagree that such new ideas exist. Consider the following - admittedly somewhat macabre - thought experiment. Imagine a human being being born in complete sensory isolation and spending its entire life in complete sensory isolation. What would such a human think? Would it think at all? What would it think about? It seems evident that such a human would not think at all because it would lack entirely any inputs to drive that thinking. That is to say, we think because we have sensory inputs to drive that thinking. Everything we think about is driven by something external to our minds, so any idea we have is ultimately grounded in some external input. So the notion of a spontaneous, out-of-nothing idea occurring to anyone just doesn't make sense.
Another sense of "new" is a relativistic one, based on what is known in a particular range of cases. Where the boundary is set to define the set of cases of pertinence is often an indicator of just how "new" a particular solution might seem. A classic example is Velcro. Within the scope of known fastening technologies of the time, Velcro was certainly a highly innovative (new) product. However, it happens that Velcro was developed as a result of analogical reasoning based on observations of how burrs became trapped in dog fur. So, one cannot say that Velcro was invented "out of nothing;" it was in fact invented as a result of reasoning about external stimuli. Indeed, I cannot find a single instance of a design - no matter how radical or innovative - that wasn't grounded in reasoning about some other existent phenomena. Under this reading, there really isn't anything new.
The newness appears when one draws an arbitrary boundary around a particular domain of interest. Velcro is new with respect to fasteners, but not with respect to biological systems; the PalmPilot was new with respect to personal computers, but not with respect to PIMs (which include paper agendas, which were, incidentally, the inspiration for the most fundamental functions of the PalmPilot); the iPhone was new with respect to other phones, but not with respect to atypical uses people had already found for iPods (where each of those atypical uses were new with respect to music players, but not new with respect to other computers of the time).
So, it would appear that innoduction is a form of inference that is unnecessary - what it can do for design theory can also be done by abduction.
- J. Eekels. 2000. On the fundamentals of engineering design science: The geography of engineering design science. Part 1. J. Eng. Design, 11(4):377-397.
- Roozenburg, N.F.M. 2002. Defining synthesis: on the senses and the logic of design synthesis. In Engineering Design Synthesis: Understanding, Approaches and Tools. A. Chakrabarti, ed. Pages 3-16. Springer.