Deductive Reasoning
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There Is No Pure Empirical Reasoning
There Is No Pure Empirical Reasoning 1. Empiricism and the Question of Empirical Reasons Empiricism may be defined as the view there is no a priori justification for any synthetic claim. Critics object that empiricism cannot account for all the kinds of knowledge we seem to possess, such as moral knowledge, metaphysical knowledge, mathematical knowledge, and modal knowledge.1 In some cases, empiricists try to account for these types of knowledge; in other cases, they shrug off the objections, happily concluding, for example, that there is no moral knowledge, or that there is no metaphysical knowledge.2 But empiricism cannot shrug off just any type of knowledge; to be minimally plausible, empiricism must, for example, at least be able to account for paradigm instances of empirical knowledge, including especially scientific knowledge. Empirical knowledge can be divided into three categories: (a) knowledge by direct observation; (b) knowledge that is deductively inferred from observations; and (c) knowledge that is non-deductively inferred from observations, including knowledge arrived at by induction and inference to the best explanation. Category (c) includes all scientific knowledge. This category is of particular import to empiricists, many of whom take scientific knowledge as a sort of paradigm for knowledge in general; indeed, this forms a central source of motivation for empiricism.3 Thus, if there is any kind of knowledge that empiricists need to be able to account for, it is knowledge of type (c). I use the term “empirical reasoning” to refer to the reasoning involved in acquiring this type of knowledge – that is, to any instance of reasoning in which (i) the premises are justified directly by observation, (ii) the reasoning is non- deductive, and (iii) the reasoning provides adequate justification for the conclusion. -
A Philosophical Treatise on the Connection of Scientific Reasoning
mathematics Review A Philosophical Treatise on the Connection of Scientific Reasoning with Fuzzy Logic Evangelos Athanassopoulos 1 and Michael Gr. Voskoglou 2,* 1 Independent Researcher, Giannakopoulou 39, 27300 Gastouni, Greece; [email protected] 2 Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, Greece * Correspondence: [email protected] Received: 4 May 2020; Accepted: 19 May 2020; Published:1 June 2020 Abstract: The present article studies the connection of scientific reasoning with fuzzy logic. Induction and deduction are the two main types of human reasoning. Although deduction is the basis of the scientific method, almost all the scientific progress (with pure mathematics being probably the unique exception) has its roots to inductive reasoning. Fuzzy logic gives to the disdainful by the classical/bivalent logic induction its proper place and importance as a fundamental component of the scientific reasoning. The error of induction is transferred to deductive reasoning through its premises. Consequently, although deduction is always a valid process, it is not an infallible method. Thus, there is a need of quantifying the degree of truth not only of the inductive, but also of the deductive arguments. In the former case, probability and statistics and of course fuzzy logic in cases of imprecision are the tools available for this purpose. In the latter case, the Bayesian probabilities play a dominant role. As many specialists argue nowadays, the whole science could be viewed as a Bayesian process. A timely example, concerning the validity of the viruses’ tests, is presented, illustrating the importance of the Bayesian processes for scientific reasoning. -
The Mathematics of Causal Relations
In P.E. Shrout, K. Keyes, and K. Ornstein (Eds.), Causality and Psychopathology: Finding the TECHNICAL REPORT Determinants of Disorders and their Cures, Oxford University Press, 47-65, 2010. R-338 September 2010 The Mathematics of Causal Relations Judea Pearl Introduction Almost two decades have passed since Paul Holland published his highly cited review paper on the Neyman-Rubin approach to causal inference [Holland, 1986]. Our understanding of causal inference has since increased severalfold, due primarily to advances in three areas: 1. Nonparametric structural equations 2. Graphical models 3. Symbiosis between counterfactual and graphical methods These advances are central to the empirical sciences because the research questions that motivate most studies in the health, social, and behavioral sciences are not statistical but causal in nature. For example, what is the efficacy of a given drug in a given population? Can data prove an employer guilty of hiring discrimination? What fraction of past crimes could have been avoided by a given policy? What was the cause of death of a given individual in a specific incident? Remarkably, although much of the conceptual framework and many of the algorithmic tools needed for tackling such problems are now well established, they are hardly known to researchers in the field who could put them into practical use. Why? Solving causal problems mathematically requires certain extensions in the standard mathematical language of statistics, and these extensions are not generally emphasized in the mainstream literature and education. As a result, large segments of the statistical research community find it hard to appreciate and benefit from the many results that causal analysis has produced in the past two decades. -
Causal Knowledge and the Development of Inductive Reasoning ⇑ Aimée K
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Journal of Experimental Child Psychology 122 (2014) 48–61 Contents lists available at ScienceDirect Journal of Experimental Child Psychology journal homepage: www.elsevier.com/locate/jecp Causal knowledge and the development of inductive reasoning ⇑ Aimée K. Bright a, , Aidan Feeney b a Psychology Division, School of Biological and Chemical Sciences, Queen Mary University of London, London E1 4NS, UK b School of Psychology, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, UK article info abstract Article history: We explored the development of sensitivity to causal relations in chil- Received 5 April 2013 dren’s inductive reasoning. Children (5-, 8-, and 12-year-olds) and Revised 27 November 2013 adults were given trials in which they decided whether a property Available online 8 February 2014 known to be possessed by members of one category was also possessed by members of (a) a taxonomically related category or (b) a causally Keywords: related category. The direction of the causal link was either predictive Category-based induction Causal knowledge (prey ? predator) or diagnostic (predator ? prey), and the property Causal asymmetry that participants reasoned about established either a taxonomic or cau- Taxonomic knowledge sal context. There was a causal asymmetry effect across all age groups, Inductive selectivity with more causal choices when the causal link was predictive than Knowledge over-generalization when it was diagnostic. Furthermore, context-sensitive causal reason- ing showed a curvilinear development, with causal choices being most frequent for 8-year-olds regardless of context. -
UNIVERSITY of CALIFORNIA Los Angeles Causal Action: A
UNIVERSITY OF CALIFORNIA Los Angeles Causal Action: A Framework to Connect Action Perception and Understanding A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Psychology by Yujia Peng 2019 ©Copyright by Yujia Peng 2019 ABSTRACT OF THE DISSERTATION Causal Action: A Framework to Connect Action Perception and Understanding by Yujia Peng Doctor of Philosophy in Psychology University of California, Los Angeles, 2019 Professor Hongjing Lu, Chair Human actions are more than mere body movements. In contrast to dynamic events involving inanimate objects, human actions have a special status in that they control interactions with the world and afford privileged access to the experience of agency and to control interactions with the world. Several causal constraints on human actions support the generation and the understanding of actions. For example, human actions inherently involve a causal structure: limb movements generally cause changes in body position along a path through the environment to achieve intentional goals. However, it remains unclear how the system that supports action perception communicates with high-level reasoning system to recognize actions, and more importantly, to achieve a deeper understanding of observed actions. My dissertation aims to ii determine whether causality imposes critical motion constraints on action perception and understanding, and how causal relations involved in actions impact behavioral judgments. The project also investigates the developmental trajectory and neural substrate of action processing, and whether a feedforward deep learning model is able to learn causal relations solely from visual observations of human actions. Through behavioral experiments, an infant eye movement study, a neural study using magnetoencephalography, and model simulations, my dissertation yields a number of insights. -
Novel Pancreatic Endocrine Maturation Pathways Identified by Genomic Profiling and Causal Reasoning
Novel Pancreatic Endocrine Maturation Pathways Identified by Genomic Profiling and Causal Reasoning Alex Gutteridge2*, J. Michael Rukstalis1,4, Daniel Ziemek3, Mark Tie´ 1, Lin Ji1,4, Rebeca Ramos-Zayas1, Nancy A. Nardone4, Lisa D. Norquay4, Martin B. Brenner4, Kim Tang1, John D. McNeish1, Rebecca K. Rowntree1* 1 Pfizer Regenerative Medicine, Cambridge, Massachusetts, United States of America, 2 Pfizer Regenerative Medicine, Cambridge, United Kingdom, 3 Pfizer Computational Sciences Center of Emphasis, Cambridge, Massachusetts, United States of America, 4 Pfizer Cardiovascular and Metabolic Diseases, Cambridge, Massachusetts, United States of America Abstract We have used a previously unavailable model of pancreatic development, derived in vitro from human embryonic stem cells, to capture a time-course of gene, miRNA and histone modification levels in pancreatic endocrine cells. We investigated whether it is possible to better understand, and hence control, the biological pathways leading to pancreatic endocrine formation by analysing this information and combining it with the available scientific literature to generate models using a casual reasoning approach. We show that the embryonic stem cell differentiation protocol is highly reproducible in producing endocrine precursor cells and generates cells that recapitulate many aspects of human embryonic pancreas development, including maturation into functional endocrine cells when transplanted into recipient animals. The availability of whole genome gene and miRNA expression data from the early stages of human pancreatic development will be of great benefit to those in the fields of developmental biology and diabetes research. Our causal reasoning algorithm suggested the involvement of novel gene networks, such as NEUROG3/E2F1/KDM5B and SOCS3/STAT3/IL-6, in endocrine cell development We experimentally investigated the role of the top-ranked prediction by showing that addition of exogenous IL-6 could affect the expression of the endocrine progenitor genes NEUROG3 and NKX2.2. -
Analysis - Identify Assumptions, Reasons and Claims, and Examine How They Interact in the Formation of Arguments
Analysis - identify assumptions, reasons and claims, and examine how they interact in the formation of arguments. Individuals use analytics to gather information from charts, graphs, diagrams, spoken language and documents. People with strong analytical skills attend to patterns and to details. They identify the elements of a situation and determine how those parts interact. Strong interpretations skills can support high quality analysis by providing insights into the significance of what a person is saying or what something means. Inference - draw conclusions from reasons and evidence. Inference is used when someone offers thoughtful suggestions and hypothesis. Inference skills indicate the necessary or the very probable consequences of a given set of facts and conditions. Conclusions, hypotheses, recommendations or decisions that are based on faulty analysis, misinformation, bad data or biased evaluations can turn out to be mistaken, even if they have reached using excellent inference skills. Evaluative - assess the credibility of sources of information and the claims they make, and determine the strength and weakness or arguments. Applying evaluation skills can judge the quality of analysis, interpretations, explanations, inferences, options, opinions, beliefs, ideas, proposals, and decisions. Strong explanation skills can support high quality evaluation by providing evidence, reasons, methods, criteria, or assumptions behind the claims made and the conclusions reached. Deduction - decision making in precisely defined contexts where rules, operating conditions, core beliefs, values, policies, principles, procedures and terminology completely determine the outcome. Deductive reasoning moves with exacting precision from the assumed truth of a set of beliefs to a conclusion which cannot be false if those beliefs are untrue. Deductive validity is rigorously logical and clear-cut. -
Development of Causal Reasoning
The Development of Causal Reasoning Oxford Handbooks Online The Development of Causal Reasoning Paul Muentener and Elizabeth Bonawitz The Oxford Handbook of Causal Reasoning Edited by Michael R. Waldmann Print Publication Date: Jun 2017 Subject: Psychology, Cognitive Psychology Online Publication Date: May 2017 DOI: 10.1093/oxfordhb/9780199399550.013.40 Abstract and Keywords Research on the development of causal reasoning has broadly focused on accomplishing two goals: understanding the origins of causal reasoning, and examining how causal reasoning changes with development. This chapter reviews evidence and theory that aim to fulfill both of these objectives. In the first section, it focuses on the research that explores the possible precedents for recognizing causal events in the world, reviewing evidence for three distinct mechanisms in early causal reasoning: physical launching events, agents and their actions, and covariation information. The second portion of the chapter examines the question of how older children learn about specific causal relationships. It focuses on the role of patterns of statistical evidence in guiding learning about causal structure, suggesting that even very young children leverage strong inductive biases with patterns of data to inform their inferences about causal events, and discussing ways in which children’s spontaneous play supports causal learning. Keywords: development, causal reasoning, learning, induction, bias Causality plays a fundamental role in human cognition, and has long been a topic of interest for many developmental researchers—causal reasoning has been proposed to be a central aspect of early learning in the physical (Baillargeon, 2004; Carey, 2009; Cohen, Amsel, Redford, & Casasola, 1998; Leslie, 1995; Spelke, 1990), psychological (Csibra & Gergely, 1998; Gopnik & Wellman, 1992; Meltzoff, 2007; White, 2014; Woodward, 2009), and biological world (Carey, 2009; Wellman & Gelman, 1992). -
1/4 New Caledonian Crows Afford Invaluable Comparative Insights Into
Target article: Osiurak and Reynaud Word counts: abstract (60 words), main text (995), references (1191), entire text (2356) New Caledonian crows afford invaluable comparative insights into human cumulative technological culture Christian Rutza,b and Gavin R. Huntc aCentre for Biological Diversity, School of Biology, University of St Andrews, St Andrews KY16 9TH, UK; bRadcliffe Institute for Advanced Study, Harvard University, Cambridge MA 02138, USA; and cUnaffiliated. +1 617 899 6744 (C.R.) [email protected] [email protected] https://aviantooluse.org Abstract The New Caledonian crow may be the only non-primate species exhibiting cumulative technological culture. Its foraging tools show clear signs of diversification and progressive refinement, and it seems likely that at least some tool-related information is passed across generations via social learning. Here, we explain how these remarkable birds can help us uncover the basic biological processes driving technological progress. Cumulative culture – the social transmission and accumulation of innovations across generations – has enabled humans to develop technologies of astonishing complexity (Boyd & Richerson 1996). Osiurak and Reynaud (O&R) present a timely re-evaluation of the potential cognitive capacities enabling this process, shifting the focus from social-learning to technical-reasoning skills. We enjoyed O&R’s fresh perspective, but were surprised that they did not examine more carefully their starting assumption that only humans possess cumulative technological culture. Two non-human species have been suggested to refine their foraging tools in a cumulative manner – one of our closest relatives, the chimpanzee, and a tropical corvid, the New Caledonian crow (Dean et al. 2014). -
Relations Between Inductive Reasoning and Deductive Reasoning
Journal of Experimental Psychology: © 2010 American Psychological Association Learning, Memory, and Cognition 0278-7393/10/$12.00 DOI: 10.1037/a0018784 2010, Vol. 36, No. 3, 805–812 Relations Between Inductive Reasoning and Deductive Reasoning Evan Heit Caren M. Rotello University of California, Merced University of Massachusetts Amherst One of the most important open questions in reasoning research is how inductive reasoning and deductive reasoning are related. In an effort to address this question, we applied methods and concepts from memory research. We used 2 experiments to examine the effects of logical validity and premise– conclusion similarity on evaluation of arguments. Experiment 1 showed 2 dissociations: For a common set of arguments, deduction judgments were more affected by validity, and induction judgments were more affected by similarity. Moreover, Experiment 2 showed that fast deduction judgments were like induction judgments—in terms of being more influenced by similarity and less influenced by validity, compared with slow deduction judgments. These novel results pose challenges for a 1-process account of reasoning and are interpreted in terms of a 2-process account of reasoning, which was implemented as a multidimensional signal detection model and applied to receiver operating characteristic data. Keywords: reasoning, similarity, mathematical modeling An important open question in reasoning research concerns the arguments (Rips, 2001). This technique can highlight similarities relation between induction and deduction. Typically, individual or differences between induction and deduction that are not con- studies of reasoning have focused on only one task, rather than founded by the use of different materials (Heit, 2007). It also examining how the two are connected (Heit, 2007). -
Introduction to Deductive Logic
Introduction to Deductive Logic Part I: Logic & Language There is no royal road to logic, and really valuable ideas can only be had at the price of close attention. Charles Saunders Peirce INTRODUCTION TO DEDUCTIVE LOGIC PART I: LOGIC AND LANGUAGE I. INTRODUCTION What is Logic? . 4 What is an argument? . 5 Three Criteria for Evaluating Arguments . 6 II. ARGUMENT ANALYSIS – PART 1 Preliminary Issues . 9 Statements and Truth Value Premises and Conclusions . 9 Statements vs Sentences 10 Simple vs Compound Statements 12 Recognizing premises and conclusions . 13 Indicator Language. 15 TWO TYPES OF ARGUMENTS Inductive Reasoning/Argument . 18 Deductive Reasoning/Argument . 19 III. ANALYSIS – PART II FORMALIZING ARGUMENT Preliminary Issue: Formal vs. Informal Argument . 24 Simple and Compound Statements . 25 Types of Compound Statements . 26 Formation Rules for Sentential . 26 DEFINING LOGICAL OPERATORS . 29 Negation . 29 Conjunction . 30 Disjunction . 31 Conditional/ Material Implication . 32 Bi-conditional . 33 APPLICATION: TRANSLATING USING LOGICAL OPERATORS . 35 TRUTH TABLE RULES/SUMMARY OF LOGICAL OPERATORS . 38 TRUTH TABLE APPLICATIONS . 39 Application I: Substitute and Calculate Method . 39 Application II: Calculating with Unknown Values . 41 Application III: Full Truth Table Method . 42 A Short Cut Technique for statements. 44 Truth Table Test for Logical Equivalence . 45 Application IV: Using Truth Tables to Facilitate Reasoning . 47 THE NEED FOR PREDICATE . 50 Using Predicate to Represent Categorical Statements . 52 Preliminary Issues– Grammar . 53 Formation Rules for Predicate . 55 Expressing Quantity . 56 APPLICATION: Symbolizing Categorical Statements using Predicate . 56 Negating Standard Form Categorical Statements. 57 Summary Chart for Standard Form Categorical Statements . 59 Extending Predicate . 61 A Universe of Discourse . -
1 Deductive Reasoning and Logical Connectives
Propositional Logic CS/Math231 Discrete Mathematics Spring 2015 1 Deductive Reasoning and Logical Connectives As we have seen, proofs play a central role in mathematics and they are based on deductive reasoning. Facts (or statements) can be represented using Boolean variables, i.e., the values of variables can only be true or false but not both. Definition 1 A statement (or proposition) is a sentence that is true or false but not both. Example 1 Examples of deductive reasoning: 1. I will have dinner either with Jody or with Ann. Jody is out of town. Therefore, I will have dinner with Ann. 2. If today is Wednesday, then I have to go to class. Today is Wednesday. Therefore, I have to go to class. 3. All classes are held either on Mondays and Wednesdays or on Tuesdays and Thursdays. There is no Discrete Math course on Tuesdays. Therefore, Discrete Math course is held on Mondays and Wednesdays. Definition 2 (premises and conclusion) A conclusion is arrived from assumptions that some state- ments, called premises, are true. An argument being valid means that if the premises are all true, then the conclusion is also true. Example 2 An example of an invalid deductive reasoning: Either 1+1=3 or 1+1=5. It is not the case that 1+1=3. Therefore, 1+1=5. p _ q p or q :p not p ) q Therefore, q If p and q are statement variables, then complicated logical expressions (compound statements) related to p and q can be built from logical connectives.