"Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it." (Eudoxus, cca. 4th century BC)
"Every stage of science has its train of practical applications and systematic inferences, arising both from the demands of convenience and curiosity, and from the pleasure which, as we have already said, ingenious and active-minded men feel in exercising the process of deduction."
"A mere inference or theory must give way to a truth revealed; but a scientific truth must be maintained, however contradictory it may appear to the most cherished doctrines of religion." (David Brewster, "More Worlds Than One: The Creed of the Philosopher and the Hope of the Christian", 1856)
"Truths are known to us in two ways: some are known directly, and of themselves; some through the medium of other truths. The former are the subject of Intuition, or Consciousness; the latter, of Inference; the latter of Inference. The truths known by Intuition are the original premises, from which all others are inferred." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1858)
"It is experience which has given us our first real knowledge of Nature and her laws. It is experience, in the shape of observation and experiment, which has given us the raw material out of which hypothesis and inference have slowly elaborated that richer conception of the material world which constitutes perhaps the chief, and certainly the most characteristic, glory of the modern mind." (Arthur J Balfour, "The Foundations of Belief", 1912)
"Whenever possible, substitute constructions out of known entities for inferences to unknown entities." (Bertrand Russell, 1924)
"An observation, strictly, is only a sensation. Nobody means that we should reject everything but sensations. But as soon as we go beyond sensations we are making inferences." (Sir Harold Jeffreys, "Theory of Probability", 1939)
"The study of inductive inference belongs to the theory of probability, since observational facts can make a theory only probable but will never make it absolutely certain." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)
"Statistics is the name for that science and art which deals with uncertain inferences - which uses numbers to find out something about nature and experience." (Warren Weaver, 1952)
"The heart of all major discoveries in the physical sciences is the discovery of novel methods of representation and so of fresh techniques by which inferences can be drawn - and drawn in ways which fit the phenomena under investigation." (Stephen Toulmin, "The Philosophy of Science", 1957)
"An analogy is a relationship between two entities, processes, or what you will, which allows inferences to be made about one of the things, usually that about which we know least, on the basis of what we know about the other. […] The art of using analogy is to balance up what we know of the likenesses against the unlikenesses between two things, and then on the basis of this balance make an inference as to what is called the neutral analogy, that about which we do not know." (Rom Harré," The Philosophies of Science" , 1972)
"[Fuzzy logic is] a logic whose distinguishing features are (1) fuzzy truth-values expressed in linguistic terms, e. g., true, very true, more or less true, or somewhat true, false, nor very true and not very false, etc.; (2) imprecise truth tables; and (3) rules of inference whose validity is relative to a context rather than exact." (Lotfi A. Zadeh, "Fuzzy logic and approximate reasoning", 1975)
"Pencil and paper for construction of distributions, scatter diagrams, and run-charts to compare small groups and to detect trends are more efficient methods of estimation than statistical inference that depends on variances and standard errors, as the simple techniques preserve the information in the original data." (W Edwards Deming, "On Probability as Basis for Action", American Statistician, Volume 29, Number 4, November 1975)
"The advantage of semantic networks over standard logic is that some selected set of the possible inferences can be made in a specialized and efficient way. If these correspond to the inferences that people make naturally, then the system will be able to do a more natural sort of reasoning than can be easily achieved using formal logical deduction." (Avron Barr, Natural Language Understanding, AI Magazine Vol. 1 (1), 1980)
"Models are often used to decide issues in situations marked by uncertainty. However statistical differences from data depend on assumptions about the process which generated these data. If the assumptions do not hold, the inferences may not be reliable either. This limitation is often ignored by applied workers who fail to identify crucial assumptions or subject them to any kind of empirical testing. In such circumstances, using statistical procedures may only compound the uncertainty." (David A Greedman & William C Navidi, "Regression Models for Adjusting the 1980 Census", Statistical Science Vol. 1 (1), 1986)
"It is difficult to distinguish deduction from what in other circumstances is called problem-solving. And concept learning, inference, and reasoning by analogy are all instances of inductive reasoning. (Detectives typically induce, rather than deduce.) None of these things can be done separately from each other, or from anything else. They are pseudo-categories." (Frank Smith, "To Think: In Language, Learning and Education", 1990)
"The essential idea of semantic networks is that the graph-theoretic structure of relations and abstractions can be used for inference as well as understanding. […] A semantic network is a discrete structure as is any linguistic description. Representation of the continuous 'outside world' with such a structure is necessarily incomplete, and requires decisions as to which information is kept and which is lost." (Fritz Lehman, "Semantic Networks", Computers & Mathematics with Applications Vol. 23 (2-5), 1992)
"The science of statistics may be described as exploring, analyzing and summarizing data; designing or choosing appropriate ways of collecting data and extracting information from them; and communicating that information. Statistics also involves constructing and testing models for describing chance phenomena. These models can be used as a basis for making inferences and drawing conclusions and, finally, perhaps for making decisions." (Fergus Daly et al, "Elements of Statistics", 1995)
"Theories rarely arise as patient inferences forced by accumulated facts. Theories are mental constructs potentiated by complex external prods (including, in idealized cases, a commanding push from empirical reality)." (Stephen J Gould, "Leonardo's Mountain of Clams and the Diet of Worms" , 1998)
"Let us regard a proof of an assertion as a purely mechanical procedure using precise rules of inference starting with a few unassailable axioms. This means that an algorithm can be devised for testing the validity of an alleged proof simply by checking the successive steps of the argument; the rules of inference constitute an algorithm for generating all the statements that can be deduced in a finite number of steps from the axioms." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)
"[…] philosophical theories are structured by conceptual metaphors that constrain which inferences can be drawn within that philosophical theory. The (typically unconscious) conceptual metaphors that are constitutive of a philosophical theory have the causal effect of constraining how you can reason within that philosophical framework." (George Lakoff, "Philosophy in the Flesh: The Embodied Mind and its Challenge to Western Thought", 1999)
"Even if our cognitive maps of causal structure were perfect, learning, especially double-loop learning, would still be difficult. To use a mental model to design a new strategy or organization we must make inferences about the consequences of decision rules that have never been tried and for which we have no data. To do so requires intuitive solution of high-order nonlinear differential equations, a task far exceeding human cognitive capabilities in all but the simplest systems." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)
"Bayesian inference is a controversial approach because it inherently embraces a subjective notion of probability. In general, Bayesian methods provide no guarantees on long run performance."
"The Bayesian approach is based on the following postulates: (B1) Probability describes degree of belief, not limiting frequency. As such, we can make probability statements about lots of things, not just data which are subject to random variation. […] (B2) We can make probability statements about parameters, even though they are fixed constants. (B3) We make inferences about a parameter θ by producing a probability distribution for θ. Inferences, such as point estimates and interval estimates, may then be extracted from this distribution."
"Statistical inference, or 'learning' as it is called in computer science, is the process of using data to infer the distribution that generated the data."
"A mental model is conceived […] as a knowledge structure possessing slots that can be filled not only with empirically gained information but also with ‘default assumptions’ resulting from prior experience. These default assumptions can be substituted by updated information so that inferences based on the model can be corrected without abandoning the model as a whole. Information is assimilated to the slots of a mental model in the form of ‘frames’ which are understood here as ‘chunks’ of knowledge with a well-defined meaning anchored in a given body of shared knowledge." (Jürgen Renn, "Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy", "The Universe of General Relativity" Ed. by A.J. Kox & Jean Eisenstaedt, 2005)
"Statistics is the branch of mathematics that uses observations and measurements called data to analyze, summarize, make inferences, and draw conclusions based on the data gathered." (Allan G Bluman, "Probability Demystified", 2005)
"In specific cases, we think by applying mental rules, which are similar to rules in computer programs. In most of the cases, however, we reason by constructing, inspecting, and manipulating mental models. These models and the processes that manipulate them are the basis of our competence to reason. In general, it is believed that humans have the competence to perform such inferences error-free. Errors do occur, however, because reasoning performance is limited by capacities of the cognitive system, misunderstanding of the premises, ambiguity of problems, and motivational factors. Moreover, background knowledge can significantly influence our reasoning performance. This influence can either be facilitation or an impedance of the reasoning process." (Carsten Held et al, "Mental Models and the Mind", 2006)
"Mental models abide by the principle of parsimony: They represent only possibilities compatible with the premises, and they represent clauses in the premises only when they hold in a possibility. Fully explicit models represent clauses when they do not hold too. The advantage of mental models over fully explicit models is that they contain less information, and so they are easier to work with. But they can lead reasoners astray. The occurrence of these systematic and compelling fallacies is shocking. The model theory predicts them, and they are a 'litmus' test for mental models, because no other current theory predicts them. They have so far resisted explanation by theories of reasoning based on formal rules of inference, because these theories rely on valid rules." (Philip N Johnson-Laird, Mental Models, Sentential Reasoning, and Illusory Inferences, [in "Mental Models and the Mind"], 2006)
"[…] statistics is the key discipline for predicting the future or for making inferences about the unknown, or for producing convenient summaries of data." (David J Hand, "Statistics: A Very Short Introduction", 2008)
"Causal inference is different, because a change in the system is contemplated - an intervention. Descriptive statistics tell you about the data that you happen to have. Causal models claim to tell you what will happen to some of the numbers if you intervene to change other numbers." (David A. Freedman, "Statistical Models: Theory and Practice", 2009)
"Mental models represent possibilities, and the theory of mental models postulates three systems of mental processes underlying inference: (0) the construction of an intentional representation of a premise’s meaning – a process guided by a parser; (1) the building of an initial mental model from the intension, and the drawing of a conclusion based on heuristics and the model; and (2) on some occasions, the search for alternative models, such as a counterexample in which the conclusion is false. System 0 is linguistic, and it may be autonomous. System 1 is rapid and prone to systematic errors, because it makes no use of a working memory for intermediate results. System 2 has access to working memory, and so it can carry out recursive processes, such as the construction of alternative models." (Sangeet Khemlania & P.N. Johnson-Laird, "The processes of inference", Argument and Computation, 2012)
"Statistics is the science, the art, the philosophy, and the technique of making inferences from the particular to the general." (John W Tukey)
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