Investigating Knowledge and Opinion

This work treats correlative concepts of knowledge and opinion, in various senses. In all senses of ‘knowledge’ and ‘opinion’, a belief known to be true is knowledge; a belief not known to be true is opinion. In this sense of ‘belief’, a belief is a proposition thought to be true—perhaps, but not necessarily, known to be true. All knowledge is truth. Some but not all opinion is truth. Every proposition known to be true is believed to be true. Some but not every proposition believed to be true is known to be true. Our focus is thus on propositional belief (“belief-that”): the combination of propositional knowledge (“knowledge-that”) and propositional opinion (“opinion-that”). Each of a person’s beliefs, whether knowledge or opinion, is the end result of a particular thought process that continued during a particular time interval and ended at a particular time with a conclusive act—a judgment that something is the case. This work is mainly about beliefs in substantive informative propositions—not empty tautologies.

We also treat objectual knowledge (knowledge of objects in the broadest sense, or “knowledge-of”), operational knowledge (abilities and skills, “knowledge-how-to”, or “know-how”), and expert knowledge (expertise). Most points made in this work have been made by previous writers, but, to the best of our knowledge, they have never before been collected into a coherent work accessible to a wide audience.

1. 1.

   We use the word ‘proposition’ in the abstract sense in which one proposition might be expressed by many different sentences. Our usage—which follows Church [8, 9] where ‘proposition’ is a near synonym for ‘thought’ in the sense of Frege’s [27] “The Thought”—is explained more fully in Corcoran [19] and [20]. Also, see Frege [28, 325].

2. 2.

   Here, ambiguity is having multiple normal meanings and a sentence is lexically ambiguous if it contains an ambiguous word (lexical item). See Corcoran [19].

3. 3.

   Being an even square is an intrinsic property of the number four, being the number of Evangelists is an extrinsic property of four. Having four letters is an intrinsic property of the word ‘four’, being a name of the number of Evangelists is an extrinsic property of ‘four’. Changes in intrinsic properties are known as ordinary changes whereas changes in extrinsic properties are variously called “Cambridge changes”, “Pickwickian changes”, “relative changes”, and others. For further discussion and examples, see Corcoran [12].

4. 4.

   In the sense of ‘belief’ used in this work, propositions are exclusively the objects of believing: what a person believes is a proposition. Thus, a person’s acceptance as true of an incoherency such as ‘Socrates is equal’ is not belief in the sense of this paper.

5. 5.

   An expression ‘my belief of [a certain entity]’ is questionable English if English at all unless the entity is something special such as a person’s statement: ‘my belief of the number one’ is ungrammatical. An expression ‘my opinion of [a certain entity]’ would be taken to refer to a propositional opinion. For example, our opinion of knowledge is that people’s lives are improved by it.

6. 6.

   For Corcoran, this is a working hypothesis; for Hamid, it is firmly held belief.

7. 7.

   Writing in 1846, Augustus De Morgan [24, 1–3] thought that negative substantive expressions such as ‘non-human’ were logically defective and would not occur in a logically perfect language [39, p. 183]. Instead, each substantive would have its own equally “positive” complementary substantive—as ‘knowledge’ has its complementary ‘opinion’.

8. 8.

   The terminology for propositions not known to be true and not known to be false is awkward and unsettled. What is called an open question is often not a question in any of the more usual senses. Moreover, what is called a hypothesis was never hypothesized by anyone. See the article “Conjecture” in Audi [5].

9. 9.

   The late Dr. Ray Lucas asked whether having made a cognitive judgment is sufficient for having a cognition. Unfortunately, the answer is no, people can lose cognitions. People can lose belief in a proposition they once knew because of a later mistake or because of memory decay. We suspect that there are propositions we once knew but no longer believe and thus no longer know.

10. 10.

    Nothing said above should be interpreted as suggesting that any given cognition is more meritorious or more worthy than any non-cognitive item of knowledge. The relative worth of two items of knowledge is beyond the scope of this essay. However, there are clearly cases in which knowledge of a certain mathematical theorem is less valuable than knowledge that a certain pill stops a certain pain.

11. 11.

    Applied to propositions, apprehension is an action while comprehension is an attitude or state [41, p. 140]. Normally, after someone apprehends a given proposition, they comprehend it for a time—often a long time during which they are only occasionally aware of the fact that they comprehend it. Apprehending a proposition takes place in a time interval—often relatively short—whose end coincides with the onset of comprehension. In a way, apprehension is to comprehension as judging is to believing: judging is an act not an attitude, believing is an attitude not an act [20].

12. 12.

    Of course, all or at least many such experiences require the subject to be pursuing a goal prior to the event. Thus, some thinkers might prefer to start the process with a goal, or even with the pursuit of the goal, or even with the desire that prompted the pursuit.

13. 13.

    See “Limiting case” and “Borderline case” in Audi [5].

14. 14.

    The word ‘probable’ is used in the original sense going back to around 1600 before the invention of “probability theory” gave it another meaning. In this sense, it applies to beliefs and contrasts with ‘certain’. See any dictionary that dates senses, for example, Definition 1 in the Merriam-Webster Collegiate Dictionary [33]. It is still widely used in the original sense where there is no question of assigning numbers to “events”. Frege uses it in the original sense in his classic 1918 paper “The Thought” [27] (p. 306).

15. 15.

    We do not know the history of the expression ‘moral certainty’. Antoine Arnauld (1612–1694) and Pierre Nicole (1625–1695) use the expression without comment as if it were a common locution in their 1662 masterpiece The Art of Thinking known as The Port-Royal Logic [4, 264, 270]. Dessi [25, xvii] traces it to John Locke (1632–1704). Dessi (loc. cit.) and Whately [48, 243] both use it in the sense just explained.

16. 16.

    The complementarity and interconnectedness of objectual, operational, and propositional knowledge has been a cornerstone of our thinking for many years. See Corcoran [10].

17. 17.

    Frege makes this point several places. However, without qualification, it is misleading to say that he said propositions do not change intrinsically—he did not emphasize the intrinsic/extrinsic distinction explained below.

18. 18.

    In fact, even belief cannot be transmitted in this sense. One person’s blood can be transfused into another’s body but one person’s belief cannot not be moved to another person or copied on another person’s mind. Beliefs are formed by judging and each judging must be autonymous. Of course, magicians, for example, trick people into making judgments they would not otherwise make.

19. 19.

    However, in the posthumously published “What are logical notions? Tarski [47], he proposed a condition for distinguishing logical from non-logical objects: individuals, sets, relations, functions, etc. This proposal does not imply a condition for distinguishing logical from non-logical concepts (senses) and thus does not yield a condition for distinguishing logical from non-logical terms (expressions).

20. 20.

    The expression ‘the truth of a proposition’ should not be detached from its context. By ‘assurance of the truth of a proposition’, we mean assurance that the proposition is true. It is a mistake to think that the truth of a proposition is an entity separate from the proposition itself.

21. 21.

    There are two difficult issues here for the Aristotle scholar. The easier is whether our indirect quotation of Aristotle—that every person by nature desires knowledge—is a fair interpretation of the famous first line of Metaphysics [2]. The other issue is whether Aristotle held the general view that we attribute to him. Scholars we consulted do not all agree. After a nuanced discussion, David Hitchcock (per. comm.) concluded: “So I think that it is fair to say that Aristotle took one cognitive goal of all human beings to be the possession of truth.” Very recent scholarship concurs. See Anagnostopoulous [1, 102f].

22. 22.

    Perhaps the classic expression of Peirce’s views is in Sects. III, IV, and V of his famous 1877 article “The Fixation of Belief” [37] reprinted in the 1992 Houser and Kloesel volume [40, 109–123]. The interpretation putting Peirce in diametrical opposition to Aristotle is almost universally shared by Peirce scholars as being a view that Peirce actually held at the time of the article. However, Peirce’s writings are replete with subtlety, irony, and scathing sarcasm. So much so, that it is hard to be certain that he was not actually expressing the opposite of what he wrote. Moreover, it might well be that he later came to embrace in a nuanced form a view he had formerly ridiculed in a naïve and exaggerated form.

23. 23.

    A person’s most firmly established beliefs are rarely those they believe most firmly, i.e. those of which they are most strongly convinced. This point relates to the contrast, dealt with elsewhere in this work, between the objective state of certainty and the subjective feeling of certitude.

24. 24.

    The word ‘skepticism’, or ‘scepticism’, derives from the Greek verb meaning “to consider carefully”, which was taken by some to mean “to consider so carefully that no conclusion is reached”. The Greek skeptic (skeptikos) did not subscribe to the view called ‘scepticism’ above; the skeptic meticulously avoided subscribing to any view at all. Today, the word ‘skepticism’, or ‘scepticism’, is used in various senses, often as above, rarely if ever in the etymological sense. See Preus [43, 237–8].

25. 25.

    Frege [27, 62] speaks of understanding as “grasping” the proposition and he speaks of judging as “acknowledging” its truth. See Frege [28, 329]. He seems oblivious of the fact that understanding is an act-process that takes time to complete. He seems likewise oblivious of the process intervening between understanding and judging. Moreover, he is vague about the nature of judging.

26. 26.

    We are aware of the literature on “knowing that one knows” centered on or stemming from “epistemic logic”, for example, Hilpinen [31]. The definitions of knowing used in that literature are so alien to those used here that little written there is relevant.

27. 27.

    Corcoran’s encyclopedia article 2007 “Knowledge and Belief” [17] was written earlier than the 2006 “An Essay on Knowledge and Belief” [15], but assigned a later publication date [32].

We would like to thank those who have made important contributions to the dialogue leading up to this work. Robert Barnes, Leigh Duffy, John Glanville (1921–2010), Carol Gould, Forest Hansen, Peter Hare (1935–2008), Amanda Hicks, Daniel Merrill, Joaquin Miller, Hassan Masoud, Paul Moser, Mary Mulhern, Carlo Penco, Anthony Preus, José Miguel Sagüillo, Michael Scanlan, John Shook, Andrew Spear, Yevgeny Yarmolinets, Joseph Zeccardi, and John Zeis all deserve credit. Many thanks also to all who participated in the crafting of this article, especially David Brewer, Joseph Corcoran, David Hitchcock, Leonard Jacuzzo, Timothy Madigan, James McNabb, Kristo Miettinen, Frango Nabrasa, Sriram Nambiar, Daniel Novotny, Charles Pailthorp, Paul Penner, David Plache, and Roberto Torretti. David Hitchcock and Daniel Novotny deserve special thanks for alerting us to errors and obscurities in the penultimate draft; they are almost co-authors even though they disagree with some of our conclusions.

Many of the scholars mentioned disagree with some, many, or most of the conclusions of this work. We should also acknowledge many previous writers to whom we are indebted for most of the points made in this work. Our main contribution was to have collected their thoughts into a coherent work accessible to a wide audience. This paper is a substantial reworking of “An Essay on Knowledge and Belief” [15]. The word ‘essay’ in its title was carefully chosen: the essay has no footnotes or references and it is much shorter than this investigation. The essay was inspired by responses to early drafts of the encyclopedia article “Knowledge and Belief” [17].^{Footnote 27}

Authors and Affiliations

1. Philosophy, University at Buffalo, Buffalo, NY, 14260-4150, USA

   John Corcoran

2. Philosophy, Colorado State University, Fort Collins, CO, 80523-1781, USA

   Idris Samawi Hamid

Corresponding author

Correspondence to John Corcoran .

Editors and Affiliations

1. City University of New York, New York, New York, USA

   Arnold Koslow

2. Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

   Arthur Buchsbaum

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