Logical Truths

[Guest Ex-monkey]

Ex-monkey, I thought it best to begin a new topic with this post of yours. -Reach

 

Ex-monkey, do you regard your brand of theism as rational? And do you know what the word means? (last time a theist claimed that xtianity was a better standard for logic than naturalism i had to explain what logic was, so just checking, theists like to use certain words they think make them sound intelligent, but fail to think such statements through).

<{POST_SNAPBACK}>

 

AUB,

 

I do regard it as so.

 

I know how I use the term. 'Rationality' is not un-equivocal, AUB. To pretend that it is shows, in fact, that you are not up to date with the state of affairs. Then there are moral issues on how we should use our reason. Or epistemic issues such as, is reason autonomous and ultimate. So, there are differing version, indeed, some elimenative materialists (cf. Churchland) deny things like: truth, reason, etc., as "folk psychology." Reason is a rational faculty whereby we can know truths about the world, it is a gift of God and a tool, thus it is not autonomous or ultimate. So, I'm sure you have a definition, but let's not pretend to be neutral about it.

 

Logic? Interesting that you "explained what it was." This is another area where there is no unified conception. So, I take it that you are just trying to bully people but when someone comes along who knows the state of the debate they see through your charade. Logic is anything but neutral. Here is a good summary of what I mean:

 

The apparent unity of logic which has been presented to many people is usually achieved through revisionist surveys of the field and through sociological prejudice. The "logic" which has been of interest to scholars throughout history is in fact many things, although some writers would hardly let on that it is so. Twenty-three centuries of Indian (Hindu and Buddhist) logic are commonly omitted altogether, despite the significant fact (among others) that therein the three traditional laws of thought from Aristotle have varying validity depending on whether we deal with negations of the nisedha (e.g., 'He will-not love') or paryudasa (e.g., 'He will not-love' or 'Not-he will love') varieties. The "logic" of thought-hygenic interest (Descartes), of all-encompassing philosophic interest (Kant, Hegel, Bradley, Husserl), of empirical interest (Mill), of mathematical interest (Boole, De Morgan), and of formal interest (Russell and Whitehead) are rarely even mentioned for distinguishing. Logics which deal with other basic concepts than quantity, disjunction, etc. are easily ignored by popular writers (e.g., Deontic, Doxastic, Modal logics). And even when we restrict our attention to recent, Western, formal logic - first-order, predicate logic with truth-functional connectives - the illusion of unity often arises either from an unwillingness to raise questions, a concession to pedagogical utility, or from exclusion of those who hold divergent convictions from an academic guild (seeing opponents as not even qualifying as true "logicians" or as being too preposterous to invite to academic conferences on logic).

 

 

 

Because formal logic has been the focus of the most intense philosophical research over the last decades, we will discuss issues germane to it. The unimpressiveness of the prima facie agreement on many logical rules or calculations here should be appreciated, not only because the material identification, translation, or interpretation of formal laws in natural languages (e.g., English, German) remains corrigible, but even more because the truisms on which logicians have agreed seem utterly impotent in settling (or even tending to settle) the major quarrels which lie immediately beyond those truisms. That "formal logic" is a "science" in the honorific sense will turn out to be a pretense of huge proportions. It will be assumed here that our alleged "science" minimally aims to explicate in precise terms the various intuitive notions of "logical truth" and then by means of rational evidence pick out those truths for codification in a formal system by which the validity of arguments can be tested. It will turn out, though, that there is serious disagreement as to what logic is about and, accordingly, how logician's claims should be warranted.

 

 

 

Let us begin, however, simply by inquiring, what are logical truths, and how is their necessity to be characterized? Wittgenstein's characterization in terms of tautologies (true under every interpretation of component propositions in the truth tables) and Carnap's characterization of L-determinates were revisions or explanations of what Leibniz meant by "true in all possible worlds." Quine wrote that logical truths are such that their truth depends only on the logical constants (syncategormatic terms) employed, rendering consideration of their descriptive terms inessential. Ryle saw logical constants as topic-neutral concepts which are supported solely by their logical powers, as discerned in the entailments which they advance. The trouble with one and all of these characterizations is that they will explain what constitutes a logical truth only to those who already understand the notion, for it is repeatedly used or assumed in the characterizations themselves (e.g., Leibniz was interested in all logically possible worlds, Quine gives no general characterization of logical constants but simply enumerates them, and Ryle's interest in entailments assumes the very logical truths which are to be explained).

 

 

 

Well, whatever "logical truths" are, let us at least ask which truths are the logical truths. The history of logic does not encourage us that an agreed upon list can be formulated by all "reasonable" men, for to our embarrassment this history is strewn with bitter controversies and conflicts. The reason for this situation is not hard to find: it turns out that the choice of logical truths is affected by numerous other kinds of questions, for instance the place of ordinary language analysis, the role in intuition, the selection of a metaphysical entity as the subject matter of logic, the understanding of reference, or of modality, or of temporality, the adequacy of nominalistic analyses of "all" statements, the nature and function of the three traditional laws of thought, etc. Not all of the disagreements can even be valued as profitable in a heuristic fashion. If one approaches logical study reverently, expecting sober agreement and stability of approach, he will have to become acquainted with the conflicts separating De Morgan and Hamilton, Mansel or Bradley and Boole or Jevons, Dewey and the logical atomists, Quine or Carnap and Strawson or Wittgenstein.

 

 

 

Philo and Diodorus argued over how to define implication, (respectively) in a truth-functional or temporalized sense, even as William of Sherwood and Peter of Spain would disagree later. Ramus hotly disputed the syllogisms of Aristotle, Valla opposed the third figure of standard syllogistic, the fourth figure was eliminated by Averroes, Zabarella, De Morgan and Jevons, and the whole issue of the syllogism was a fertile ground for continuing debates between the Cartesians and Schoolmen. Should singular propositions be admitted to syllogistic (Hospinianus, Russell) or made equivalent to universal ones (Leibniz, Wallis, Euler)? Are logical operations of subtraction and division uninterpretable (Jevons, Schroder) or significant (Venn)? Should a proposition such as 'All A is B' be interpreted extensionally as 'All A's are contained in B' (Hamilton, De Morgan, Boole) or intensionally as 'Property A contains property B' (Leibniz, Lambert, Jevons, Bradley)? The question of whether universal or categorical propositions have existential import, overlooked by Aristotle, could not be ignored after the discussions of Abelard, Leibniz, Venn, Brentano, and others. Discord has existed over negative terms, definite descriptions, and null classes (as the writings of Russell alone testify). Not only must we countenance these and other disagreements in the study of logic, we must observe that there has been no general agreement even as to the method by which the disagreements could be settled. Since these disagreements define effect the acceptance of logical rules or the validity of arguments, they are surely unsettling in a field allegedly characterized by invariant, obvious, and absolute proof.

 

 

 

The tendency will be for the dogged advocates of an honorific view of the discipline of logic to retrench, I suppose, and contend that at least the "three laws of thought" are objectively certain and beyond question. Identity, contradiction, and excluded middle will be the new, restricted realm of certainty. But little hope can be offered for this revised confidence in "scientific" objectivity and agreement. The ancient Epicureans were vigorous in rejecting the law of excluded middle against Stoic logicians. Medieval scholastics, considering the question of truth in statements expressing future contingencies, were led to reject excluded middle (and to suggest a many-valued logic, as did Peter de Rivo). And modern physicists who have been concerned with philosophical aspects of quantum mechanics have also rejected the traditional law of excluded middle in logic. Although some metaphysical positions cast doubt upon the acceptability of the law (e.g., an Aristotelian view of potentiality in which a thing can be both potentially-B and not potentially-B, or a Hegelian view where things are historically defined over against their negations), it is particularly in terms of an epistemological outlook that the law has been found unacceptable in the last century by the intuitionist school of mathematics or logic (e.g., L. E. J. Brouwer, A. Heyting, in Philosophy of Mathematics, eds. Benacerraf and Putnam).

 

 

 

Intuitionist logicians propound a strong form of verificationism, saying that only propositions which can actually be recognized as true or false can be admitted to be meaningful; it is not enough to know what the conditions of verification could conceivably be, if we could never be in a position to tell whether the verification is actually accomplished or not. This emphasis leads to unique explanations of the logical constants, resulting in a whole new network of inferences which repudiates classic cases of inferential proof. In particular the truth-table definition of 'or' becomes inadequate, for it just may happen that we are not in a position to be warranted in asserting A or in a position to be warranted in asserting B. Even if B is taken as the negation of A, we cannot a priori assume that we must be in a position either to verify or to falsify just any claim; some claims are simply undecidable. Consequently the intuitionist school of logicians reject the law of excluded middle, the law of double negation, and proof by reductio ad absurdum (i.e., deducing a contradiction from the negation of your thesis). Indeed, scholars working on many-valued logics (in contrast to the bivalent traditional logic where every proposition is either true or false) have shown that any number of values can be assigned to the truth tables as an interpretation of a formal system of logic, and the system will attain formal adequacy nonetheless. Intuitionist and deviant logics are evidence that the traditional laws of thought are unsuccessful candidates for parade examples of the objective and invariant certainty of formal logic.

 

 

 

Now then, we do not have a rational and certain answer to the question, what are logical truths? Nor do we have such an answer for the question, which are the logical truths? There are embarrassing conflicts over those truths, so we cannot help but go on and ask how logicians come to know or be confident about any particular logical truth. Russell and others have contended that these logical truths are known a priori, independent of experience. Why, then, is there no universal agreement among reasonable men about them? When, then, do paradoxes arise in their use? For instance the theory of sets, which is fundamental to modern formal logic, allows for the set of all sets which are not members of themselves; this creates a contradiction because the set in question, if it is a member of itself, is not a member of the set mentioned, whereas if it is not a member of itself, then it IS a member of the set mentioned - thus either way, it is both. Apart from ad hoc rescuing devices, this self-contradiction in the very foundation of formal logic allows for the deduction of any and all propositions, which is more than unacceptable for a system of logic. Furthermore, if logical truths are justified a priori and are thereby universal, unchanging, eternal truths, why should they in fact (or why should they be thought to) apply repeatedly in the realm of contingent experience? Why should they be assumed to have anything to do with history, or why should reasoning about history have these "laws of thought" imposed upon it? Moreover, it is strange that, for an a priori system like elementary logic ( containing only truth-functional compounds and singular sentences or existential and universal generalizations involving individual variables), it has been proved that it is impossible to gain a decision procedure for judging the validity of the system as a whole (cf. A. Church, Journal of Symbolic Logic, 1936).

 

 

 

The justification of logical truths along a posteriori lines was proposed by Mill; we gain confidence in them through repeated experience, which is then generalized. Of course, some of the suggested logical truths are so complex or unusual that it is difficult to believe anyone has perceived their instances in experience. But even restricting attention to the others, it should be seen that if their truth cannot be decided independently of experience, then they actually become contingent and lose their necessity. Why should a law of logic which is verified in one domain of experience be taken as true for unexperienced domains as well? If the a priori and a posteriori lines of justification for logical truths are unconvincing, perhaps these propositions or rules are purely a linguistic convention about certain symbols (Ayer, Wittgenstein); the laws of logic would not be taken as inexorably dictated, but rather we impose their necessity on our language. Why, then, are not contradictory systems deemed equally rational? Why are arbitrary conventions like the logical truths so useful in dealing with problems in the world of experience? It is certainly odd, also, that if the system of elementary logic is conventionally chosen, there should be a proposition which is true (of which we are intuitively convinced) and yet unprovable according to the axioms - which is what Godel famously demonstrated (in his article, "On Formally Undecidable Propositions . . . , " originally 1931).

 

 

 

Although the preceding discussion only suggests a program for cross-examining various alternative ways of justifying logical truths, it does give some reason to think that this issue is not an absolutely clear and certain matter in philosophy, and it does remind us that the approaches taken to the question are far from uniform. If the question cannot be clearly answered, we can well go on to ask, does the logician have a rational basis for his claims? When we consider that the lectures and essays by logicians are not likely filled with an uninterrupted series of tautologies, we can examine those propositions which he is most concerned to convey (e.g., "The Barbara syllogism is a valid form of argument," "A proposition has the opposite truth value from its negation"), and at least ask the more general question, what type of evidence does he have for such teachings? Is it the same as the sort of evidence utilized by the biologist, the mathematician, the lawyer, the mechanic, the artist? How different is it from these types of evidence? Anyone who reads the relevant contemporary literature in the philosophy of logic will once again be impressed with two things regarding such questions about the type of evidence available for logicians' claims: first, some authors fail even to reflect upon them, and second, among those who do there is rank Disagreement. Is this really the paradigm of objective, settled, rationality?

 

 

 

The variant approaches to the type of evidence we have for logicians' claims really traces back quite naturally to another question for which logicians offer conflicting answers - namely, the metaphysical question of what kind of entity is mentioned in logicians' claims. If categorically distinct types of objects are thought to be involved, then necessarily categorically distinct modes of cognition or methods of verification will be claimed as well. For instance, should a materialist and a spiritualist agree as to the evidential basis for the claims they will make, one would surely be confused. Plato's realism and rationalism go hand in hand, just as do Hobbes' nominalism and empiricism. Thus metaphysical commitments regarding logicians' claims will be quite relevant to the types of rational support logicians offer for those claims. (Those who wish to resist this truth should consider if their view, that the nature of reality has no bearing whatsoever on logical truths and functions, is not itself a highly dogmatic, metaphysical commitment.)

 

 

 

When we turn to the specification of the ultimate subject matter in the study of logic, we find unquestioned invariance (e.g., Pierce claimed that there were at least a hundred definitions of logic). To the general question, what basic type of entity is mentioned in logicians' claims?, traditional answers include: (1) inferences, which are comprised of judgments made up of concepts (e.g., L. J. Russell, Wm. Thomson, J. G. Hibben), (2) arguments, comprised of propositions made up of terms (Bolzano, Mill, Bosanquet, W. E. Johnson, C. I. Lewis), or (3) proofs, comprised of sentences made up of names (Hilbert, Carnap, Quine). Especially today in the philosophy of logic do the best minds in the field, by their own admission, talk about utterly different things with radically divergent kinds of properties, relations, and modes of cognition. As to the entity which is mentioned in logicians' claims, Frege took the bearer of truth to be a proposition (cf. Mind, vol. 65; Philosophical Writings of Gottlob Frege, eds. Geach and Black) which was existing independently of thought and discourse as a non-sense-perceptible object "grasped" by a special mode of cognition. Strawson takes it to be a statement, an act of utterance involving words, reference, and some kind of internal relations to appropriate circumstances (cf. Introduction to Logical Theory); it is not independent of thought and discourse, but it is non-sense-perceptible. A third major kind of answer offered today holds that the bearer of truth is a sentence, an event of utterance comprised of the physical phenomena of sound sequences interrelated by conditioned response (e.g., Quine, Philosophy of Logic; Word and Object); contrary to Strawson, they have no internal relations and are not immaterial, and contrary to Frege, they are not existing independent of discourse. As the fundamental entity dealt with in logicians' claims, classes or sets are proposed by Putnam (cf. Philosophy of Logic); although they are seen as abstract, it is awkward to think of them as the bearers of truth.

 

 

 

The unsettled nature of the discipline of logic is nowhere more clearly indicated than in the fact that the leading scholars in the field cannot even agree as to (1) what their claims are about, or (2) what kind of rational evidence can be offered for those claims. What little, trivial agreement might appear to be found in certain token inscriptional sequences similar from writer to writer (e.g., "If A is B, and if B is C, then A is C") are emptied of any rational significance by differences which are as fundamental as those that have been noted. Morris Cohen, in A Preface to Logic, freely admits: "if by logic is meant a clear, accurate, and orderly intellectual procedure, then the subject of logic, as presented in current textbooks, comes near being the most illogical in our chaotic curriculum." Logic does not turn out to be an invariant field of elementary self-evident beliefs and set procedures by which all reasonable and educated men have arrived uniformly and with absolute certainty at agreed upon truths, rules, and evaluations of arguments. Nor has it been found that logic sustains relationship to all other fields of study (including epistemology and metaphysics) which is solely and uniquely a one-way foundational relationship to them; we have seen that epistemological and metaphysical presuppositions significantly influence positions taken in "formal logic" - in which case the discipline can hardly be said to be utterly neutral and objective. The last ditch stand for the honorific conception of "science" which was introduced earlier, lifting high the banner of formal logic, must now raise a white flag. Even as with the other disciplines of scholarly study, logic is found wanting in thorough justification and lacking in unity. Given the honorific conception, not even formal logic can truly count as "scientific."

[SmallStone]

When you quote stuff you might want to credit the sources. You look like a plagiarist otherwise.

 

Original text

[SmallStone]

Ex-monkey, I thought it best to begin a new topic with this post of yours. -Reach

AUB,

 

I do regard it as so.

 

I know how I use the term. 'Rationality' is not un-equivocal, AUB.  To pretend that it is shows, in fact, that you are not up to date with the state of affairs.  Then there are moral issues on how we should use our reason.  Or epistemic issues such as, is reason autonomous and ultimate.  So, there are differing version, indeed, some elimenative materialists (cf. Churchland) deny things like: truth, reason, etc., as "folk psychology."  Reason is a rational faculty whereby we can know truths about the world, it is a gift of God and a tool, thus it is not autonomous or ultimate.  So, I'm sure you have a definition, but let's not pretend to be neutral about it.

 

Logic?  Interesting that you "explained what it was."  This is another area where there is no unified conception.  So, I take it that you are just trying to bully people but when someone comes along who knows the state of the debate they see through your charade.  Logic is anything but neutral.  Here is a good summary of what I mean:

 

The apparent unity of logic which has been presented to many people is usually achieved through revisionist surveys of the field and through sociological prejudice. The "logic" which has been of interest to scholars throughout history is in fact many things, although some writers would hardly let on that it is so. Twenty-three centuries of Indian (Hindu and Buddhist) logic are commonly omitted altogether, despite the significant fact (among others) that therein the three traditional laws of thought from Aristotle have varying validity depending on whether we deal with negations of the nisedha (e.g., 'He will-not love') or paryudasa (e.g., 'He will not-love' or 'Not-he will love') varieties. The "logic" of thought-hygenic interest (Descartes), of all-encompassing philosophic interest (Kant, Hegel, Bradley, Husserl), of empirical interest (Mill), of mathematical interest (Boole, De Morgan), and of formal interest (Russell and Whitehead) are rarely even mentioned for distinguishing. Logics which deal with other basic concepts than quantity, disjunction, etc. are easily ignored by popular writers (e.g., Deontic, Doxastic, Modal logics). And even when we restrict our attention to recent, Western, formal logic - first-order, predicate logic with truth-functional connectives - the illusion of unity often arises either from an unwillingness to raise questions, a concession to pedagogical utility, or from exclusion of those who hold divergent convictions from an academic guild (seeing opponents as not even qualifying as true "logicians" or as being too preposterous to invite to academic conferences on logic).

 

 

 

Because formal logic has been the focus of the most intense philosophical research over the last decades, we will discuss issues germane to it. The unimpressiveness of the prima facie agreement on many logical rules or calculations here should be appreciated, not only because the material identification, translation, or interpretation of formal laws in natural languages (e.g., English, German) remains corrigible, but even more because the truisms on which logicians have agreed seem utterly impotent in settling (or even tending to settle) the major quarrels which lie immediately beyond those truisms. That "formal logic" is a "science" in the honorific sense will turn out to be a pretense of huge proportions. It will be assumed here that our alleged "science" minimally aims to explicate in precise terms the various intuitive notions of "logical truth" and then by means of rational evidence pick out those truths for codification in a formal system by which the validity of arguments can be tested. It will turn out, though, that there is serious disagreement as to what logic is about and, accordingly, how logician's claims should be warranted.

 

 

 

Let us begin, however, simply by inquiring, what are logical truths, and how is their necessity to be characterized? Wittgenstein's characterization in terms of tautologies (true under every interpretation of component propositions in the truth tables) and Carnap's characterization of L-determinates were revisions or explanations of what Leibniz meant by "true in all possible worlds." Quine wrote that logical truths are such that their truth depends only on the logical constants (syncategormatic terms) employed, rendering consideration of their descriptive terms inessential. Ryle saw logical constants as topic-neutral concepts which are supported solely by their logical powers, as discerned in the entailments which they advance. The trouble with one and all of these characterizations is that they will explain what constitutes a logical truth only to those who already understand the notion, for it is repeatedly used or assumed in the characterizations themselves (e.g., Leibniz was interested in all logically possible worlds, Quine gives no general characterization of logical constants but simply enumerates them, and Ryle's interest in entailments assumes the very logical truths which are to be explained).

 

 

 

Well, whatever "logical truths" are, let us at least ask which truths are the logical truths. The history of logic does not encourage us that an agreed upon list can be formulated by all "reasonable" men, for to our embarrassment this history is strewn with bitter controversies and conflicts. The reason for this situation is not hard to find: it turns out that the choice of logical truths is affected by numerous other kinds of questions, for instance the place of ordinary language analysis, the role in intuition, the selection of a metaphysical entity as the subject matter of logic, the understanding of reference, or of modality, or of temporality, the adequacy of nominalistic analyses of "all" statements, the nature and function of the three traditional laws of thought, etc. Not all of the disagreements can even be valued as profitable in a heuristic fashion. If one approaches logical study reverently, expecting sober agreement and stability of approach, he will have to become acquainted with the conflicts separating De Morgan and Hamilton, Mansel or Bradley and Boole or Jevons, Dewey and the logical atomists, Quine or Carnap and Strawson or Wittgenstein.

 

 

 

Philo and Diodorus argued over how to define implication, (respectively) in a truth-functional or temporalized sense, even as William of Sherwood and Peter of Spain would disagree later. Ramus hotly disputed the syllogisms of Aristotle, Valla opposed the third figure of standard syllogistic, the fourth figure was eliminated by Averroes, Zabarella, De Morgan and Jevons, and the whole issue of the syllogism was a fertile ground for continuing debates between the Cartesians and Schoolmen. Should singular propositions be admitted to syllogistic (Hospinianus, Russell) or made equivalent to universal ones (Leibniz, Wallis, Euler)? Are logical operations of subtraction and division uninterpretable (Jevons, Schroder) or significant (Venn)? Should a proposition such as 'All A is B' be interpreted extensionally as 'All A's are contained in B' (Hamilton, De Morgan, Boole) or intensionally as 'Property A contains property B' (Leibniz, Lambert, Jevons, Bradley)? The question of whether universal or categorical propositions have existential import, overlooked by Aristotle, could not be ignored after the discussions of Abelard, Leibniz, Venn, Brentano, and others. Discord has existed over negative terms, definite descriptions, and null classes (as the writings of Russell alone testify). Not only must we countenance these and other disagreements in the study of logic, we must observe that there has been no general agreement even as to the method by which the disagreements could be settled. Since these disagreements define effect the acceptance of logical rules or the validity of arguments, they are surely unsettling in a field allegedly characterized by invariant, obvious, and absolute proof.

 

 

 

The tendency will be for the dogged advocates of an honorific view of the discipline of logic to retrench, I suppose, and contend that at least the "three laws of thought" are objectively certain and beyond question. Identity, contradiction, and excluded middle will be the new, restricted realm of certainty. But little hope can be offered for this revised confidence in "scientific" objectivity and agreement. The ancient Epicureans were vigorous in rejecting the law of excluded middle against Stoic logicians. Medieval scholastics, considering the question of truth in statements expressing future contingencies, were led to reject excluded middle (and to suggest a many-valued logic, as did Peter de Rivo). And modern physicists who have been concerned with philosophical aspects of quantum mechanics have also rejected the traditional law of excluded middle in logic. Although some metaphysical positions cast doubt upon the acceptability of the law (e.g., an Aristotelian view of potentiality in which a thing can be both potentially-B and not potentially-B, or a Hegelian view where things are historically defined over against their negations), it is particularly in terms of an epistemological outlook that the law has been found unacceptable in the last century by the intuitionist school of mathematics or logic (e.g., L. E. J. Brouwer, A. Heyting, in Philosophy of Mathematics, eds. Benacerraf and Putnam).

 

 

 

Intuitionist logicians propound a strong form of verificationism, saying that only propositions which can actually be recognized as true or false can be admitted to be meaningful; it is not enough to know what the conditions of verification could conceivably be, if we could never be in a position to tell whether the verification is actually accomplished or not. This emphasis leads to unique explanations of the logical constants, resulting in a whole new network of inferences which repudiates classic cases of inferential proof. In particular the truth-table definition of 'or' becomes inadequate, for it just may happen that we are not in a position to be warranted in asserting A or in a position to be warranted in asserting B. Even if B is taken as the negation of A, we cannot a priori assume that we must be in a position either to verify or to falsify just any claim; some claims are simply undecidable. Consequently the intuitionist school of logicians reject the law of excluded middle, the law of double negation, and proof by reductio ad absurdum (i.e., deducing a contradiction from the negation of your thesis). Indeed, scholars working on many-valued logics (in contrast to the bivalent traditional logic where every proposition is either true or false) have shown that any number of values can be assigned to the truth tables as an interpretation of a formal system of logic, and the system will attain formal adequacy nonetheless. Intuitionist and deviant logics are evidence that the traditional laws of thought are unsuccessful candidates for parade examples of the objective and invariant certainty of formal logic.

 

 

 

Now then, we do not have a rational and certain answer to the question, what are logical truths? Nor do we have such an answer for the question, which are the logical truths? There are embarrassing conflicts over those truths, so we cannot help but go on and ask how logicians come to know or be confident about any particular logical truth. Russell and others have contended that these logical truths are known a priori, independent of experience. Why, then, is there no universal agreement among reasonable men about them? When, then, do paradoxes arise in their use? For instance the theory of sets, which is fundamental to modern formal logic, allows for the set of all sets which are not members of themselves; this creates a contradiction because the set in question, if it is a member of itself, is not a member of the set mentioned, whereas if it is not a member of itself, then it IS a member of the set mentioned - thus either way, it is both. Apart from ad hoc rescuing devices, this self-contradiction in the very foundation of formal logic allows for the deduction of any and all propositions, which is more than unacceptable for a system of logic. Furthermore, if logical truths are justified a priori and are thereby universal, unchanging, eternal truths, why should they in fact (or why should they be thought to) apply repeatedly in the realm of contingent experience? Why should they be assumed to have anything to do with history, or why should reasoning about history have these "laws of thought" imposed upon it? Moreover, it is strange that, for an a priori system like elementary logic ( containing only truth-functional compounds and singular sentences or existential and universal generalizations involving individual variables), it has been proved that it is impossible to gain a decision procedure for judging the validity of the system as a whole (cf. A. Church, Journal of Symbolic Logic, 1936).

 

 

 

The justification of logical truths along a posteriori lines was proposed by Mill; we gain confidence in them through repeated experience, which is then generalized. Of course, some of the suggested logical truths are so complex or unusual that it is difficult to believe anyone has perceived their instances in experience. But even restricting attention to the others, it should be seen that if their truth cannot be decided independently of experience, then they actually become contingent and lose their necessity. Why should a law of logic which is verified in one domain of experience be taken as true for unexperienced domains as well? If the a priori and a posteriori lines of justification for logical truths are unconvincing, perhaps these propositions or rules are purely a linguistic convention about certain symbols (Ayer, Wittgenstein); the laws of logic would not be taken as inexorably dictated, but rather we impose their necessity on our language. Why, then, are not contradictory systems deemed equally rational? Why are arbitrary conventions like the logical truths so useful in dealing with problems in the world of experience? It is certainly odd, also, that if the system of elementary logic is conventionally chosen, there should be a proposition which is true (of which we are intuitively convinced) and yet unprovable according to the axioms - which is what Godel famously demonstrated (in his article, "On Formally Undecidable Propositions . . . , " originally 1931).

 

 

 

Although the preceding discussion only suggests a program for cross-examining various alternative ways of justifying logical truths, it does give some reason to think that this issue is not an absolutely clear and certain matter in philosophy, and it does remind us that the approaches taken to the question are far from uniform. If the question cannot be clearly answered, we can well go on to ask, does the logician have a rational basis for his claims? When we consider that the lectures and essays by logicians are not likely filled with an uninterrupted series of tautologies, we can examine those propositions which he is most concerned to convey (e.g., "The Barbara syllogism is a valid form of argument," "A proposition has the opposite truth value from its negation"), and at least ask the more general question, what type of evidence does he have for such teachings? Is it the same as the sort of evidence utilized by the biologist, the mathematician, the lawyer, the mechanic, the artist? How different is it from these types of evidence? Anyone who reads the relevant contemporary literature in the philosophy of logic will once again be impressed with two things regarding such questions about the type of evidence available for logicians' claims: first, some authors fail even to reflect upon them, and second, among those who do there is rank Disagreement. Is this really the paradigm of objective, settled, rationality?

 

 

 

The variant approaches to the type of evidence we have for logicians' claims really traces back quite naturally to another question for which logicians offer conflicting answers - namely, the metaphysical question of what kind of entity is mentioned in logicians' claims. If categorically distinct types of objects are thought to be involved, then necessarily categorically distinct modes of cognition or methods of verification will be claimed as well. For instance, should a materialist and a spiritualist agree as to the evidential basis for the claims they will make, one would surely be confused. Plato's realism and rationalism go hand in hand, just as do Hobbes' nominalism and empiricism. Thus metaphysical commitments regarding logicians' claims will be quite relevant to the types of rational support logicians offer for those claims. (Those who wish to resist this truth should consider if their view, that the nature of reality has no bearing whatsoever on logical truths and functions, is not itself a highly dogmatic, metaphysical commitment.)

 

 

 

When we turn to the specification of the ultimate subject matter in the study of logic, we find unquestioned invariance (e.g., Pierce claimed that there were at least a hundred definitions of logic). To the general question, what basic type of entity is mentioned in logicians' claims?, traditional answers include: (1) inferences, which are comprised of judgments made up of concepts (e.g., L. J. Russell, Wm. Thomson, J. G. Hibben), (2) arguments, comprised of propositions made up of terms (Bolzano, Mill, Bosanquet, W. E. Johnson, C. I. Lewis), or (3) proofs, comprised of sentences made up of names (Hilbert, Carnap, Quine). Especially today in the philosophy of logic do the best minds in the field, by their own admission, talk about utterly different things with radically divergent kinds of properties, relations, and modes of cognition. As to the entity which is mentioned in logicians' claims, Frege took the bearer of truth to be a proposition (cf. Mind, vol. 65; Philosophical Writings of Gottlob Frege, eds. Geach and Black) which was existing independently of thought and discourse as a non-sense-perceptible object "grasped" by a special mode of cognition. Strawson takes it to be a statement, an act of utterance involving words, reference, and some kind of internal relations to appropriate circumstances (cf. Introduction to Logical Theory); it is not independent of thought and discourse, but it is non-sense-perceptible. A third major kind of answer offered today holds that the bearer of truth is a sentence, an event of utterance comprised of the physical phenomena of sound sequences interrelated by conditioned response (e.g., Quine, Philosophy of Logic; Word and Object); contrary to Strawson, they have no internal relations and are not immaterial, and contrary to Frege, they are not existing independent of discourse. As the fundamental entity dealt with in logicians' claims, classes or sets are proposed by Putnam (cf. Philosophy of Logic); although they are seen as abstract, it is awkward to think of them as the bearers of truth.

 

 

 

The unsettled nature of the discipline of logic is nowhere more clearly indicated than in the fact that the leading scholars in the field cannot even agree as to (1) what their claims are about, or (2) what kind of rational evidence can be offered for those claims. What little, trivial agreement might appear to be found in certain token inscriptional sequences similar from writer to writer (e.g., "If A is B, and if B is C, then A is C") are emptied of any rational significance by differences which are as fundamental as those that have been noted. Morris Cohen, in A Preface to Logic, freely admits: "if by logic is meant a clear, accurate, and orderly intellectual procedure, then the subject of logic, as presented in current textbooks, comes near being the most illogical in our chaotic curriculum." Logic does not turn out to be an invariant field of elementary self-evident beliefs and set procedures by which all reasonable and educated men have arrived uniformly and with absolute certainty at agreed upon truths, rules, and evaluations of arguments. Nor has it been found that logic sustains relationship to all other fields of study (including epistemology and metaphysics) which is solely and uniquely a one-way foundational relationship to them; we have seen that epistemological and metaphysical presuppositions significantly influence positions taken in "formal logic" - in which case the discipline can hardly be said to be utterly neutral and objective. The last ditch stand for the honorific conception of "science" which was introduced earlier, lifting high the banner of formal logic, must now raise a white flag. Even as with the other disciplines of scholarly study, logic is found wanting in thorough justification and lacking in unity. Given the honorific conception, not even formal logic can truly count as "scientific."

<{POST_SNAPBACK}>

Quoted for posterity.

 

I saw you browsing this thread a little while ago. You had your chance to properly attribute the text you stole from Dr. Bahnsen and chose not to do so. Don't say I'm not fair.

 

Rameus demonstrated what an intellectual fool you are and now I've demonstrated what an intellectual cheat you are. Your work here is through. Be gone.

[Reality Amplifier]

Ouch!

[Guest Ex-monkey]

Rameus did no such thing. I challenge you to take the debate to your local college Phi. prof and ask him to evaluate it.

 

I did not say I wrote it, I didn't mention it so that people would read it and not just say, "oh, another TAGer, Grag Bahnsen" and not even read it.

 

Anyway, way to deal with the arguments... you hack.

[webmdave]

Rameus did no such thing.  I challenge you to take the debate to your local college Phi. prof and ask him to evaluate it.

 

I did not say I wrote it, I didn't mention it so that people would read it and not just say, "oh, another TAGer, Grag Bahnsen" and not even read it.

 

Anyway, way to deal with the arguments... you hack.

 

 

I didn't SAY I wrote it.... you hack...

[Asimov]

hack....

 

is it just me, or is there some irony in what he said?

[mrtruth]

I did not say I wrote it, I didn't mention it so that people would read it and not just say, "oh, another TAGer, Grag Bahnsen" and not even read it.

 

I believe you ex-monkey. However....you know how it looks....

[chefranden]

Well I read the whole thing. While it does illustrate argument about what is reasonable, I don't see how it defends Christianity as reasonable. Perhaps Ex-monkey was only answering question 2 -- do you know what logic is? At first I assumed Ex-monkey was the author, but then it began to seem too well written for a post -- who goes to that much trouble in a forum?

 

One would expect that a Christian would not try to lead anyone on like that. --- not!!!

 

I suppose though that a person that follows Calvin's god would feel justified in perpetrating a little pious fraud. Since we are obviously not the elect, we need not be treated with respect by an otherwise "honorable" person who is of the elect.

[♦ nivek ♦]

I have a fucking headache...

 

MankeePaul uses page after page of assorted bullshit to try and talk around a subject that oughta be as plain as a bug in my teeth at 80 mph...

 

If the *trVth of daGoodelard* was so goddamn obvious, why does it take eleventy-zillion pages of shit piled on cold stale bread to make it paletable?

 

Mankeebot and his sort use all this neato obtuse crap in an attempt to impress folks with their legendary_in_their_own_minds prowness in theo-ology...

 

Some poor dull_knife_in_camp_drawer sort such as daFatman looks at this piled up offal in Dave's frontroom floor and wonders what or who it was supposed to impress..

 

n

[Zach]

Logic... is another area where there is no unified conception.

I find this strange, since you purport to use the idea of "logic" to prove the existence of God.

[Fweethawt]

When you quote stuff you might want to credit the sources. You look like a plagiarist otherwise.

 

Original text

 

SS,

 

You noticed the very same thing that I did once I got about half-way through that post. I said to myself, "Self, this dude copied and pasted.", then sure enough, there you were bustin' his nuggets for the whole forum to see.

 

<<<shakes SmallStone's hand>>>

 

 

Then I realized, here I sit, a poor, helpless, and eternally condemned soul who always gives credit to whom it is due whenever I'm aware of the author of writings that I post. I'm so evil.

 

 

[SmallStone]

Rameus did no such thing.

Ok.

I challenge you to take the debate to your local college Phi. prof and ask him to evaluate it.

It would be more appropriate to take your post to my local college Phi. prof and ask him if he would consider it to be an intellectually honest presentation.

I did not say I wrote it, ...

Think local college Phi. prof would accept that? C'mon. I assume that you want your posts and arguments to be carefully and thoughtfully considered. You seem to have a bent for the academic so I approached your post with the same mindset that one might have when grading a paper or reading a scholarly work. Isn't that what you want? Why then should my expectations be any different?

... I didn't mention it so that people would read it and not just say, "oh, another TAGer, Grag Bahnsen" and not even read it.

People are going to say "oh, the same old TAGer" when they see you've authored a post anyway. Properly attributed material isn't going to scare people off. This is worse than "the dog ate my homework". Only you know your intent, but it was dishonest regardless of it.

Anyway, way to deal with the arguments... you hack.

Way to present arguments. If approaching -your- post seriously, and then feeling cheated when I discover it is a plagiarization makes me a hack, then I'm a hack.

[Fweethawt]

Only you know your intent, but it was dishonest regardless of it.

<<<playing the Ex-Monkey card here>>>

 

How do you know that what I did was dishonest? By what mental faculties and tools of logic and reason do you come to this conclusion? How do you know that you aren't being deceived?

 

HAHA! I've beaten you at your own game, loser!

 

HAHA! I win!!!!

 

<<<going back to Fwee mode>>>

 

God damn that hurt! I sure as hell won't try that again!

 

[Fweethawt]

AUB,

 

I do regard it as so.

 

I know how I use the term. 'Rationality' is not un-equivocal, AUB.  To pretend that it is shows, in fact, that you are not up to date with the state of affairs.  Then there are moral issues on how we should use our reason.  Or epistemic issues such as, is reason autonomous and ultimate.  So, there are differing version, indeed, some elimenative materialists (cf. Churchland) deny things like: truth, reason, etc., as "folk psychology."  Reason is a rational faculty whereby we can know truths about the world, it is a gift of God and a tool, thus it is not autonomous or ultimate.  So, I'm sure you have a definition, but let's not pretend to be neutral about it.

 

Logic?  Interesting that you "explained what it was."  This is another area where there is no unified conception.  So, I take it that you are just trying to bully people but when someone comes along who knows the state of the debate they see through your charade.  Logic is anything but neutral.  Here is a good summary of what I mean:

 

AUB,

 

Before you go through the trouble of separating Ex-Monkey's contribution to your argument from what he copied and pasted from somewhere else, I've taken the liberty of doing so. Of course, I have no doubts of your ability to see through his charade.

[SmallStone]

Then I realized, here I sit, a poor, helpless, and eternally condemned soul who always gives credit to whom it is due whenever I'm aware of the author of writings that I post. I'm so evil. 

Tube amps sound best when they are hot and on the verge of melting down. I look forward to trading a few guitar licks in hell with ya. What, with all the satanic influence in rock music, there has to be some instruments laying around there somewhere.

[Loren]

[Fweethawt]

Tube amps sound best when they are hot and on the verge of melting down. I look forward to trading a few guitar licks in hell with ya. What, with all the satanic influence in rock music, there has to be some instruments laying around there somewhere. 

 

Sounds good to me! I'll bring the (cold) beer.

 

(Heck! Might as well threadjack this. It was over once you busted him anyway)

 

 

But anyway, we finally got around to getting that Epi. Les Paul for my son. The quilt-top isn't anywhere near as pronounced as it was in any of the photographs that I found. The body is very dark and you can't really see the quilt pattern unless you're right on top of it. My son prefers it this way (which is kinda cool once you realize why). He said that he didn't want anything real fancy or flashy and that he'd rather have this guitar that looks so much darker as to be quite unique compared to the others.

 

Oh yeah, I almost forgot... it raaaaaaaaawks!!!!

 

Neither one of us knew what we were missing until we heard the difference between a nice guitar and the junk that we've been playing. It's like night'n day! It's like black'n white.

 

It's like Ex-Monkey'n Goldie... ummm, waitaminute!!

 

Well, you get the idea.

 

It's nice. We like it, and we're glad that we got it.

[Reach]

I'm going to go see if there are any more posts that need to be moved.

[Fweethawt]

I'm going to go see if there are any more posts that need to be moved.

 

Dear Reach, please don't subject yourself to this.

 

This thread here is more than enough to show this poster's credibility. The chain-reaction alone will trickle down with each post that he makes from this point on.

[Fweethawt]

ooOOOooops! Were you talkin' 'bout Loren or Ex-Monkey?

 

 

(I didn't see the twitchin' fish until after I made that post.)

 

[MrSpooky]

So, there are differing version, indeed, some elimenative materialists (cf. Churchland) deny things like: truth, reason, etc., as "folk psychology."

 

You are BLATANTLY wrong there. Eliminative materialists argue that CONSCIOUSNESS is "folk psychology," NOT reason. This is a huge error that no serious student of epistemology/philosophy of mind would make.

 

Sweet god, you have no philosophical training at all do you, Paul? You're just throwing whatever random long-winded philosophy you can at us in the hopes that in our confusion we'll relent and say "Wow, you might have a point but I'm too lazy to read all that crap so I think you're smarter than me on this!"

 

Is your primary philosophy "if you can't convince em, confuse em"? If so, you share the same philosophy as Garfield the cat.

[Fweethawt]

Is your primary philosophy "if you can't convince em, confuse em"? 

 

MrSpooky,

 

Isn't this the primary directive behind all of theology? To me, I see this as the main power behind Christianity™. The confusion.

[MrSpooky]

Nah, some theologists make genuine attempts.

[Asimov]

I was too lazy to read it...