Living
Ontologists (a list of authors with an interest in ontology, with
synthetic bibliographies)
INTRODUCTION
"The essay before you is the fruit of some fifteen years of investigation into the logical syntax of natural language. In the summer of 1965 I read a paper to the Congress on Logic and Scientific Method at Bedford College, London, that presented an algorithm for the algebraic treatment of syllogistic arguments in which categorical propositions were transcribed as fractions and reciprocals.(1) I spent the next two years looking for a more general algorithm with greater
expressive power, one that could
transcribe relational, multi-general propositions as well as simple categoricals. (...)The first article on the more general calculus was published in Mind, January 1970, as The Calculus of Terms. Unfortunately its message had little effect although I followed it by a series of articles that exploited the new notation and exposed some important consequences for the philosophy of language. It became clear that the current Fregean logic had fully replaced the more traditional logic of terms and that articles could
not do justice to the neo-classical alternative that I was advocating.
I had for some years been planning to write a book on the logic of categories but the lack of response to my more recent interests, the logic of terms and its relation to natural syntax, strongly suggested that I must first do book-length justice to these latter topics. I began writing this essay in 1975 and, after several long interruptions and two revisions, completed it in the summer of 1980. I still hope to write the book on category theory. In the present work chapter
13) I do little more than indicate
how traditional logic's way with contrariety leads to the conception of categories that is at the basis of Ryle's seminal work in the forties and my own more formal treatment of categories in the early sixties. Indeed it was my recognition of the need for a notion of contrariety that would allow for saying, for example, that Saturday is neither fed nor unfed (which renders both 'Saturday is fed' and 'Saturday is unfed' 'category mistakes') that prompted me to re-examine traditional Aristotelian logic with its
characteristic distinction between contrary terms or predicates and contradictory propositions. This distinction is absent in modern logic which uses the forms 'Px' and '-Px' to represent contrary predicates thereby conflating the two oppositions of contrariety and contradiction so fundamental to the classical term-theoretic standpoint. (2) The current use of propositional negation as the sole form of opposition 'precludes the kind of internal term and predicate structure that makes it possible to treat negation
as a means of changing around concepts inside the meanings of terms and predicates'. The quoted words are Jerrold Katz's but they are typical of the sort of reaction one gets from linguists who find the restricted grammar of 'standard' logical languages to be at odds with their intuitions into the logical grammar of empirical languages.
More generally the theory of logical form that has its source in the formation rules for standard languages poses severe problems for the linguist. The older subject-predicate logic with its classical binary noun-phrase verb-phrase analysis of sentences has been discredited and while some linguists appear prepared to abandon the classical analysis in favour of analyses that conform more closely to the syntax of modern predicate logic others may welcome a rehabilitated
classical logic of 'categorical' sentences
that leaves the fundamental binary structure in place."
(1) 'On a Fregean Dogma'. Apparently I was not alone in representing categorical propositions as fractions. Charles Merchant, a mathematician at the University of Arizona, subsequently wrote me of his independent work on this algorithm.
(2) Early treatments of the distinction between negating a sentence and denying predicate may be found in my 'Predicability' (1963) and 'Truth Functional counterfactuals' (1964).
From: Fred Sommers - The logic of natural language - Oxford, Clarendon Press, 1982 pp. VII-VIII.
"Today's orthodox logic came into existence about a hundred years ago when it replaced the traditional syllogistic logic, which itself had been the orthodoxy for many centuries. The arguments for abandoning the old logic were not conclusive. Once entrenched, the new logic felt no need for supporting arguments. Today logic students are given at best some bad old arguments against the old logic, and then are simply presented with the new logic to be learned. No one asks 'Why?'. But Sommers has. He has challenged
the deeply entrenched presumption that no syllogistic logic can measure up to the great power and beauty of the predicate calculus. What is more, not only has Sommers shown the emperor to have no clothes, he has produced a fine new suit. He has returned to the venerable but forgotten logic of Aristotle, Ockham, and Leibniz, and has shown that it does have hidden assets which make it more than adequate as an alternative to the orthodox system. So I think this rebellion is well worth joining. And, of course, there's
that pleasure I referred to earlier. Sommers speaks of "the perverse pleasure of advocacy-in this day and age-of Aristotle over Frege."I have put this collection together for several reasons. As a supplement to Sommers' own work it illustrates the broad scope of Sommers' challenge to modern orthodox views about logic and language. Not all of those whose work is represented here fully endorse Sommers' programme. Some may explicitly reject parts of it. But all recognize its importance."
From: George Englebretsen (ed). - The new syllogistic - New York, Peter Lang, 1987 - Preface by the Editor pp. X-XI
"Frederic Sommers was born on 1 January 1923 in New York City. He was educated at Columbia University, where he received his BA and then his PhD in philosophy in 1955, writing a dissertation on "An Empiricist Ontology: A Study in the Metaphysics of Alfred North Whitehead." Sommers began his academic career at Columbia University, where he was assistant professor of philosophy from 1955 to 1963. He moved to Brandeis University in 1964 as associate professor
of philosophy, was promoted to full professor in 1966, and held the Harry Austryn Wolfson Chair of Philosophy from 1965 until his retirement in 1993.
Sommers was a staunch proponent of a traditionalist view of logic, albeit in a "modern" guise. He has consistently expressed the view that progress in logic should have stopped, if not with Leibniz, than at least before Frege, devising a variant of syllogistic very close to that undertaken by Leibniz. His "Calculus of Terms" applies a system of pluses and minuses to the subjects and predicates of categorical syllogisms, to indicate inclusion and exclusion,
the copula and the negation of the copula, as well as for affirmation and denial, with a universal statement having the form + (–...) or – (+...) for the subject term and a particular statement having the form + (+...) or – (–...) for the subject term. His system is essentially that of Leibniz's, with Leibniz's "=" and "±" replaced in Sommers's notation by "+" and "–" respectively. In Logic of Natural Language Sommers developed the system in more detail
together with a consideration of its purported philosophical implications. He argued that his calculus of terms is significantly different from the predicate logic; but Gregory MCCulloch [1984] argued that there really is no such difference. Sommers claims that his calculus of terms is an elaboration of Leibniz's proposal.
Sommers argued that the subject–predicate semantic analysis of syllogistic propositions with the proper treatment, retains as much deductive power as Frege's calculus, and in a important sense is more expressively powerful than Frege's function-theoretic quantification theory, because it is closer to natural language while being able to handle polyadic relations.
In Sommers's calculus, relational terms are represented in the form 'R ± A ± B ±.... ±K', where R is the relation and some/all A, some/all B, ..., some/all K are objects of R. Thus Sommers is able to analyze such propositions as "All censors withhold some
books from minors" as "W + B – M."
Sommers's "Ordinary Language Tree" for mapping relations among Aristotelian categories was based upon his efforts to arithmeticize Aristotelian syllogistic as a calculus of terms. In Sommers's tree, genera and species give way to subjects and predicates, treated as classes. His book The Logic of Natural Language (1982) provides a detailed, systematic and unified elaboration of the Ordinary Language Tree and the Calculus of Terms and explores the philosophical
import of this logical system. His Invitation to Formal Reasoning: The Logic of Terms (2000) provides a textbook elaboration of the logic of terms."
From: Irving H. Anellis - SOMMERS, Frederic Tamler (1923- ) - in: John R. Shook (ed.) - The dictionary of modern American philosophers - Bristol, Thoemmes, 2005.
EXCERPTS FROM HIS PUBLICATIONS (in progress)
"The thesis I will be arguing for belongs to the premodern -- which is to say, pre-Fregean-tradition of logical theory whose major figures from Aristotle to Leibniz never doubted that the sentences of a natural language like Greek or English that entered into deductive reasoning could, for logical purposes, be parsed in ways familiar to the grammarian. Implicit in the program of traditional formal logic is the idea of a logical syntax of natural language in which
the grammarians' nounphrase/verb-phrase
analysis is the fundamental pattern. (...)The idea of a logical syntax of natural language stands opposed to what the Fregean believes about logical form. Frege himself held that an adequate account of inferences expressed in natural language requires translation into a new idiom, the idiom of a language expressly constructed for use by logicians.
This new logical language is no mere convenience: Frege believed that the syntax of natural language was logically useless, misleading, and incoherent. Being convinced of this, Frege did not criticize the grammarian for misconstruing natural language. On the contrary, from Frege's standpoint the grammarian could well be right in his description of the syntax of natural language. If so the inadequacy is not in the grammarian but in his subject-matter. Michael Dummett aptly
sums up Frege's reaction to the phenomenon
that the natural languages lack a perspicuous logical grammar with the words 'so much the worse for natural language'." pp. 1-2
From: Fred Sommers - The logic of natural language - Oxford, Clarendon Press, 1982.
COMPLETE BIBLIOGRAPHY
"The passing of privileged uniqueness," Journal of Philosophy 49: 392-396 (1952).
"Review: Das 'physikalische Modell' und die 'metaphysische Wirklichkeit'; Versuch einer Metaphänomenologie, by Erwin Nickel," Journal of Philosophy 50: 332-334 (1953).
"The ordinary language tree," Mind 68: 160-185 (1959).
"An important part of any investigation into the meaning of an expression E consists of finding what may be called its sense location. This is done by noting which expressions may be conjoined with E and which may not. "E is that expression which goes well with A, C, or G in a sentence but E fails to make sense when used with B, D, F or H, etc." When the mutual sense relations of A, B, C, D, E, F, G . . . are known, then we have a map in which each expression has a sense location with respect to the other expressions under consideration. The question we shall consider is whether the natural language provides any rules for the construction of such a map, whether there is, as it were, an invariant structure to "linguistic cartography" in terms of which it would be possible to give the sense location of any of the expressions in the language. To this question we shall eventually offer an affirmative answer.
The theory of meaning adopted here is a current one. It is the theory of meaning-in-use. Employing a convenient distinction of Ryle's between two kinds of knowing, we may say that a knowledge of meaning is a "knowing how" rather than a "knowing that": to know the meaning of an expression is to know how to use it. Such knowledge includes an ability to formulate a piece of non-absurd discourse containing the expression. Thus to know the meaning of a word is to know how to formulate some sentences containing the word, to know the meaning of a sentence is to know how to formulate some coherent discourse containing the sentence. It is almost true to say that the meaning is this use, i.e. the meaning of E (if "E" is a word or phrase) is the set of sentences containing E and that my knowledge of the meaning of E grows (though not in direct proportion) with my ability to formulate more and more sentences in which E has a proper use. A complete knowledge of E would then be represented by the set of all such sentences. The trouble with this view is that even such a set would not specify uniquely the meaning of any one expression since the set would also specify the meaning of all those expressions which have the same use-at this level of use. For example, the word " short " might be specified by the sentences in which it has a non-absurd occurrence from a purely semantic point of view, but those sentences may also specify the word "tall". We must therefore keep in mind that a map of sense relations giving the locations of a group of expressions does not tell the whole story of "their use in the language", i.e., their meanings. Nevertheless, we shall see that such a map removes ambiguity, ensuring univocity for the expressions located on it. For this reason we shall identify the sense of an expression with its location on a map. This entails a distinction between sense and meaning, a distinction which we shall enforce rather than justify. The sense of an expression will be its location with respect to other expressions, its semantic range. It is what it "makes sense" with as contrasted with what it fails to make sense with. Its meaning is governed only in part by sense rules. " Tall " and " short " may have the same " sense " ; it is because of other rules governing their use that they diverge in meaning. Thus, giving the sense of an expression is not yet the same as giving its meaning. One who wishes to know more about the meaning of a given located expression will enquire at that address." pp. 160-161.
"Review of: An introduction to Wittgenstein's Tractatus by G. E. M. Anscombe," Philosophy 36: 374-377 (1961).
With J. Jarvis
"Meaning relations and the analytic," Journal of Philosophy 60: 524-534 (1963).
"In his critique of the analytic-synthetic distinction Quine distinguishes two classes of analytic statements: (a1) those that are logically true and (a2) those that lean on extralogical meaning relations. In this paper the same critique that Quine applies against a2 statements is used against a1 statements. By showing that both suffer the same fate at Quine's hands, it is shown that Quine's vital contrast is not a contrast at all and that his criticism goes further than he wants it to go. The paper concludes that the "flight from intension" can become a flight away from the grounds presupposed for any application of logical and linguistic rules."
"Types and ontology," Philosophical Review 72: 327-363 (1963).
Reprinted, with minor corrections, in: Peter Frederick Strawson (ed.) - Philosophical logic - Oxford, Oxford University Press, 1967 pp. 138-169 and in Dale Jacquette (ed.) - Philosophy of logic. An anthology - Oxford, Basil Blackwell 2002 pp. 103-119.
"In this paper (*) I shall be examining several notions of types which have important application in natural languages. I shall show that one of Russell's definitions of a type can be combined with one of Ryle's to give us two other and more powerful type conceptions which are free of the criticisms advanced against each of the former. The results cast considerable light on the relation of `a language' to the sorts of things one can use the language to make statements about; for example, it becomes clear that the number of `sorts of things' discriminated by any natural language is always finite. But far more important, the new type concepts enable us to exhibit formally the type structure of any natural language. It is this structure which determines the way the language discriminates different sorts of things. Since the question of ontology is `What sorts of things are there?' the results may be construed as a formal ontology. The old Russell programme for an ontology which is defined by a logically correct (or corrected) language is thereby reinstated, though in a revised form. That programme has foundered on the type problem for natural languages. Black, for example, has brought out grave difficulties in Russell's type theory as it applies to natural languages, and he used those difficulties to promote scepticism about the Russell programme. But if I am right, a simple and adequate theory of types governs natural language and dictates its ontological commitments to different sorts of things."
(*) There are four sections to the paper. Section I isolates the problem of types for natural language and develops four type concepts appropriate to it. Section II reformulates these concepts syntactically and reconsiders Black's general criticism of a formal theory of types for natural language. In Section III the relation of types to ambiguity, and a problem raised by Black, is examined in detail. Section IV is constructive; the type-structural principle is stated and proved. The ontological meaning of the principle is discussed and the principle is illustratively applied.
"A program for coherence," Philosophical Review 73: 522-527 (1964).
"The following are some points made in reply to criticism of the author's Types and ontology: (1) if p is a property, define the category of p (cp) as the set of individuals that can "significantly" be said to have p. (2) if any "individual" belongs both to cp and cq, then either cp includes cq or cq includes cp or cp=cq. (3) an ontology is coherent only if it satisfies (2) for all individuals.
Suppose that spirits cannot be characterized as colored or colorless, i.e., they are not in c-colored. Assume also that chairs are not in c-sad. Then neither category includes the other. yet persons are in both. To avoid incoherence we must deny that persons are individuals.
Coherent alternatives to Cartesianism put chairs in c-sad (panpsychism) or spirits in c-colored. The thesis supports Russell's general idea than any coherent ontology is formally isomorphic to linguistic type structure."
Predicability. In Philosophy in America. Edited by Black Max. Ithaca: Cornell University Press 1965. pp. 262-281
"A reply to Mr. Odegard's "On closing the truth-value gap"," Analysis 25: 66-68 (1965).
"Why is there something and not nothing?," Analysis 26: 177-181 (1966).
"The question is not why it is possible there is something but (granting that something is possible) why is there something? Why not nothing?
This can be answered by way of an ontological proof. For this purpose we define a neglected but important kind of possibility which we call categorial. We say for example that things older than the square root of 2 are not possible things or that unfed theorems are 'categorially' impossible. A thing older than the square root of 2 is not a possible thing because while there is nothing that is older than the square root of 2, neither is there anything that fails to be. Again the statement `some theorems are fed' is a category mistake. There is nothing that is an unfed theorem and nothing that fails to be one since what failed to be one would be a fed theorem or an unfed non-theorem, or a fed non-theorem and there are no such things. So understood, categorial impossibility is existentially definable. More generally, if D is a monadic descriptive term and D is its logical contrary (2) (applicable to all those D-less things that are 'privative' to the state of being D) then D-things are categorially impossible, if and only if there is nothing that is D and nothing that is -D.
By this definition things that are red and blue (all over)-though presumably impossible in some other way-are categorially possible since any table is either red (failing to be blue) or blue (failing to be red) or it fails to be red and also fails to be blue. The logical contrary of the term `red and blue' is truly affirmable of all material objects of whatever colour and also of those that are colourless.
Without having defined possibility in any general way, we are accepting as a premiss of our argument that something is possible. We assume further that whatever is not a categorially possible thing is not a possible thing.
Now suppose there were nothing. It is then true for every predicate term P, that nothing is P. It is also true that there is nothing that fails to be P so that P-things are categorially impossible. If P-things are categorially impossible, they are not possible things. Since this holds for every P, nothing at all is possible. But we have assumed that something is possible and this is incompatible with the nihilist hypothesis. We see then that if something is possible, something is actual.
The same argument can be viewed another way. If something is possible it is categorially possible. For something to be possible there must be some terms predicable of some things. But if there were nothing at all, all terms would be like 'older than the square root of 2'. That some terms are predicable can be argued from the fact that-as matters actually stand-there are many things and many terms truly applicable to those things. But if there were nothing at all, not only would terms like `old' not be truly applicable, they would be altogether impredicable. Nothing would then be possible. But we recall that our question was not `why is anything even possible?' And we see again that if anything is possible, something is actual." pp. 177-178.
(1) Heidegger considers this the crucial question for the philosophy of existence. What is given here is the traditional or "essentialist" reply.
(2) The relation of contrariety holding between a pair of terms (or attributes) does not force us to consider either one of the pair to be negative. Just as being D is a privation of D, so (equally) is being D (or -D) a privation of D. Coloured objects, for instance, fail to be colourless.
On a Fregean dogma. In Problems in the philosophy of mathematics. Edited by Lakatos Imre. Amsterdam: North-Holland 1966. pp. 47-81
Proceedings of the International Colloquium in the Philosophy of Science (Bedford College, 1965).
"What we can say about God," Judaism 15: 61-73 (1966).
"Do we need identity?," Journal of Philosophy 66: 499-504 (1969).
"Identity is shown to be definable within traditional syllogistic logic. the idea is to treat singular terms as general terms syntactically. this means we allow singular terms in predicate positions and also allow them to be prefixed by 'every', 'some' and 'no' when in subject position.
However universal and particular singular statements are logically equivalent: if K is a singular term then K is p every K is p some K is p. This equivalence is called the law of wild quantity.
Identity is defined thus: J is identical with K df. some J is K. This definition together with the law of wild quantities gives all the formal properties of the identity relation."
"On concepts of truth in natural languages," Review of Metaphysics 23: 259-286 (1969).
"Remarking on alternatives to his conception of truth Tarski rejects a formulation associated with correspondence theories:
If we should decide to extend the popular usage of the term "designate" by applying it not only to names, but also to sentences, and if we agreed to speak of the designata of sentences as "slates of affairs" we could possibly use for the same purpose the following phrase:
(C) A sentence is true if it designates an existing state of affairs. However [this] formulation can lead to various misunderstandings for [it is not] sufficiently precise and clear . . . . It is up to us to look for a more precise expression of our intuitions. (1)
The purpose Tarski speaks of is "to do justice to our intuitions which adhere to the classical Aristotelian conception of truth." Tarski takes this to be some form of correspondence theory. He has earlier considered and rejected an even less satisfactory formula of this sort: 'a sentence is true if it corresponds to reality'. His own semantic conception of truth is meant to be a more precise variant doing justice to the correspondence standpoint. In this spirit I shall presently suggest a revised version of (C).
(1) A. Tarski, "The Semantic, Conception of Truth," Philosophy and Phenomenological Research 4 (1944). Reprinted in H. Feigl and W. Sellars, Readings in Philosophical Analysis (New York, 1945), p. 54. (Page reference is to this reprinting.)
"The calculus of terms," Mind 79: 1-39 (1970).
Reprinted in: George Englebretsen (ed.) The new syllogistic - New York, Peter Lang, 1987
"Confirmation and the natural subject," Philosophical Forum 2: 245-250 (1970).
"Structural ontology," Philosophia.Philosophical quarterly of Israel 1: 21-42 (1971).
"Whether a certain sort of things exists is commonly disputed in philosophy. I argue that in some important classical instances the dispute is grounded in another more fundamental one: whether certain entities are individuals or composite. Disputes over individuality or compositeness are generated when certain accepted conditions for individuality seem not to be satisfied. In the last part of the paper I examine the formal condition for non-compositeness (it is not yet a criterion for individuality) tracing it to its logical source. The condition is shown to provide the structural constraints for coherent ontologies."
Existence and predication. In Logic and ontology. Edited by Munitz Milton. New York: New York University Press 1973. pp. 159-174
Contributions to a seminar on ontology held under the auspices of the New York University Institute of Philosophy for the year 1970-1971.
The logical and the extra-logical. In Methodological and historical essays in the natural and social sciences. Edited by Cohen Robert. and Wartofsky Marx. Dordrecht: Reidel 1973. pp. 235-252
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"Distribution matters," Mind 84: 27-46 (1975).
Leibniz's program for the development of logic. In Essays in memory of Imre Lakatos. Edited by Cohen Robert., Feyerabend Paul, and Wartofsky Marx. Dordrecht: Reidel Publishing Company 1976. pp. 589-615
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Frege or Leibniz? In Studies on Frege. Logic and semantics. Edited by Schirn Matthias. Stuttgart-Bad Cannstatt: Frommann-Holzboog 1976. pp. 11-34
Volume III
Logical syntax in natural language. In Issues in the philosophy of language. Proceedings of the 1972 Oberlin colloquium in philosophy. Edited by MacKay Alfred and Merrill Daniel. New Haven: Yale University Press 1976. pp. 11-42
On predication and logical syntax. In Language in focus: foundations, methods and systems. Essays in memory of Yehoshua Bar-Hillel. Edited by Kasher Asa. Dordrecht: Reidel Publishing Company 1976. pp. 41-53
Dualism in Descartes: the logical ground. In Descartes: critical and interpretative essay. Edited by Hooker Michael. Baltimore: John Hopkins University Press 1978. pp. 223-233
"The grammar of thought," Journal of Social and Biological Structures 1: 39-51 (1978).
Are there atomic propositions? In Midwest Studies in Philosophy. Volume VI. The foundations of analytic philosophy. Edited by French Peter, Uehling Jr.Theodore E., and Wettstein Howard. Minneapolis: University of Minnesota Press 1981. pp. 59-68
This paper is chapter on of The logic of natural language by Fred Sommers, Oxford, Clarendon Press, 1982.
The logic of natural language. Oxford: Oxford University Press 1982.
Linguistic grammar and logical grammar. In How many questions? Essays in honor of Sidney Morgenbesser. Edited by Cauman Leigh et al. Indianapolis: Hackett Publishing Co. 1983. pp. 180-194
"The grammar of thought: a reply to Dauer," Journal of Social and Biological Structures 6: 37-44 (1983).
"The logic of natural language: a reply to Geach," Times Literary Supplement (1983).
January 14th
"The logic of natural language: a further reply to Geach," Times Literary Supplement (1983).
February 18th
Truth and existence. In The new syllogistic. Edited by Englebretsen George. New York: Peter Lang 1987. pp. 299-304
Virtue and vice in everyday life: introductory readings in ethics. Edited by Hoff Sommers Christina and Sommers Fred. San Diego: Harcourt Brace Jovanovich 1989.
Sixth edition: Belmont, Thomson Wadsworth, 2004.
"Predication in the logic of terms," Notre Dame Journal of Formal Logic 31 (1): 106-126 (1990).
The enemy is us: objectivity and its philosophical detractors. In The imperiled Academy. Edited by Dickman Howard. New Brunswick: Transaction Publishers 1993. pp. 239-268
Saying what we think. In Affirmative action and the University: a philosophical inquiry. Edited by Cahn Steven M. Philadelphia: Temple University Press 1993. pp. 291-294
"The world, the facts, and primary logic," Notre Dame Journal of Formal Logic 34 (2): 169-182 (1993).
"Naturalism and realism," Midwest Studies in Philosophy 19: 22-38 (1994).
Existence and correspondence to facts. In Formal ontology. Edited by Poli Roberto and Simons Peter. Dordrecht: Kluwer 1996. pp. 131-158
"Putnam's born-again realism," Journal of Philosophy 94: 453-471 (1997).
An invitation to formal reasoning. The logic of terms. Aldershot: Ashgate 2000.
Co-author: George Englebretsen.
The book "introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers.
This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is, its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights from Aristotle's syllogistic, Scholastic logicians, Leibniz, and the 19th century British algebraists.
Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory."
Term functor grammars. In Variable-free semantics. Edited by Böttner Michael and Thümmel Wolf. Osnabrück: Secolo Verlag 2000. pp. 68-89
The Holocaust and moral philosophy. In Virtue and vice in everyday life. Edited by Hoff Sommers Christina and Sommers Fred. Belmont: Thomson Wadsworth 2004. pp. 150-155
"On the future of logical instruction," American Philosophical Association Newsletter on Teaching Philosophy 1: 176-180 (2004).
Intellectual autobiography. In The old new logic. Essays on the philosophy of Fred Sommers. Edited by Oderberg David S. Cambridge: The MIT Press 2005. pp. 1-23
Comments and replies. In The old new logic. Essays on the philosophy of Fred Sommers. Edited by Oderberg David S. Cambridge: The MIT Press 2005. pp. 211-231
"Belief de Mundo," American Philosophical Quarterly 42: 117-124 (2005).
"Analyzes the theory of belief based on the account of existence and nonexistence as attributes of the world. Argument about the doxastic object in de dicto belief as primitive epistemic act; Truthmaking facts of the positive and negative existential characteristics of the domain under consideration; Approach of the propositionalists towards substitutivity paradoxes."
"Ratiocination: an empirical account," Ratio 21: 115-133 (2009).
"Modern thinkers regard logic as a purely formal discipline like number theory, and not to be confused with any empirical discipline such as cognitive psychology, which may seek to characterize how people actually reason. Opposed to this is the traditional view that even a formal logic can be cognitively veridical -- descriptive of procedures people actually follow in arriving at their deductive judgments (logic as Laws of Thought). In a cognitively veridical logic, any formal proof that a deductive judgment, intuitively arrived at, is valid should ideally conform to the method the reasoning subject has used to arrive at that judgment. More specifically, it should reveal the actual reckoning process that the reasoning subject more or less consciously carries out when they make a deductive inference. That the common logical words used in everyday reasoning -- words such as 'and', 'if,''some', 'is''not,' and 'all -'- have fixed positive and negative charges has escaped the notice of modern logic. The present paper shows how, by unconsciously recognizing 'not' and 'all' as 'minus-words', while recognizing 'and', 'some', and 'is' as 'plus words', a child can intuitively reckon, for example, 'not (-) all (-) dogs are (+) friendly' as equivalent to 'some (+) dogs aren't (-) friendly': -(-D+F) = +D-F."
The new syllogistic. Edited by Englebretsen George. New York:
Peter Lang 1987. Preface IX; Introduction 1; 1. Fred Sommers: The
calculus of terms (reprinted from Mind, 89, (1970) 11; 2. Peter
Swiggart: De Morgan and Sommers p. 57; 3. B. H. Slater: Back to Leibniz or
on from Frege? 87; 4. Peter Frederick Strawson: Review: The logic of
natural language (reprinted from The Journal of Philosophy, 79,
(1982) 99; 5. Richard M. Martin: On the semantics of Sommers' 'Some S'
(reprinted from Mind, modality, meaning and method (1983) 105; 6.
John Bacon: Sommers and modern logic 121; 7. Michael Lockwood: Proofs and
pronouns: extending the system 161; 8. W. H. Friedman: Algebraic rules for
syllogisms and antilogisms 213; 9. Aris Noah: The two term theory of
predication 223; 10. George Englebretsen: Natural syntax and Sommers' theory
of logical form 245; 11. Richard Purtill: Some practical and theoretical
features of Sommers' cancellation method 273; 12. Charles Sayward: Some
problems with TFL [Traditional Formal Logic] 283; 13. Fred Sommers: Truth
and existence 299; 14. George Englebretsen: Logical polarity 305; Notes on
the contributors p. 313; Bibliography p. 315-322
The old new logic. Essays on the philosophy of Fred Sommers.
Edited by Oderberg David S. Cambridge: The MIT Press 2005. Contents:
Preface and acknowledgments VII; Foreword by P. F. Strawson XI-XII; 1. Fred
Sommers: Intellectual autobiography 1; 2. George Englebretsen: Trees, terms,
and truth: the philosophy of Fred Sommers 25; 3. E. J. Lowe: Syntax and
ontology: reflections on three logical systems 49; 4. Frank C. Keil:
Exploring boundary conditions on the structure of knowledge: some nonobvious
influences of philosophy on psychology 67; 5. Alan Berger: General terms,
anaphora, and rigid designation 85; 6. Patrick Suppes: The syntax and
semantics of English prepositional phrases 101; 7. William C. Purdy:
Modeling anaphora in TFL 111; 8. Steven Lindell: An elementary term logic
for physically realizable models of information 135; 9. Aris Noah: Sommers's
cancellations technique and the method of resolution 169; 10. David S.
Odeberg: Predicate logic and bare particulars 183; 11. Comments and replies
211; Works by Fred Sommers 233; Contributors 237; Index 239
Altham J.E.J., "Ambiguity and predication," Mind 80: 253-257
(1971). "Recommends abandoning Sommers' rule about ambiguity, in his
Predictability. The rule enforces many implausible judgments. Three
arguments for it are defective. One involves confusions over negation of a
universal conditional, one rests on a seemingly arbitrary definition, the
third rests on an unrealistic assumption about universes of discourse."
Brody B.A., "Sommers on predicability," Philosophical Studies 23:
138-140 (1972). "Sommers has proposed a principle as to when
cross-categorial predication is univocal. In this note, I offer some
counterexamples, both to his principle and to the premises from which he
derives it."
Cogan Robert, "A criticism of Sommers' language tree," Notre Dame
Journal of Formal Logic 17: 308-310 (1976). "In The Ordinary
Language Tree and three later papers, Fred Sommers has made a number of
valuable contributions to formal type theory. Anyone familiar with this work
of Sommers understands why it is philosophically attractive: the logical
ingenuity shown by Sommers is admirable. However, presuming such familiarity
I shall argue that Sommers' restriction to ordinary language is a necessary
yet counterformal way of securing mapping applicability for his work, and
that it obscures a major obstacle to such application: the fact that genuine
doubt about sense-value is systematic in a way rendering it unresolvable by
his formal methods. I shall first distinguish between "doubt" in the
ordinary sense, and genuine doubt. Next I will show that Sommers' examples
of sense arguments are not ones in which genuine doubt is resolved and then
define the sense in which genuine doubt is systematic, using his own
symbolism. Fourth, I will explain how his restriction to ordinary language
tends to obscure this fact, and fifth, in what way the restriction is both
necessary and counter-formal."
De Sousa Ronald Bon, "The tree of English bears bitter fruit," The
Journal of Philosophy 63: 37-46 (1966). 6. "A discussion of Fred
Sommers' proposal for a new "test of coherence" for ontologies based on a
revised theory of types. The theory leads to intolerably counterintuitive
proliferations of senses of terms in natural languages. Its "proof" is shown
to rest on the very propositions which the theory is supposed to establish.
It presupposes the existence of a well defined set of grammatical but absurd
sentence types. This assumption takes two forms. on the first
interpretation, it prohibits an individual from turning up in two different
categories; on the second interpretation, it amounts to the principle of
transitivity of predication. But the first is supposed to be a "consequence"
of the theory, ruling out Strawsonian persons; and the second turns up as a
"theorem"."
Elgood A.G., "Sommers's rules of sense," Philosophical Quarterly
20: 166-169 (1970). "There has recently been some discussion on Sommers's
rules of sense. Dan Passel (1969) has drawn attention to the incompleteness
of one of these rules (R (U)) but is prepared to accept it as " correct ",
meaning "that no mistakes about terms having a use with one another follow
from its use". Mrs. Susan Haack (1967) has produced what she considers
counter-examples to another rule, that for enforcing ambiguity, and R. Van
Straaten has alleged that these examples are not well-formed and therefore
are not counterexamples. He doubts "for strictly logical reasons" whether
anyone can produce a counter-example. Since he does not give any such
reasons, and since I find the foundations for Sommers's own derivations
unsatisfactory, I offer apparent counter-examples of my own. One
counter-example can be used to invalidate several of Sommers's important
sense rules. This is so because they have a common logical structure. This
logical structure I shall now display."
Greenberg Robert S., "Individuals and the theory of predication," The
Journal of Philosophy 69: 435-448 (1972). "As is known, Fred Sommers
has provided rules of sense (*) which can be used to determine: (a) whether
certain terms can occur together in a significant subject-predicate
sentence, (b) whether things covered by certain terms belong to the same
type of thing, and (c) whether certain terms of a theory must be construed
as being ambiguous, if the theory is to be coherent. Problems such as these
fall within the area of philosophy sometimes called theory of
predication, type theory, or, more generally, ontology, and hence
the purpose of a large part of Sommers' program is to provide methods for
distinguishing and placing in a coherent structure what are generally called
categories."
"Predicability" (1965) and "Types and ontology" (1963).
Griffin Nicholas, "Do we need predication?," Dialogue.Canadian
Philosophical Review 16: 653-663 (1977). "The paper is concerned with
the standard distinction between the 'is' of identity and the 'is' of
predication. It deals, in particular with attempts by Fred Sommers ("Journal
of Philosophy", 1969) and Michael Lockwood ("Philosophical Review", 1975) to
show that the distinction is ill-founded since identity statements are
predications of singular terms. This proposal is criticized mainly on the
grounds that the notion of a singular term depends upon identity and thus
can't be used in a program to eliminate identity. An alternative means of
removing the distinction between the 'is' of identity and the 'is' of
predication, by eliminating predication in favour of relative identities
using Geach's suggestion that "x" is "F" is equivalent to "x" is the same
"F" as something, is briefly sketched."
Haack Susan, "Equivocality: a discussion of Sommers' views," Analysis
28: 159-165 (1967).
Hacking Ian, "Aristotelian categories and cognitive domains,"
Synthese 126: 473-515 (2001). "This paper puts together an ancient
and a recent approach to classificatory language, thought, and ontology. It
includes on the one hand an interpretation of Aristotle's ten
categories,with remarks on his first category, called (or translated as)
substance in the Categories or What a thing is in the Topics. On the other
hand is the idea of domain-specific cognitive abilities urged in
contemporary developmental psychology. Each family of ideas can be used to
understand the other. Neither the metaphysical nor the psychological
approach is intrinsically more fundamental; they complement each other. The
paper incidentally clarifies distinct uses of the word "category" in
different disciplines, and also attempts to make explicit several notions of
"domain". It also examines Aristotle's most exotic and least discussed
categories, being-in-a-position (e.g., sitting) and having-(on) (e.g.,
armour). Finally the paper suggests a tentative connection between Fred
Sommers' theory of types and Aristotle's first category."
Kasher Asa, "Sommers' concept of natural syntax," Philosophical
Studies (Ireland) 20: 139-143 (1972). "It is shown that syntactic
principles are not sufficient for the solution of semantic paradoxes. Light
is shed on Sommers' conception of natural syntax in On concepts of truth
in natural languages (1969), by showing that his solution is also
semantic in nature."
Keating B.F., "Lockwood and Mill on connotation and predication,"
Analysis 4: 183-188 (1979).
Kelley David. The art of reasoning. New York: W. W. Norton & Co.
1994. See Chapter 9: Categorical syllogisms pp. 233-280.
Lockwood Michael, "On predicating proper names," The Philosophical
Review 84: 471-498 (1975). "Mill's account of proper names
presupposes -- contrary to current logical theory -- that in an identity
sentence such as 'Cicero is Tully', 'is' has the same meaning as in
sentences which are unquestionably of the 'S is P' form. The purpose of this
article is to defend Mill's assumption and explore its implications. It is
argued that Mill is inconsistent in holding both that, in the above
sentence, 'Tully' is a genuine predicate and that proper names lack
connotation. This tension may be removed, however, if we allow that proper
names do connote, but that what they connote is merely the having of a
certain identity."
Lockwood Michael, "A question of connotation: an answer to Keating,"
Analysis 39: 189-194 (1979).
Martin Robert L., "Sommers on denial and negation," Nos 3:
219-226 (1969). "Sommers' arguments in Predicability (1965) for a
distinction between denial and negation (the former applying primarily to
predicates, the latter to sentences) are criticized and found not to sustain
the distinction. In response to his claim that the distinction permits a
simple formal resolution of the predication paradoxes, I present a
strengthened version of these paradoxes for which, apparently, the suggested
resolution fails."
Massie David, "Sommers' Tree theory: a reply to de Sousa," The
Journal of Philosophy 64: 185-193 (1967). "In a recent article in
this Journal Ronald Bon de Sousa attempts to criticize Fred Sommers'
category theory, the"tree" theory, as described in "Types and Ontology."
Sommers' paper is an important and brilliant contribution to formal
linguistic analysis, and deserves critical attention. De Sousa, however,
seems to have failed to understand it, in general and in detail; thus his
remarks, which tend to be abusive in tone, are unilluminating and largely
irrelevant. Since de Sousa may give the impression of having been as careful
as he ought to have been, he can easily be misleading on some elementary but
essential points in Sommers' theory, and for that reason his comments call
for an answer."
McCulloch Gregory. Frege, Sommers, singular reference. In Frege:
tradition and influence. Edited by Wright Crispin. Oxford: Blackwell
1984. pp. 110-125 "In his provocative recent book [The logic of
natural language, 1982] Fred Sommers sets out to formulate a traditional
term logic (hereafter TFL) that is a genuine and significant alternative to
the Fregean type of logic (MPL) currently accepted as standard. (1) Broadly
speaking, his procedure has two components. On the one hand, he tries to
develop a logical syntax, based on the TFL model, that is roughly the equal
of MPL in terms of expressive and inferential power. On the other, he
engages in a sustained effort to show how such a logic would be free of
certain logical and semantic commitments, allegedly typical of MPL, that
are, according to Sommers, implausible or otherwise unsatisfactory. In
the present paper I do not question the extent of Sommers's success in the
first task; nor do I try directly to defend MPL against his strictures. My
concern is with one fundamental difference between the two logical
frameworks as Sommers sees them. This supposed difference concerns
expressions like proper names that appear to make straightforward singular
reference to particular objects. Sommers argues at length that many of the
significant differences alleged to hold between the two logics can be traced
to the way that they handle such expressions. This contention he links to
his claim that whereas the basic propositions of MPL are singular, those of
TFL are general; and this in turn he links to his view that the two logics
are based upon significantly different accounts of the first-order
generality expressed by words like 'all' and 'some' (Sommers, Ch. 1-5,
11-12). I try to show that these claims are greatly exaggerated. Even if
one grants that Sommers succeeds in giving a novel, TFL-style account of
first-order generality, it is a mistake to think, as Sommers does, that this
novelty consists in an interesting avoidance of commitment to the idea of
singular reference. This is, furthermore, an entirely distinct issue from
that of the semantic treatment of proper names. Sommers's claims gain a
spurious' plausibility because of his failure to keep these distinct
questions apart. And finally, anyway, we see that one's adoption of logical
framework - TFL or MPL - does not materially affect one's options when
dealing with proper names: both logics can accommodate any of the usual
alternatives. If I am right in all this, the appearance of deep differences
over singular reference just dissolves. Sommers's book deserves careful
and extended attention. Both in the effort to reinstate TFL as a worthwhile
approach, and in the claim to have succeeded, Sommers finds himself in
opposition to much received 'Fregean' opinion in logic, semantics, and the
philosophy of language. Illumination is to be had from a piecemeal treatment
of the many issues raised here. This paper is just one restricted
contribution to that enterprise."
(1) 'MPL' and 'TFL' are Sommers's
own abbreviations for 'Modern Predicate Logic' and 'Traditional Formal
Logic' respectively. He attempts no precise definition of what a logic must
be like if it is to count as MPL-type, but seems to have in mind logics that
employ quantifier/variable notations in a more or less orthodox manner.
Similarly, his use of 'logic' is quite flexible, and is used to apply not
merely to a given calculus but to this plus the concepts, notions, and
presuppositions that a standard semantic interpretation would employ. I
follow him in this, although certain dangers in this are highlighted in
II and III.
Mendelsohn Richard L., "Frege two senses of 'is'," Notre Dame Journal
of Formal Logic 28: 139-160 (1987). 24. "It is widely believed that
there are two senses of 'is', the 'is' of identity and the 'is' of
predication, and that this distinction was clearly drawn by Frege in On
Concept and Object, although it was anticipated by others, perhaps, e.g., by
Plato in the Sophist. As opposed to this received view, I will argue that
Frege had not successfully distinguished two senses of 'is', indeed that his
argument leads to precisely the opposite conclusion; on the other hand, the
distinction Plato had supposedly drawn in the Sophist, which seems to rest
on a semantics Frege was explicitly rejecting, is, given that semantic
framework, viable. Frege had introduced this distinction in order to
buttress his view that proper names could not serve as genuine predicates: a
proper name occupying ostensible predicate position could not be functioning
as a predicate because the 'is' in such a statement would have to be the
'is' of identity, not the 'is' of predication. I will argue that Frege
had been mistaken on this point as well. More generally, I will argue that
Frege's theoretical analysis of language is not, as he had thought,
incompatible with proper names being allowed to play a genuinely predicative
role. My remarks are prompted by Michael Lockwood's stimulating article,
On Predicating Proper Names (1975), which contains an extensive and detailed
criticism of Frege's position."
Murphree Wallace A., "Numerical Term logic," Notre Dame Journal of
Formal Logic 39: 346-362 (1998). "This paper is an attempt to show
that my work to establish numerically flexible quantifiers for the syllogism
can be aptly combined with the term logic advanced by Sommers, Englebretsen,
and others."
Nelson John D., "On Sommers' reinstatement of Russell's ontological
program," The Philosophical Review 73: 517-521 (1964). "In this
discussion-paper I question four theses that I took Sommers to be advancing,
among others, in Types and ontology: (1) that types are indifferent
to predicate denial; (2) that a formal method of type discrimination can
establish as correct a specific ontology; (3) that subjects of sentences can
be located by certain described formal methods; and (4) that there must be
one category that includes all others.
See the reply by Sommers: A
program for coherence - Philosophical Review, 1964, pp. 522-527.
Nelson John D., "An examination of Sommers' truth-functional
counterfactuals," Theoria 31: 61-63 (1965).
Noah Aris, "Predicate functors and the limits of decidability in logic,"
Notre Dame Journal of Formal Logic 21: 701-707 (1980).
Passell Dan, "On Sommers' logic of sense and nonsense," Mind:
132-133 (1969). "Sommers' rule, R(U), for testing sense arguments, taken
as an assertion about what makes sense, fails to state a necessary condition
of what makes sense. Counterexamples to that assertion occur with terms
taken from the same node of his ordinary language tree. For one example, the
color terms, alabaster, blue, cream, dun, which obviously do make sense
together, cannot be classified as making sense together by the rule. This is
because the condition required by the rule for determining that two terms
make sense cannot be met for terms at the same node."
Peterson Philip L., "Contraries and the Cubes and Disks of Opposition,"
Metaphilosophy 26: 107-137 (1995). "Prior, Sommers, and McIntosh
hold that propositional contrariety is derivative, based on term
contrariety. I argue that propositional contrariety is basic. In a proper
Aristotelian square, one proposition is contrary to another if and only if
the one properly entails the denial of the other. Term contrariness
produces a "cube" of opposition. Contrariety can be further elaborated on
"bare" cubes and disks. Geach's analyses involving multiple quantifiers give
no support for term-contrariness-as-basic, and there is little hope for
developing H. W. B. Joseph's vague idea about "furtherest apart" on a
quantitative scale."
Purdy William C., "On the question: 'Do we need Identity?'," Notre
Dame Journal of Formal Logic 33: 593-603 (1992). 31. "This paper
formalizes and extends Sommers' position on identity. This formalization is
compared with MPL to define precisely the difference in expressive power.
The formal language defined for this investigation is similar to the
language of MPL (modern predicate logic). The similarity will not only
facilitate comparison, but perhaps will also make this formal language more
palatable to readers whose experience and/or predisposition favors MPL."
Reinhardt L.R., "Dualism and categories," Proceedings of the
Aristotelian Society 66: 71-92 (1965).
Richmond Samuel A., "Sommers on predicability," The Journal of
Philosophy 68: 138-142 (1971). "Sommers has introduced a rule for
enforcing ambiguity which indicates the conditions under which a term cannot
univocally bridge a type difference. I argue that the theory of predication
from which the rule follows is either false or ambiguous in one of its
crucial concepts. Sommers suggests the theory of predication may better set
the bounds of metaphysics than the theory of knowledge. But the theory of
predication itself needs to be justified by showing its epistemic
utilities."
Richmond Samuel A., "A possible empirical violation of Sommers' rule for
enforcing ambiguity," Philosophical Studies 28: 363-366 (1975).
"In an article entitled "Predicability," Fred Sommers has introduced a rule
for enforcing ambiguity which indicates the logical conditions under which a
predicate cannot univocally bridge a type difference. the rule places
unacceptable a priori restrictions on future empirical discoveries. The
plausibility of the rule can be explained by the fact that violation of it
in constructing empirical universal generalizations results in dualism and
detracts from the unity of science. Dualism exists when there are two
sets of predicates such that members of each set enter into universally
general statements only with members of the same set."
Routley Richard, "Categories. Expressions or things?," Theoria
35: 215-238 (1969). "Rival views on the composition of categories hold
that categories are categories of things, that they are categories of
expressions, or that they are both simultaneously. In view of the
significance paradoxes-analogues of the modal paradoxes - here introduced,
all these positions must be rejected, and two different sorts of
meaninglessness distinguished. This distinction leads to the formulation of
two distinct category theories, one apparently concerned with things, the
other with descriptions. A case is made out for inclusive categories and
against exclusive categories. Systematic ambiguity is attacked and shown to
be tantamount to exclusiveness of categories. To allow for inclusive
categories the usual notion of 'in the same category as' must be abandoned
and replaced by a relative notion, except for certain sorts of categories -
minimal categories. A definition of 'in the same category as' is proposed
for minimal categories; and some aspects of Ryle's theory and Sommers's
theory are examined in the light of these results."
Sayward Charles and Voss Stephen H., "Absurdity and spanning,"
Philosophia.Philosophical Quarterly of Israel 2: 227-238 (1972). "On
the basis of observations J. J. C. Smart once made concerning the absurdity
of sentences like 'the seat of the bed is hard', a plausible case can be
made that there is little point to developing a theory of types,
particularly one of the sort envisaged by Fred Sommers. The authors defend
such theories against this objection by a partial elucidation of the
distinctions between the concepts of spanning and predicability and between
category mistakenness and absurdity in general. The argument suggests that
further clarification of the concepts of spanning and category mistakenness
should be sought in reflection upon the more familiar concepts of a sort of
thing and a predicate category."
Sayward Charles, "A defense of Sommers," Philosophical Studies
29: 343-347 (1976). "Among the theses of Sommers' type theory are these:
every individual belongs to some type; every category is a union of types. A
recent criticism of Sommers is directed at these two theses. I argue that
the criticism is mistaken."
Sayward Charles, "Are there infinitely many sorts of things?,"
Philosophia.Philosophical Quarterly of Israel 8: 17-30 (1978).
Sayward Charles, "The Tree theory and isomorphism," Analysis 41:
6-11 (1981). "A main thesis of Fred Sommers' type theory, is that an
isomorphism exists between any natural language and the categories
discriminated by that language. Here I give an explanation of what this
claim comes to. And then I argue that, so understood, the claim is
incompatible with Zermelo-Fraenkel set theory. Finally, I argue against
trying to salvage the isomorphism thesis by appealing to some other set
theory."
Shearson W.A., "Speaking of philosophy: a reply to Paul Churchland,"
Dialogue.Canadian Philosophical Review 16: 502-506 (1977). "In his
critique of George Englebretsen's Speaking of persons (1975), Paul
Churchland has failed, on several accounts, to grasp the intent of
Englebretsen's work. Most importantly, he has not seen that the main task
there was to defend a particular theory of persons (videlicet attributism).
Much of Churchland's confusion is shown to follow from his inability to
connect Englebretsen's work with the logico-linguistic studies of F. Sommers
on the one hand and the metaphysical studies of P. F. Strawson on the
other."
Suzman Jonathan, "The ordinary language lattice," Mind 81:
434-436 (1972). "F. Sommers ("Mind" 1959, "Philosophical Review" 1963)
claims the predicates (monadic) of natural languages, if grouped by a
relation u, or cosignificance, generate topological trees. if true, this
would have wide philosophical significance; Sommers' ontology rests on this
claim about trees. but it is false, in that the u-relation can be shown not
to generate trees but lattices. if any natural languages do have the tree,
rather than the lattice structure this would need empirical demonstration.
this is proved with the help of two notions, that of the significance range
of a term, and that of a constructible predicate true of all items in a
terms significance range. it is also shown that u is in fact a vacuous tie,
in that all terms are so related."
Swiggart Peter, "The limits of statement denial," Mind 81:
437-442 (1972). "This paper discusses Fred Sommers' distinction between
statement negation and statement denial, as outlined in 'Predicability' and
other papers. First I show that the formal nature of the distinction
requires us to regard a given statement as having only a single denial. This
point dissipates Sommers' proposed solution to the counterfactual problem,
since that solution depends upon the existence of multiple denials of a
given statement. Sommers' difficulty is traced to the assumption that an
ordinary language sentence like 'S is unclean' can be recognized as a
statement denial. But such recognition proves to be inherently ambiguous.
Sommers' terminology can be an effective means of introducing the results of
type analysis into standard logical notation, but strict and possibly
intolerable limits must be placed upon its use in formulating basic type
theory or as a help in solving traditional philosophical problems."
Van Straaten R., "Sommers' rule and equivocity," Analysis 29:
58-61 (1968).
Van Straaten R., "A modification of Sommers' rule," Philosophical
Studies 22: 16-20 (1971).
Van Straaten R., "Sommers on Strawson's and Descartes' ontology,"
Mind 80: 148-149 (1971).
PUBLICATIONS AVAILABLE ON LINE
Project Euclid - Two articles by Fred Sommers published in the Notre Dame Journal of Formal Logic (in PDF format)
Predication in the logic of terms, Notre Dame Journal of Formal Logic 31 (1): 106-126 (1990)
The world, the facts, and primary logic, Notre Dame Journal of Formal Logic 34 (2): 169-182 (1993)
(click on the image to see the PDF file)