Teaching About How Scientists Make Inferences with Science You Can’T See from Seeds of Science/Roots of Reading®

Total Page:16

File Type:pdf, Size:1020Kb

Teaching About How Scientists Make Inferences with Science You Can’T See from Seeds of Science/Roots of Reading® Strategy Guide Teaching About How Scientists Make Inferences with Science You Can’t See from Seeds of Science/Roots of Reading® Introduction permission. This strategy guide introduces an approach for teaching about how scientists use evidence to make inferences. The ability to gather and further evaluate evidence is central to scientific inquiry, especially when scientists investigate things that are not directly observable. This guide without includes an introductory section about how scientists use evidence to use make inferences, a general overview of how to use this strategy with many science texts, and a plan for teaching how scientists gather evidence to make inferences with the Seeds of Science/Roots of Reading® book classroom Science You Can’t See. than other use or Book Summary Science Background Science You Can’t See introduces readers to the Some scientists investigate things that they work of three scientists who study phenomena cannot observe directly. For example, scientists redistribution, that cannot be observed directly. Karen Chin cannot see dinosaurs, the bottom of the ocean, studies dinosaurs using fossilized remains. or atoms and molecules. Still, scientists want to resale, Edward Saade investigates the depth of know more about these things, so they gather for the ocean floor using sound waves. Farid El evidence about them in other ways. For example, Not Gabaly makes images of magnetic atoms using they make observations of fossil dinosaur an electron microscope. Each of these three droppings or measure the amount of time it scientists must make inferences to answer their takes sound to travel to the bottom of the ocean. California. questions. Their inferences are based on evidence Although atoms and molecules are too small to of that they collect during their investigations. see, scientists use very powerful microscopes to Readers learn that scientists gather and gather evidence about them. Once scientists have interpret evidence and draw conclusions based gathered evidence, they use it to make inferences University on this evidence. about the things they are investigating. For the example, when scientists figure out what is in of a fossil dinosaur dropping, they can then make inferences about what the dinosaur ate when it Regents About This Book was alive. They are not observing the dinosaur The eating—they are using evidence to make an Reading Level Guided Reading Level*: R inference. Similarly, by measuring the amount of time it takes for sound to travel to the ocean Key Vocabulary Copyright floor, scientists are able to make inferences about © accurate, evaluate, evidence, inference, observation how deep the ocean is and what the ocean floor is Text Features bold print, captions, diagrams, glossary, headings, like. Over time, scientists gather more evidence illustrations, labels, maps, photographs, table of and become more and more sure of the inferences contents they have made. *Guided Reading Levels based on the text characteristics from Fountas and Pinnell, Matching Books to Readers. 5 6 1 About Making Inferences between what can be directly observed and inferences that can be made from these Scientists answer questions by gathering and observations. [The coat, the umbrella, the evaluating evidence. One way scientists gather wet shoes. It is raining.] evidence is through firsthand observation; however, sometimes scientists ask questions • Have students practice making observations about things that are not immediately and inferences. Invite them to observe observable. For example, scientists cannot a photograph or an object and share directly observe an extinct organism or the the observations they make. List their surface of a faraway planet. In these instances, observations first, then ask students to make scientists use inferential reasoning to figure out inferences based on their observations. Some permission. answers to their questions based on evidence examples include the following: gathered through observations and from a. Observation: An apple has a missing chunk. further information that they or other scientists have Inference: Someone took a bite of the apple. already discovered about the topic. Scientists without b. Observation: A girl is dressed in shorts understand that inferences are always subject use to revision as new evidence becomes available and a jersey and is holding a basketball. or new ways of thinking emerge. Understanding Inference: The girl is on a basketball team. that observations are based only on what one c. Observation: There are shoe-shaped classroom can detect firsthand can help students learn footprints in the mud. Inference: A person than how scientists make inferences. Distinguishing has been here. between observations and inferences can help other students better understand how scientists use d. Observation: There are pieces of eggshell use evidence to answer questions. in a nest. Inference: A bird hatched from or the egg. Teaching About How Scientists • Ask students to preview the text you have selected and identify one or more questions redistribution, Make Inferences that a scientist can investigate. Focus students’ attention on sources of evidence that the resale, The following guidelines can be used to teach how scientist might use to answer the question(s). for scientists make inferences based on observations. • Have students read the text and pay careful Not • Select an appropriate text. Choose a book or attention to the parts that explain how the an article that discusses the work of various scientist gathers evidence. You may wish to scientists. Good examples include books about have students use the Evidence and Inferences California. paleontologists, astronomers, chemists, or copymaster, included in this guide, to help of other scientists who rely on evidence to make focus their reading. inferences. • Discuss different types of evidence with University • Tell students that scientists learn about the students. Guide students in listing some the world by observing, but that they cannot ways that the scientists gather evidence of always observe everything firsthand. Explain to inform their inferences. Discuss what that scientists often use evidence to make inferences the scientists make based on the Regents inferences about something they are studying. evidence. Encourage students to summarize The Explain that an inference is like a good guess the reasoning that the scientists used to make based on evidence. their inferences. • Provide students with a short list of • Continue using the strategy as students read Copyright © observations that can be used to make an other science texts. Remind students to look inference. For example: A boy comes inside closely at observable evidence as they read and wearing a coat. The boy is holding an umbrella. investigate in science. Find opportunities to His shoes are wet. Ask students to make an discuss the distinction between observations inference based on these observations. [It and inferences and discuss what inferences is raining outside.] Discuss the differences scientists make using evidence. 2 3 What question is What evidence does What inferences does 4. Invite students to read the book in a way that the scientist investigating? the scientist use? the scientist make? is consistent with your classroom routines, How and what did fossil dinosaur the dinosaur was a giving students as much independence as dinosaurs eat? droppings T. rex it ate smaller possible. dinosaurs and crushed bones as it ate 5. Distribute the Evidence and Inferences How deep is the bouncing sound waves how deep the ocean is student sheets and direct students’ attention ocean floor in computer model of in different places to the chart on the board. Ask students to different places? ocean temperature where fish live in the ocean identify the questions that each of the three scientists investigated. Record these questions permission. What patterns do images made by magnetic cobalt on the chart and have students do the same magnetic atoms form electrons bouncing off atoms can clump in very, very small the atoms together in groups on their student sheets. further pieces of metal? 6. Explain that students will revisit the book, focusing on the evidence that each scientist without Teaching About How gathered in order to make inferences to use answer their questions. Scientists Make Inferences with Science You Can’t See 7. Model recording information about the first classroom scientist’s evidence and inferences. Ask students to reread pages 7–8 and identify the than Getting Ready evidence that Karen Chin used to investigate 1. Make a copy of the Evidence and Inferences other her question. [Fossil dinosaur droppings.] copymaster for each student. use Record this on the chart and have students do or 2. Create a blank chart on the board, using the the same on their student sheets. model on this page. Sample responses are 8. Have students reread page 9 and discuss what shown in green; you will fill these in with inferences Karen Chin made based on the students during class. evidence. Record these as well. redistribution, During Class 9. Instruct students to reread the remainder of resale, 1. Briefly explain the difference between the book and record on their student sheets for observations and inferences. Explain that the evidence and inferences that the other two Not an observation is something that can be scientists used. perceived with one or more of the five senses 10. After students gather information from the (sight, sound, smell, taste,
Recommended publications
  • Reliability of Mathematical Inference
    Reliability of mathematical inference Jeremy Avigad Department of Philosophy and Department of Mathematical Sciences Carnegie Mellon University January 2020 Formal logic and mathematical proof An important mathematical goal is to get the answers right: • Our calculations are supposed to be correct. • Our proofs are supposed to be correct. Mathematical logic offers an idealized account of correctness, namely, formal derivability. Informal proof is viewed as an approximation to the ideal. • A mathematician can be called on to expand definitions and inferences. • The process has to terminate with fundamental notions, assumptions, and inferences. Formal logic and mathematical proof Two objections: • Few mathematicians can state formal axioms. • There are various formal foundations on offer. Slight elaboration: • Ordinary mathematics relies on an informal foundation: numbers, tuples, sets, functions, relations, structures, . • Formal logic accounts for those (and any of a number of systems suffice). Formal logic and mathematical proof What about intuitionstic logic, or large cardinal axioms? Most mathematics today is classical, and does not require strong assumptions. But even in those cases, the assumptions can be make explicit and formal. Formal logic and mathematical proof So formal derivability provides a standard of correctness. Azzouni writes: The first point to observe is that formalized proofs have become the norms of mathematical practice. And that is to say: should it become clear that the implications (of assumptions to conclusion) of an informal proof cannot be replicated by a formal analogue, the status of that informal proof as a successful proof will be rejected. Formal verification, a branch of computer science, provides corroboration: computational proof assistants make formalization routine (though still tedious).
    [Show full text]
  • Misconceived Relationships Between Logical Positivism and Quantitative Research: an Analysis in the Framework of Ian Hacking
    DOCUMENT RESUME ED 452 266 TM 032 553 AUTHOR Yu, Chong Ho TITLE Misconceived Relationships between Logical Positivism and Quantitative Research: An Analysis in the Framework of Ian Hacking. PUB DATE 2001-04-07 NOTE 26p. PUB TYPE Opinion Papers (120) ED 2S PRICE MF01/PCO2 Plus Postage. 'DESCRIPTORS *Educational Research; *Research Methodology IDENTIFIERS *Logical Positivism ABSTRACT Although quantitative research methodology is widely applied by psychological researchers, there is a common misconception that quantitative research is based on logical positivism. This paper examines the relationship between quantitative research and eight major notions of logical positivism:(1) verification;(2) pro-observation;(3) anti-cause; (4) downplaying explanation;(5) anti-theoretical entities;(6) anti-metaphysics; (7) logical analysis; and (8) frequentist probability. It is argued that the underlying philosophy of modern quantitative research in psychology is in sharp contrast to logical positivism. Putting the labor of an out-dated philosophy into quantitative research may discourage psychological researchers from applying this research approach and may also lead to misguided dispute between quantitative and qualitative researchers. What is needed is to encourage researchers and students to keep an open mind to different methodologies and apply skepticism to examine the philosophical assumptions instead of accepting them unquestioningly. (Contains 1 figure and 75 references.)(Author/SLD) Reproductions supplied by EDRS are the best that can be made from the original document. Misconceived relationships between logical positivism and quantitative research: An analysis in the framework of Ian Hacking Chong Ho Yu, Ph.D. Arizona State University April 7, 2001 N N In 4-1 PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIALHAS BEEN GRANTED BY Correspondence: TO THE EDUCATIONAL RESOURCES Chong Ho Yu, Ph.D.
    [Show full text]
  • Applying Logic to Philosophical Theology: a Formal Deductive Inference of Affirming God's Existence from Assuming the A-Priori
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Tomsk State University Repository Вестник Томского государственного университета Философия. Социология. Политология. 2020. № 55 ОНТОЛОГИЯ, ЭПИСТЕМОЛОГИЯ, ЛОГИКА УДК 16 + 17 + 2 + 51-7 DOI: 10.17223/1998863Х/55/1 V.O. Lobovikov1 APPLYING LOGIC TO PHILOSOPHICAL THEOLOGY: A FORMAL DEDUCTIVE INFERENCE OF AFFIRMING GOD’S EXISTENCE FROM ASSUMING THE A-PRIORI-NESS OF KNOWLEDGE IN THE SIGMA FORMAL AXIOMATIC THEORY For the first time a precise definition is given to the Sigma formal axiomatic theory, which is a result of logical formalization of philosophical epistemology; and an interpretation of this formal theory is offered. Also, for the first time, a formal deductive proof is constructed in Sigma for a formula, which represents (in the offered interpretation) the statement of God’s Existence under the condition that knowledge is a priori. Keywords: formal axiomatic epistemology theory; two-valued algebra of formal axiology; formal-axiological equivalence; a-priori knowledge; existence of God. 1. Introduction Since Socrates, Plato, Aristotle, Stoics, Cicero, and especially since the very beginning of Christianity philosophy, the possibility or impossibility of logical proving God’s existence has been a nontrivial problem of philosophical theology. Today the literature on this topic is immense. However, even in our days, the knot- ty problem remains unsolved as all the suggested options of solving it are contro- versial from some point of view. Some respectable researchers (let us call them “pessimists”) believed that the logical proving of God’s existence in theoretical philosophy was impossible on principle, for instance, Occam, Hume [1], and Kant [2] believed that any rational theoretic-philosophy proof of His existence was a mistake (illusion), consequently, a search for the logical proving of His existence was wasting resources and, hence, harmful; only faith in God was relevant and useful; reason was irrelevant and use- less.
    [Show full text]
  • The Routledge Companion to Islamic Philosophy Reasoning in the Qurn
    This article was downloaded by: 10.3.98.104 On: 25 Sep 2021 Access details: subscription number Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London SW1P 1WG, UK The Routledge Companion to Islamic Philosophy Richard C. Taylor, Luis Xavier López-Farjeat Reasoning in the Qurn Publication details https://www.routledgehandbooks.com/doi/10.4324/9781315708928.ch2 Rosalind Ward Gwynne Published online on: 03 Sep 2015 How to cite :- Rosalind Ward Gwynne. 03 Sep 2015, Reasoning in the Qurn from: The Routledge Companion to Islamic Philosophy Routledge Accessed on: 25 Sep 2021 https://www.routledgehandbooks.com/doi/10.4324/9781315708928.ch2 PLEASE SCROLL DOWN FOR DOCUMENT Full terms and conditions of use: https://www.routledgehandbooks.com/legal-notices/terms This Document PDF may be used for research, teaching and private study purposes. Any substantial or systematic reproductions, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 2 REASONING- IN THE QURʾAN Rosalind Ward Gwynne Introduction Muslims consider the Qurʾa-n to be the revealed speech of God—sublime, inimitable and containing information that only God knows. It has been analyzed in every pos- sible way—theologically, linguistically, legally, metaphorically—and some of these analyses have presented their results as the conclusions of reasoning in the Qurʾa-n itself, whether explicit or implicit.
    [Show full text]
  • Logical Inference and Its Dynamics
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilPapers Logical Inference and Its Dynamics Carlotta Pavese 1 Duke University Philosophy Department Abstract This essay advances and develops a dynamic conception of inference rules and uses it to reexamine a long-standing problem about logical inference raised by Lewis Carroll's regress. Keywords: Inference, inference rules, dynamic semantics. 1 Introduction Inferences are linguistic acts with a certain dynamics. In the process of making an inference, we add premises incrementally, and revise contextual assump- tions, often even just provisionally, to make them compatible with the premises. Making an inference is, in this sense, moving from one set of assumptions to another. The goal of an inference is to reach a set of assumptions that supports the conclusion of the inference. This essay argues from such a dynamic conception of inference to a dynamic conception of inference rules (section x2). According to such a dynamic con- ception, inference rules are special sorts of dynamic semantic values. Section x3 develops this general idea into a detailed proposal and section x4 defends it against an outstanding objection. Some of the virtues of the dynamic con- ception of inference rules developed here are then illustrated by showing how it helps us re-think a long-standing puzzle about logical inference, raised by Lewis Carroll [3]'s regress (section x5). 2 From The Dynamics of Inference to A Dynamic Conception of Inference Rules Following a long tradition in philosophy, I will take inferences to be linguistic acts. 2 Inferences are acts in that they are conscious, at person-level, and 1 I'd like to thank Guillermo Del Pinal, Simon Goldstein, Diego Marconi, Ram Neta, Jim Pryor, Alex Rosenberg, Daniel Rothschild, David Sanford, Philippe Schlenker, Walter Sinnott-Armstrong, Seth Yalcin, Jack Woods, and three anonymous referees for helpful suggestions on earlier drafts.
    [Show full text]
  • Passmore, J. (1967). Logical Positivism. in P. Edwards (Ed.). the Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan
    Passmore, J. (1967). Logical Positivism. In P. Edwards (Ed.). The Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan. LOGICAL POSITIVISM is the name given in 1931 by A. E. Blumberg and Herbert Feigl to a set of philosophical ideas put forward by the Vienna circle. Synonymous expressions include "consistent empiricism," "logical empiricism," "scientific empiricism," and "logical neo-positivism." The name logical positivism is often, but misleadingly, used more broadly to include the "analytical" or "ordinary language philosophies developed at Cambridge and Oxford. HISTORICAL BACKGROUND The logical positivists thought of themselves as continuing a nineteenth-century Viennese empirical tradition, closely linked with British empiricism and culminating in the antimetaphysical, scientifically oriented teaching of Ernst Mach. In 1907 the mathematician Hans Hahn, the economist Otto Neurath, and the physicist Philipp Frank, all of whom were later to be prominent members of the Vienna circle, came together as an informal group to discuss the philosophy of science. They hoped to give an account of science which would do justice -as, they thought, Mach did not- to the central importance of mathematics, logic, and theoretical physics, without abandoning Mach's general doctrine that science is, fundamentally, the description of experience. As a solution to their problems, they looked to the "new positivism" of Poincare; in attempting to reconcile Mach and Poincare; they anticipated the main themes of logical positivism. In 1922, at the instigation of members of the "Vienna group," Moritz Schlick was invited to Vienna as professor, like Mach before him (1895-1901), in the philosophy of the inductive sciences. Schlick had been trained as a scientist under Max Planck and had won a name for himself as an interpreter of Einstein's theory of relativity.
    [Show full text]
  • What Is Inference? Penalty
    WHAT IS INFERENCE? OR THE FORCE OF REASONING by Ulf Hlobil Dipl.-Psych., University of Trier, 2008 Magister Artium in Philosophy, University of Trier, 2009 M.A. in Philosophy, University of Pittsburgh, 2012 Submitted to the Graduate Faculty of the Kenneth P. Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2016 UNIVERSITY OF PITTSBURGH KENNETH P. DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Ulf Hlobil It was defended on May 31, 2016 and approved by Robert Brandom, Distinguished Professor of Philosophy John McDowell, Distinguished University Professor of Philosophy Kieran Setiya, Professor of Philosophy James Shaw, Associate Professor of Philosophy Dissertation Director: Robert Brandom, Distinguished Professor of Philosophy ii Copyright © by Ulf Hlobil 2016 iii WHAT IS INFERENCE? OR THE FORCE OF REASONING Ulf Hlobil, PhD University of Pittsburgh, 2016 What are we doing when we make inferences? I argue that to make an inference is to attach inferential force to an argument. Inferential force must be understood in analogy to assertoric force, and an argument is a structure of contents. I call this the “Force Account of inference.” I develop this account by first establishing two criteria of adequacy for accounts of inference. First, such accounts must explain why it is absurd to make an inference one believes to be bad. The upshot is that if someone makes an inference, she must take her inference to be good. Second, accounts of inference must explain why we cannot take our inferences to be good—in the sense that matters for inference—by merely accepting testimony to the effect that they are good.
    [Show full text]
  • The “Positive Argument” for Constructive Empiricism and Inference to the Best Explanation Moti Mizrahi Florida Institute Of
    The “Positive Argument” for Constructive Empiricism and Inference to the Best Explanation Moti Mizrahi Florida Institute of Technology [email protected] Abstract: In this paper, I argue that the “positive argument” for Constructive Empiricism (CE), according to which CE “makes better sense of science, and of scientific activity, than realism does” (van Fraassen 1980, 73), is an Inference to the Best Explanation (IBE). But constructive empiricists are critical of IBE, and thus they have to be critical of their own “positive argument” for CE. If my argument is sound, then constructive empiricists are in the awkward position of having to reject their own “positive argument” for CE by their own lights. Keywords: Constructive Empiricism; Inference to the Best Explanation; Positive Argument; Scientific Realism According to Bas van Fraassen (1980, 73), the “positive argument” for Constructive Empiricism (CE), is that “it makes better sense of science, and of scientific activity, than realism does and does so without inflationary metaphysics.” Although van Fraassen would not characterize it as such, this “positive argument” for CE looks like an Inference to the Best Explanation (IBE), for in IBE, “a hypothesis is accepted on the basis of a judgment that it best explains the available evidence” (Psillos 2007, 442). And a “good explanation makes sense out of that which it is intended to explain” (Sinnott-Armstrong and Fogelin 2015, 198; emphasis added). In van Fraassen’s “positive argument,” CE is said to be supported by the premise that it “makes better 1 sense of,” or provides a better explanation for, scientific activity than Scientific Realism (SR) does.
    [Show full text]
  • Scholasticism, the Medieval Synthesis CVSP 202 General Lecture Monday, March 23, 2015 Encountering Aristotle in the Middle-Ages Hani Hassan [email protected]
    Scholasticism, The Medieval Synthesis CVSP 202 General Lecture Monday, March 23, 2015 Encountering Aristotle in the middle-ages Hani Hassan [email protected] PART I – SCHOLASTIC PHILOSOPHY SCHOLASTIC: “from Middle French scholastique, from Latin scholasticus "learned," from Greek skholastikos "studious, learned"” 1 Came to be associated with the ‘teachers’ and churchmen in European Universities whose work was generally rooted in Aristotle and the Church Fathers. A. Re-discovering Aristotle & Co – c. 12th Century The Toledo school: translating Arabic & Hebrew philosophy and science as well as Arabic & Hebrew translations of Aristotle and commentaries on Aristotle (notably works of Ibn Rushd and Maimonides) Faith and Reason united From Toledo, through Provence, to… th by German painter Ludwig Seitz Palermo, Sicily – 13 Century – Under the rule of Roger of Sicily (Norman (1844–1908) ruler) th William of Moerbeke (Dutch cleric): greatest translator of the 13 century, and (possibly) ‘colleague’ of Thomas Aquinas. B. Greek Philosophy in the Christian monotheistic world: Boethius to scholasticism Boethius: (c. 475 – c. 526) philosopher, poet, politician – best known for his work Consolation of Philosophy, written as a dialogue between Boethius and 'Lady Philosophy', addressing issues ranging from the nature and essence of God, to evil, and ethics; translated Aristotle’s works on logic into Latin, and wrote commentaries on said works. John Scotus Eriugena (c. 815 – c. 877) Irish philosopher of the early monastic period; translated into Latin the works of pseudo-Dionysius, developed a Christian Neoplatonic world view. Anselm (c. 1033 – 1109) Archbishop of Canterbury from 1093 to 1109; best known for his “ontological argument” for the existence of God in chapter two of the Proslogion (translated into English: Discourse on the Existence of God); referred to by many as one of the founders of scholasticism.
    [Show full text]
  • Wittgenstein Vs. Frege and Russell
    teorema Vol. XL/2, 2021, pp. 45-61 ISNN 0210-1602 [BIBLID 0210-1602 (2021) 40:2; pp. 45-61] Are Rules of Inference Superfluous? Wittgenstein vs. Frege and Russell Gilad Nir RESUMEN En el Tractatus 5.132 Wittgenstein argumenta que la justificación inferencial depen- de solo de la comprensión de las premisas y la conclusión y no está mediada por ningún otro acto adicional. Tomando lo anterior como base, Wittgenstein defiende que las reglas de inferencia de Frege y Russell “carecen de sentido” y son “superfluas”. Esta línea de argumento es problemática, puesto que no está claro que pueda haber una explicación viable de la inferencia de acuerdo con la cual no haya tal mediación. Muestro que el re- chazo por parte de Wittgenstein de las reglas de inferencia puede estar motivado si se tie- ne en cuenta su interpretación holista de la relación entre inferencia y comprensión. PALABRAS CLAVE: Wittgenstein, Frege, Russell, inferencia, holismo. ABSTRACT In Tractatus 5.132 Wittgenstein argues that inferential justification depends solely on the understanding of the premises and conclusion, and is not mediated by any further act. On this basis he argues that Frege’s and Russell’s rules of inference are “senseless” and “superfluous”. This line of argument is puzzling, since it is unclear that there could be any viable account of inference according to which no such mediation takes place. I show that Wittgenstein’s rejection of rules of inference can be motivated by taking ac- count of his holistic construal of the relation between inference and understanding. KEYWORDS: Wittgenstein, Frege, Russell, Inference, Holism.
    [Show full text]
  • The Quran and the Secular Mind: a Philosophy of Islam
    The Quran and the Secular Mind In this engaging and innovative study Shabbir Akhtar argues that Islam is unique in its decision and capacity to confront, rather than accommodate, the challenges of secular belief. The author contends that Islam should not be classed with the modern Judaeo–Christian tradition since that tradition has effectively capitulated to secularism and is now a disguised form of liberal humanism. He insists that the Quran, the founding document and scripture of Islam, must be viewed in its own uniqueness and integrity rather than mined for alleged parallels and equivalents with biblical Semitic faiths. The author encourages his Muslim co-religionists to assess central Quranic doctrine at the bar of contemporary secular reason. In doing so, he seeks to revive the tradition of Islamic philosophy, moribund since the work of the twelfth century Muslim thinker and commentator on Aristotle, Ibn Rushd (Averroës). Shabbir Akhtar’s book argues that reason, in the aftermath of revelation, must be exer- cised critically rather than merely to extract and explicate Quranic dogma. In doing so, the author creates a revolutionary form of Quranic exegesis with vitally significant implications for the moral, intellectual, cultural and political future of this consciously universal faith called Islam, and indeed of other faiths and ideologies that must encounter it in the modern secular world. Accessible in style and topical and provocative in content, this book is a major philosophical contribution to the study of the Quran. These features make it ideal reading for students and general readers of Islam and philosophy. Shabbir Akhtar is Assistant Professor of Philosophy at Old Dominion University in Norfolk, Virginia, USA.
    [Show full text]
  • Logic in Philosophy of Mathematics
    Logic in Philosophy of Mathematics Hannes Leitgeb 1 What is Philosophy of Mathematics? Philosophers have been fascinated by mathematics right from the beginning of philosophy, and it is easy to see why: The subject matter of mathematics| numbers, geometrical figures, calculation procedures, functions, sets, and so on|seems to be abstract, that is, not in space or time and not anything to which we could get access by any causal means. Still mathematicians seem to be able to justify theorems about numbers, geometrical figures, calcula- tion procedures, functions, and sets in the strictest possible sense, by giving mathematical proofs for these theorems. How is this possible? Can we actu- ally justify mathematics in this way? What exactly is a proof? What do we even mean when we say things like `The less-than relation for natural num- bers (non-negative integers) is transitive' or `there exists a function on the real numbers which is continuous but nowhere differentiable'? Under what conditions are such statements true or false? Are all statements that are formulated in some mathematical language true or false, and is every true mathematical statement necessarily true? Are there mathematical truths which mathematicians could not prove even if they had unlimited time and economical resources? What do mathematical entities have in common with everyday objects such as chairs or the moon, and how do they differ from them? Or do they exist at all? Do we need to commit ourselves to the existence of mathematical entities when we do mathematics? Which role does mathematics play in our modern scientific theories, and does the em- pirical support of scientific theories translate into empirical support of the mathematical parts of these theories? Questions like these are among the many fascinating questions that get asked by philosophers of mathematics, and as it turned out, much of the progress on these questions in the last century is due to the development of modern mathematical and philosophical logic.
    [Show full text]