Reasoning – from math to any arbitrary problem

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Using this chatbot can help uncover the reasoning used in decision making. The chatbot test the reasoning abilities of AI large language models. It can be used to test solving basic mathematical problems –  e.g., “Solve for x: 2x + 5 = 11” or more complex nuanced problems that require nuanced reasoning. Given a problem you present it will first select all the types of reasoning that are applicable. It is self-evaluating and attempts to avoid typical human flaws in reasoning which AI is prone to do because of its creative word pattern generation mechanism (aka hallucinations). Once you have a reply to your problem statement you can continue to discuss by asking it to explain the logical reasoning it used, as well as which human flaws in reasoning that it avoided. You can prompt it to give you the formal logic, the first order logic, the higher order logic, as well as explore further the flaws typical in human decision making by testing the assumptions it is making as well as asking about your own assumptions about the problem.

Types of Reasoning:

Here are the 27 types of reasoning, along with an example for each:

  • Deductive Reasoning: Taking a generally true statement and applying it to a specific instance. Example: All mammals have lungs. Therefore, your pet dog, being a mammal, possesses lungs.
  • Inductive Reasoning: Starting with specific observations or facts and using them to form a generalized conclusion. Example: You notice that each time you eat a certain fruit, you experience an upset stomach. Based on these observations, you generalize that this particular fruit is likely causing your stomach upset.
  • Abductive Reasoning: Creating a probable explanation or hypothesis for a certain observation or set of facts. Example: You see wet pavement outside. The most plausible explanation might be that it just rained.
  • Analogical Reasoning: Drawing a comparison between two similar situations to make a point or draw a conclusion. Example: You want to explain the function of a cell in a human body. You could use an analogy of a factory where different parts have specific jobs, like parts of a cell.
  • Causal Reasoning: Identifying relationships between cause and effect. Example: Ms. Thompson noticed that whenever her dog is given a particular brand of dog food, it gets an upset stomach. Therefore, Ms. Thompson concludes that this particular dog food is not suited for her dog.
  • Critical Reasoning: The ability to analyze, evaluate, and form a judgment on an argument or a claim. Example: As an investor, you come across a new startup claiming to be the ‘next big thing’. Instead of taking their word, you critically evaluate their business plan, team, and market potential before deciding whether to invest.
  • Diagnostical Reasoning: Identifying the root cause of an issue by analyzing the symptoms or evidence at hand. Example: Your car isn’t starting. You notice the lights in the car aren’t coming on either. So, you reason the car’s battery might be the problem.
  • Moral Reasoning: The process of determining right from wrong in a given situation. Example: You find a wallet on the street. It contains money and an ID card. You reason that the ethical thing to do would be to return the wallet to its owner, even though you could easily keep the money.
  • Syllogistic Reasoning: A formal method of reasoning that uses deductive logic to draw conclusions from two or more propositions that are assumed to be true. Example: All birds can fly. A penguin is a bird. Therefore, one might incorrectly reason that a penguin can fly.
  • Probabilistic Reasoning: Involving making predictions about events based on known probabilities. Example: If a weather forecast says there is a 90% chance of rain, you would probably bring an umbrella when you go out, reasoning that it’s highly likely to rain.
  • Counterfactual Reasoning: Contemplating how different outcomes could have resulted if certain factors had been different. Example: If the driver had not been distracted by the phone, the car accident might not have occurred.
  • Intuitive Reasoning: Drawing a conclusion or making a decision based on an instinctive feeling rather than conscious reasoning. Example: Without knowing why, you might intuitively feel like a certain house is the right one to buy, despite seeing several other technically superior options.
  • Retroductive Reasoning: A form of inference where the best possible explanation for a specific event or occurrence is drawn. Example: A doctor observes a range of disparate symptoms in a patient and works backward to diagnose the potential disease causing them.
  • Reductive Reasoning: Simplifying broad concepts into smaller, more manageable ones. Example: From a broad study of global warming, you might reduce topics to individual elements such as greenhouse gas emissions, deforestation, and ocean temperature changes.
  • Transductive Reasoning: Drawing specific conclusions from two unrelated events that happen simultaneously. Example: A child watches you pressing a button on a remote, simultaneously the TV turns on. The child may conclude that the TV only works when you press the button.
  • Fallacious Reasoning: A logical fallacy that leads to invalid argumentation. Example: Assuming that something is better simply because it’s more expensive or popular, which is known as the ‘appeal to popularity’ or ‘bandwagon’ fallacy.
  • Historical Reasoning: Involves using the past to understand the present and predict future circumstances. Example: Considering how past pandemics were dealt with to devise strategies for managing a current health crisis.
  • Pragmatic Reasoning: Decision-making based on practicality or what is realistically workable. Example: A company facing a financial crunch might cut certain budgets to stay afloat in the short term, even though long-term innovation might be hampered as a result.
  • Dialectical Reasoning: Involves the juxtaposition of contrasting ideas or propositions, aiming to resolve the contradictions and establish truth. Example: In philosophy, thesis and antithesis are presented as conflicting views, and through a process of argument and counter-argument, a synthesis is attempted that resolves the conflict.
  • Empirical Reasoning: Refers to conclusions drawn from observed or experimented data. Example: A scientist makes an observation that animals in colder climates tend to be larger. After conducting large-scale data collection and analysis across diverse climate zones, the scientist confirms this pattern and reasons that in colder climates, larger body size may aid in preserving heat, a concept known as Bergmann’s rule.
  • Practical Reasoning: Involves making decisions based on what should or ought to be done to achieve a specific goal or objective. Example: A student needs better grades to get into a selective college. Knowing this, she decides to allot more time to study each day, limit distractions, and seek out additional academic resources.
  • Formal Reasoning: A specific type of problem-solving based on rigid rules of logic. Example: In mathematics, if ‘A’ equals ‘B’, and ‘B’ equals ‘C’, then it is always true that ‘A’ equals ‘C’.
  • Statistical Reasoning: Involves interpreting, analysing, and drawing conclusions from data sets to understand and react to phenomena. Example: Analysts look at the data from a marketing campaign, noticing patterns and trends. For instance, they might deduce that sales numbers increase each time a particular ad runs, allowing them to make future marketing decisions.
  • Lateral Reasoning: Also known as lateral thinking, involves approaching problems in inventive and unconventional ways. Example: An entrepreneur devises a new way to cut costs in production, not by tweaking the current process (as would be the traditional approach), but by completely reinventing it.
  • Reflective Reasoning: Involves the process of meta-thinking – thinking about how and why we think a certain way. Example: If you’ve had an argument and reacted angrily, reflective reasoning helps you review your own thoughts and emotions during the incident, and evaluate whether your response was reasonable or if other factors unduly influenced your reaction.
  • Quantitative Reasoning: Revolves around solving problems with the help of mathematical concepts and reasoning. Example: If a company wants to estimate future earnings, they might use past sales data, apply growth rates, and predict future revenue.
  • Circular Reasoning: When the premise is the same as the conclusion; the argument is repeating itself without bringing any new information. Example: Someone might say, “I’m trustworthy because I always keep my word,” but being trustworthy and keeping one’s word are the same concept, making the reasoning circular and ineffective.

Flaws in Human Reasoning – that should be avoided, along with their definitions and examples:

  • Cognitive Biases: These are systematic patterns of deviation from norm or rationality in judgment.
    • Confirmation Bias: Favoring information that confirms existing beliefs and ignoring contradictory evidence.
      • Example: A person who believes that climate change is not real only reads articles from sources that support this view and ignores scientific studies that show evidence of climate change.
    • Hindsight Bias: Believing an event was predictable after it has already occurred.
      • Example: After a stock market crash, people might say, “I knew it was going to happen,” even if they didn’t predict it beforehand.
    • Anchoring Bias: Over-relying on an initial piece of information, even if it’s irrelevant.
      • Example: When negotiating the price of a used car, the first price offered (the anchor) can heavily influence what the buyer is willing to pay, even if that initial price is unreasonable.
    • Availability Heuristic: Overestimating the likelihood of events that are easily recalled, even if they are not representative.
      • Example: People might overestimate the risk of dying in a plane crash because these events are highly publicized and easily come to mind, even though car accidents are far more common.
    • Belief Bias: Allowing the believability of a conclusion to influence the evaluation of the logical strength of an argument.
      • Example: People might accept a poorly reasoned argument if the conclusion aligns with their existing beliefs and reject a well-reasoned argument if the conclusion contradicts their beliefs.
    • Overconfidence: Overestimating one’s own abilities and knowledge.
      • Example: A student might wait until the last minute to study for an exam because they are overconfident in their ability to quickly learn the material.
    • Illusion of Control: Believing that one has more control over outcomes than they actually do.
      • Example: Someone might repeatedly choose their own lottery numbers, believing this gives them a better chance of winning, even though the outcome is purely random.
    • Framing Effect: Making different decisions based on how information is presented.
      • Example: People are more likely to choose a surgery with a “90% survival rate” than one with a “10% mortality rate,” even though these two statements describe the same outcome.
    • Loss Aversion: Feeling the pain of a loss more strongly than the pleasure of an equivalent gain.
      • Example: People might be more hesitant to sell a stock that has decreased in value, hoping to avoid the feeling of loss, even if it would be a financially sound decision to sell.
    • Bandwagon Effect: Following the opinions or actions of the majority, even if they are not well-founded.
      • Example: A person might start supporting a particular political candidate simply because they see that most of their friends and colleagues support that candidate.
  • Reliance on Intuition and Heuristics: These involve making judgments based on mental shortcuts or gut feelings.
    • Premature Intuition: Making judgments based on gut feelings without sufficient evidence or analysis.
      • Example: A manager might hire a candidate based on a “good feeling” during the interview, without thoroughly reviewing their qualifications and experience.
    • Over-reliance on “System 1” thinking: Using fast, intuitive reasoning instead of slower, more analytical “System 2” thinking.
      • Example: Quickly accepting a seemingly straightforward solution to a complex problem without taking the time to analyze it thoroughly.
  • Ignoring Important Information:
    • Ignoring Base Rates: Failing to consider the overall probability of an event when making judgments.
      • Example: Being overly concerned about a rare disease after seeing a news report about it, without considering how uncommon the disease actually is in the general population.
    • Prosecutor’s Fallacy: Misinterpreting the probability of evidence given an assumption as the probability of the assumption given the evidence.
      • Example: In a criminal trial, if the probability of a specific piece of DNA evidence being found in an innocent person is very low, the prosecutor might incorrectly argue that the probability of the defendant being innocent given the evidence is also very low.
    • Ignoring Heterogeneity: Failing to account for individual differences and complexities when making generalizations.
      • Example: Assuming that all members of a particular demographic group share the same opinions or characteristics.
    • Ignoring Dependencies: Failing to consider the influence of multiple factors when making predictions.
      • Example: Predicting the success of a new product solely based on its features, without considering market trends, competition, and economic conditions.
  • Fallacies in Reasoning: These are flaws in the structure of an argument that render the argument invalid.
    • Ad Hominem: Attacking the person making an argument rather than the argument itself.
      • Example: Dismissing a scientist’s argument about climate change by saying they are politically motivated, rather than addressing the scientific evidence.
    • Straw Man: Misrepresenting someone’s argument to make it easier to attack.
      • Example: Person A argues for stricter gun control. Person B misrepresents their argument by saying Person A wants to take away all guns from everyone, and then attacks this exaggerated claim.
    • Appeal to Ignorance: Claiming something is true because it has not been proven false.
      • Example: “No one has proven that ghosts don’t exist, therefore ghosts must be real.”
    • Slippery Slope: Arguing that a particular action will inevitably lead to a series of increasingly negative consequences.
      • Example: “If we allow students to use phones in class, soon they will be watching movies, then they will stop paying attention altogether, and eventually, the quality of education will drastically decline.”
    • False Dilemma: Presenting only two options when more exist.
      • Example: “You are either with us, or against us.”
    • Hasty Generalization: Drawing conclusions before having enough information.
      • Example: After meeting two rude people from a certain city, concluding that everyone from that city is rude.
    • Confusing Correlation with Causation: Concluding that two things are causally related because they are correlated.
      • Example: Ice cream sales and crime rates tend to increase during the summer. Concluding that increased ice cream sales cause higher crime rates (or vice versa) is a fallacy, as both might be influenced by a third factor like warmer weather.
    • Circular Reasoning: When the premise is the same as the conclusion; the argument is repeating itself without bringing any new information [Our Conversation History].
      • Example: “This law is necessary because it is the law.”