1. Compare and contrast deductive and inductive reasoning. Use examples to explain.
Deductive and inductive reasoning share the aim of holding valid arguments and are based on evidence however deductive reasoning uses top-down logic by moving from generalisation to more specifics, for example, testing a theory through a hypothesis. Deductive reasoning draws a conclusion which are very much or certainly valid as long as the premises which allowed the conclusion to be reached has some truth (Eysenck & Keane, 2015).
Whereas, inductive reasoning uses bottom-up logic by looking at specifics and then drawing generalisations, for example, looking at a population data within a specific time period and then using that data to predict what the population will be in the future. Furthermore, inductive reasoning does not reach a valid conclusion but reaches a probabilistic generalised one which may or may not be true. This is done by looking at a set of evidence. (Liew, Grisham & Hayes, 2018).
A popular form of deductive reasoning is syllogism.
One type is categorical syllogism, where two premises (statements): a minor and a major reach a logical conclusion, altogether forming three components. It follows the pattern and logic of If A is part of C then B is also a part of C. An example is:
Every shark is a fish. (minor premise)
Therefore, every shark can swim. (conclusion)
However, the conclusion reached is not always valid even if logical. To prove a syllogism valid, the axiomatic method should be carried out.
A valid syllogism must meet any of the five axioms which can include both premises being negative so there is no valid conclusion. This is somewhat similar to inductive reasoning as it is not always guaranteed to be valid but inductive uses method types such as generalisation, predictions etc to reach its conclusion which may not be correct or logical. An example using inductive reasoning with a predictive type is: I visited this pond last year where all the swans were white. Therefore, when I visit again, all the swans will probably be white.
2. Why do we find Wasons selection task so difficult?
Wasons selection task is shown as an abstract and indicative task (Evans, 2003). During the task, participants are shown for example, 4 cards: A, G, 7, 8. Task follows the rule of If P then Q so to correctly carry out the task, participants should select the card which has an A (P card) and the 8 card (not Q card) so the rule can be falsified. However, only approximately 10% of participants followed this rule. (Sperber, Cara & Girotto, 1995).
Due to Wasons selection task having a low success rate consistently over a large range of instructional variations, there has been much research carried out. This has led to many theories on why majority of people find the selection task so difficult.
One explanation is misinterpretation of the conditional statements in the task where participants may respond incorrectly due to having a misperception of what the task is asking of them or failing to reason logically and accurately from that misperception. It may even be both. (Osman & Laming, 1999). This may be because most participants perceive the rule to be a bi-conditional so end up looking at all 4 cards.
However, an early explanation of the Wasons selection task being difficult can be shown through the insight model. It states success in the task comes from how insightful we are when looking at the problem logically. From this, comes three levels of insight which show the importance of falsification; no insight which is a prediction of matching bias, partial insight where participants take all cards in to consideration even additional cards which may confirm the rule or falsify it and full insight which shows participants select the cards which can falsify the rule (Ragni, Kola & Johnson-Laird, 2017).
The original selection task does not have real-life context so it was found concrete content can help make reasoning easier as it uses familiar scenarios in its statements. This is shown when an experiment had the rule every time I go to Manchester, I go by car where 60% of participants correctly selected the cards. (Wason and Shapiro, 1971).
3. What are the predictions of Subjective Expected Utility theory for human decision making. How have deviations been explained?
Subjective Expected Utility (SEU) theory is based on five axiomatic foundations and are what contribute to the predictions for human decision making. The theory claims if a person is to stay within these axioms then they will be able to maximise their expected utility in their decision. Examples of the axiomatic foundations are the weak-order axiom which states preferences are transitive or the Archimedean axiom which are continuous in regard to the preference relationship. It simply means that no alternative to C should be less or more desirable than its other options. In other words, it is well-ordered (Karni, 2014).
From these five rules, three predictions for decision-making preferences have been derived: principle of transitivity, principle of invariance and principle of independence. However, these principles can be violated. For example, the invariance principle says when people are presented with the same options then the way that they process that decision should always have the same outcome. But this has not always been correct as shown in the Asian flu problem (Tversky & Kahneman, 1981) as framing effect can have an influence on a persons choice of decision. Framing effect is when there are different descriptions of a problem and because of this, there is a huge change in risk preferences. People using framing effect are more drawn to being risk-aversive when looking at gains in a problem but are risk-seeing when looking at the losses. The framing effect has been consistent in many other studies which have statistically shown an important framing effect (Druckman, 2000). This strongly supports the violation of invariance principle.
Prospect theory is a deviation to SEU theory and takes in to consideration the violation of the invariance principle. The theory states a person bases their choice on a reference point e.g. status-quo and are more alert about risks when looking at losses but with gains, they are risk-averse. This relates and supports the framing bias. Also, the last one is loss-aversion where losing something is more disheartening than the pleasure from gaining something (Bendor, 2001).
4. Using a specific puzzle or problem of your own choice, write out a plan (including diagram) of how to solve it using a state-action tree. Note: Do not use an example outlined in the lecture.
Figure 1. State-action tree of an 8 puzzle-problem
Figure 1 is a problem which can be solved using the state-action tree. This is done by looking at the sequence of actions which leads from the initial starting state (A) to the goal state being achieved (C4). The state-action tree shows all possible routes. A is shown as the initial starting state and this is perceived as the root of the tree. It is at the top because state-action trees are upside down. There are 4 operators which act as the rule, only these can be used to solve this problem: move the blank left, move the blank right, move the blank up or move the blank down (Sullivan, 2012). For the goal state to be achieved, the focus is solely on moving the blank space, so all numbers are in the correct order.
Due to the problem being short and simple, it is best to use a systematic search method: depth first or breadth first to solve it. However, looking at figure 1, it is best to use depth first as this explores the search further from the root node (initial starting state). Depth first search always expands on the initial state and then works downwards, expanding the deepest node and following one branch of the search tree hence exploring it vertically. Using this method will achieve the goal state with fewest costs as there will be less sequence of actions but the solution found may not be the best one. However, it is much less time-consuming than the breadth first search (Latham, 2017).
5. What is creativity and how can it be assessed?
Creativity is when one thinks outside of the box when looking at unusual or insightful solutions. The creative solutions should be useful, utilising and be approved by society. Creativity is a concept shown in many different ways in different authorities: it is problem-solving in a mathematics perspective but innovation in education (Gomez, 2007). The four Ps framework has been established in studying the perspectives on creativity: person, product, place and process (Runco & Kim, 2018).
In psychology, the main approaches to assessing creativity is the psychometric approach and the biographic and autobiographic approach. When assessing creativity from a psychometric outlook, Guilford (1956) is famous for his work on believing divergent thinking to be a crucial factor of creativity (Wu, Jung & Zhang, 2016). He established a four-measure divergent production which essentially looks at the maximum effort of an individual on how many possible solutions they can think of when looking at the same problem. This has been used in many contexts which assess creativity such as music, for example, a psychometric test; Measures of Musical Divergent Production (MMDP) combined Guilfords divergent productions four devised measures: fluency, flexibility, originality and quality in the MMDP. Examples on how these measures were demonstrated are shown by fluency being assessed on how many improvised phrases were shown as this measure is about how many responses an individual can produce. Whereas, the flexibility measure was demonstrated when tested on the varied use of musical content as this is a measurement of how many types of responses are given. (Gorder, 1980).
The biographic and autographic approach shows creativity is assessed on 4 stages in the creative process (Wallas, 1926). These stages are preparation, incubation, illumination and verification. For example, the incubation stage follows on from preparation where the brain absorbs information from different materials to then letting it go by consciously not thinking about it through substituting it with another activity as this leads to better creativity (Stillman, 2016). However, the role of the incubation stage is controversial as it remains unsure whether unconscious work theory leads to creative thinking or conscious work theory (Ritter & Dijksterhuis, 2014).