Why logic works

[DavidOdden]

I'm not certain how cognitive science could explain the subject matter at hand, since one would need to use the tools of study in order to study them.

Are you referring to the historical chicken-and-egg problem that we don't know whether The First Logician in fact developed a formal notation and then looked for a use for it, or discovered an epistemological fact and sought a way of packaging it? Now hopefully it is clear to you (from everything I've ever said on the topic here) that I think that anyone interested in the area should know symbolic logic, if for no other reason so that they have an explicit method for focusing on different apects of reasoning. Cognitive science can use whatever arbitrary and lousy tools it wants to in the search for better tools, as long as cognitive scientists don't take the flaws of some kind of system of formal deduction to automatically mean anything about reasoning.

These studies do not, and cannot, investigate such things as the law of non-contradiction any more than the computer sciences can (merely because they study a given piece of hardware that may perform operations which we interpret as application of non-contradiction).

Au contraire, cognitive science can reveal whether existential quantification, horseshoe (as used), or disjunction are valid aspects of reasoning.

For I’m not sure how a language differs from a symbolic system.

Language is a type of symbolic system. Mathematics is another. (Grafitti) tagging is a third. Hence my reference to the genus-species way of looking at things.

But the symbolism is supposed to reveal their necessity.

And you're not saying that symbolism causes necessary-truth. I don't see how symbolism reveals the necessity of any

Indeed, it is unfathomable to me how they might possibly be false. So I contend that it's impossible for them to fail to preserve truth, and that naturally leads me to hold that they're necessary.

You are clandestinely appealing to empirical considerations: you've reflected extensively on what the facts of reality are, and concluded that certain of these claims of symbolic logic are indeed true. This is fine, since you are letting reality be the ajudicator of the validity of proposed logical laws and relationships. If you don't do this and if you approach logic from the pure-rationalist perspective, then there should be no limit on what you can fathom. If I were to challenge your logic my saying that I can fathom a universe which does not have the Law of the Excluded Middle, I don't see what you could say other than "Hmmm. I have nothing to say about that".

Anyway, I don't think anybody holds that we have a collection of symbols representing the whole of valid reasoning. What is claimed is that these symbolic representations show some part of valid reasoning, or at the very least, of rule-following.

Apart the better-known insufficiency problem, there is also the necessity problem. We all know that horseshoe is unnecessary; I have not seen evidence that existential quantification is necessary for modeling reasoning, and I suspect that universal quantification as such is not, that the job is properly done by concept-formation and definition (however I don't know whether there is a substantive difference between that and what one does with upside down A).

[Thomas M. Miovas Jr.]

Not to see the difference, but for it to be intelligible that there is a difference. Suppose you have no laws of logic, and so you have no law of non-contradiction, and so you see a cat and at the same time it is a bicycle. Nothing is to stop the catcycle from being the dogskates that they are. Only non-contradiction, or something very like it, can keep away such absurdity.

That's not necessarily the claim being made here, though. This logic, outside of which thought is impossible, may be (in fact, I suspect, is) a feature of reality, like mathematics.

My point is that the laws of logic do not exist in the human mind prior to making observations about reality. The law of non-contradiction does not exist in the world making everything comply with being itself instead of being something else -- it is what it is because it is, and it does not require something acting on it, say God or the laws of logic written into the fabric of the universe, in order to be what it is. So, no, logic is not a feature of reality, but rather is man's grasp of reality using his mind in a manner that does not contradict reality. How does he know not to do this without having the laws of logic, as in how did the first logician figure it out? Well, he observed reality and he observed how his mind operated in order to understand the world, then he derived the laws of logic from that necessity of his mind conforming to reality before he could go on to steps beyond simple observations.

No one is going to see a catcycle, because catcycles do not exist. I suppose someone could build a bike with cat-like features (fur and a tail and maybe even make cat noises), but it is what it is and it is not a cat. Having one's own mind conform to reality -- to what one observes -- is the root of logic; it is not as if someone came up with a schema in his head without looking at reality and then tried it to see if it worked. The most fundamental aspects of human cognition are self-evident and inductive. I mean, one can misidentify a cat as a bicycle and try to hope on one and peddle it, but it won't get you anywhere and may leave you with a few scratches

As to should everyone learn formal logic; in a certain sense, yes, because having it formalized makes it easier to check one's premises, just as language makes it easier to think something through; however, I wouldn't say everyone ought to know what the symbols mean in a logicians formulation. On those lines, it would be like saying everyone ought to learn vector calculus, which I don't think is the case. One can be quite logical without reducing one's sentences to the logician's symbols. I haven't formally study logic in that sense, but I can still be logical. I have studied vector calculus, but I've never used it since college. Basically, I took Dr. Peikoff's course on logic, which was written mainly in English and not a lot of symbolism. I suppose in the same way one can use vector calculus to figure out complicated dynamics, one can use highly symbolic logic to figure out complicated scenarios, but I don't use it that way, I simply think it through based on the facts as I understand them.

[aleph_0]

Are you referring to the historical chicken-and-egg problem that we don't know whether The First Logician in fact developed a formal notation and then looked for a use for it, or discovered an epistemological fact and sought a way of packaging it? Now hopefully it is clear to you (from everything I've ever said on the topic here) that I think that anyone interested in the area should know symbolic logic, if for no other reason so that they have an explicit method for focusing on different apects of reasoning. Cognitive science can use whatever arbitrary and lousy tools it wants to in the search for better tools, as long as cognitive scientists don't take the flaws of some kind of system of formal deduction to automatically mean anything about reasoning.Au contraire, cognitive science can reveal whether existential quantification, horseshoe (as used), or disjunction are valid aspects of reasoning.Language is a type of symbolic system. Mathematics is another. (Grafitti) tagging is a third. Hence my reference to the genus-species way of looking at things.And you're not saying that symbolism causes necessary-truth. I don't see how symbolism reveals the necessity of any

You are clandestinely appealing to empirical considerations: you've reflected extensively on what the facts of reality are, and concluded that certain of these claims of symbolic logic are indeed true. This is fine, since you are letting reality be the ajudicator of the validity of proposed logical laws and relationships. If you don't do this and if you approach logic from the pure-rationalist perspective, then there should be no limit on what you can fathom. If I were to challenge your logic my saying that I can fathom a universe which does not have the Law of the Excluded Middle, I don't see what you could say other than "Hmmm. I have nothing to say about that".Apart the better-known insufficiency problem, there is also the necessity problem. We all know that horseshoe is unnecessary; I have not seen evidence that existential quantification is necessary for modeling reasoning, and I suspect that universal quantification as such is not, that the job is properly done by concept-formation and definition (however I don't know whether there is a substantive difference between that and what one does with upside down A).

I'm not familiar with the historical chicken-and-egg problem, though I found nothing objectionable in the paragraph that followed it (nor do I suspect many philosophers and logicians would. The controversy over how to capture more logic than is contained in classical symbolic logic is wide-spread and growing. You may be aware of Priests textbook on non-classical logic, and Bennett's book Conditionals.

In the next paragraph, though, you say that cognitive science can show whether laws of quantification and ⊃ are valid. I would be interested to know the details.

As for whether language is a subset of symbolic systems, what is it that brings you to this conclusion?

The reason why the symbolism reveals necessary truth-preservation is the same way that symbolism reveals the necessity that x ∙ (y + z) = xy + xz. It just distills everything in a very manageable and clear form. You could, of course, do everything in an English equivalent, where we say, "Consider only the definition of 'or' by which it conjoins into a single sentence two statements that are each either true or false; and consider only the definition of 'not' by which it forms a new sentence when affixed to some other sentence which is either true or false, and this new sentence is incompatible with the sentence that is its component. In such a case, for any first sentence and second sentence, when we know that either the first sentence is true or the second sentence is true--one can be false, but not both--and we know that the first sentence is not true, we can conclude that the second is true." And this scheme will hold true of any two sentences that have truth-value. We can see that it's necessary, but the symbolism brings it out, especially with more complicated arguments.

Now when you say that I'm clandestinely appealing to empirical considerations to make my claim that the truths of logic are necessary, I'm not sure which empirical facts I have invoked. I have not observed--or at the very least, am not now aware of--any observation which has made it necessary that these laws apply to everything. I do not reflect on what I have seen or known, but I introspect on what I could possibly see or know. I have required some considerable training in thought to be able to identify such a capacity for language, identification, philosophy, and so forth. But this is just the means by which I have come to identify the question, none of which has supplied me with the means to know the answer, as is exemplified by the fact that I make use of none of it in my own internal contemplation when I judge that the truths of logic are necessary. So if I appeal to any empirical fact, it is far beyond anything I am aware of, to the point that I contest no empirical fact could be made use of in answering the question. In any case, though, it should be certain that there are things beyond which I can fathom. Namely, contradictions. If you say that you can fathom a universe without the Law of Non-Contradiction, then I say, "I find that beyond false, which is at least intelligible." I can make sense of each word in isolation, but not together as a sentence--as all contradictions must proceed.

I'm not convinced that ⊃ isn't necessary, or at least that some truth-functional logical operator isn't necessary to capture some portion of proper human reason. And until the full method of concept-formation has been developed, from its root up to the formation of any valid concept whatsoever, I take it ⊃ and ∀ are decent starts. At the very least, useful in mathematical reasoning, which is a part of human reason.

[Edit for font and some substantive details in the 4th paragraph]

Edited January 31, 2009 by aleph_0

[aleph_0]

My point is that the laws of logic do not exist in the human mind prior to making observations about reality. The law of non-contradiction does not exist in the world making everything comply with being itself instead of being something else -- it is what it is because it is, and it does not require something acting on it, say God or the laws of logic written into the fabric of the universe, in order to be what it is. So, no, logic is not a feature of reality, but rather is man's grasp of reality using his mind in a manner that does not contradict reality. How does he know not to do this without having the laws of logic, as in how did the first logician figure it out? Well, he observed reality and he observed how his mind operated in order to understand the world, then he derived the laws of logic from that necessity of his mind conforming to reality before he could go on to steps beyond simple observations.

No one is going to see a catcycle, because catcycles do not exist. I suppose someone could build a bike with cat-like features (fur and a tail and maybe even make cat noises), but it is what it is and it is not a cat. Having one's own mind conform to reality -- to what one observes -- is the root of logic; it is not as if someone came up with a schema in his head without looking at reality and then tried it to see if it worked. The most fundamental aspects of human cognition are self-evident and inductive. I mean, one can misidentify a cat as a bicycle and try to hope on one and peddle it, but it won't get you anywhere and may leave you with a few scratches

As to should everyone learn formal logic; in a certain sense, yes, because having it formalized makes it easier to check one's premises, just as language makes it easier to think something through; however, I wouldn't say everyone ought to know what the symbols mean in a logicians formulation. On those lines, it would be like saying everyone ought to learn vector calculus, which I don't think is the case. One can be quite logical without reducing one's sentences to the logician's symbols. I haven't formally study logic in that sense, but I can still be logical. I have studied vector calculus, but I've never used it since college. Basically, I took Dr. Peikoff's course on logic, which was written mainly in English and not a lot of symbolism. I suppose in the same way one can use vector calculus to figure out complicated dynamics, one can use highly symbolic logic to figure out complicated scenarios, but I don't use it that way, I simply think it through based on the facts as I understand them.

We must have the laws of logic, though, if we are to make anything of our observations. Observations unguided by laws of logic come to no conclusions. We could not go from apperception or percepts to concepts without being informed of some rules of how to do it and how not to do it. These rules, then, are logic. Non-contradiction, identity, and so on. Taking your man who learns the laws of logic--how did he make his observations in the first place, if not with logic to tell him how to go from his observations to his conclusions?

[DavidOdden]

In the next paragraph, though, you say that cognitive science can show whether laws of quantification and ⊃ are valid. I would be interested to know the details.

One example involves looking at the formalizations of grammatical rules. We have a class of linguistic phenomena involving "identity-set" pairings that involves subsets of phonetic properties. Some of them involve "are identical" such as the pairs {p,b}, {t,d}, {k,g} -- the identity property in question is what's known as "place of articulation" -- so that two-segment sequences can be partitioned into the targeted pairs (sequences that undergo the rule) {{p,b}, {p,p}, {b,b}, {t,d}, {t,t}, {d,d}, {k,g}, {k,k},{g,g}} versus the excluded ones {{p,t}, {p,d}, {p,k}, {p,g}, {t,k}, {t,g}....}. So here we have the notion "for all of this set of properties, they are the same" which is crucial in the statement of the rule. Interestingly, human language phonological rules never operate in terms of "there exists some in this set of properties which are the same". The asymmetry between whether you find "all same" vs. "some same" doesn't make any formal sense. But as part of a cognitive theory that existential quantifiers are illegitimate qua cognitive tool, this is explicable.

The nature of the difference is obvious, I think, that universal quantification expresses a generalization and existential quantification does not. Apart from its function in symbolic systems, what do we need it for, when we have the specific instance -- "This cow is white; that cow is red"? Of course this conclusion could be shown to be wrong experimentally, if you could somehow cook up an experiment that shows that people are aware of or use a referent-neutered existential statement separate from their knowledge of any concrete instances.

As for whether language is a subset of symbolic systems, what is it that brings you to this conclusion?

I suppose some decades of studying and teaching about the nature of language, my knowledge of what "symbolic system" means, and specifically addressing the question of the difference between "language" and "symbolic system".

Now when you say that I'm clandestinely appealing to empirical considerations to make my claim that the truths of logic are necessary, I'm not sure which empirical facts I have invoked.

Invoke as in argue from, here? None. But I can't figure out how you can find the denial of the Law of the Excluded Middle to be "unfathomable", except on the assumption that because it is a fact that you know about reality, you cannot imagine denying reality.

I have not observed--or at the very least, am not now aware of--any observation which has made it necessary that these laws apply to everything.

Then why do you find "A&^A" to be unfathomable?

I do not reflect on what I have seen or known, but I introspect on what I could possibly see or know.

How can you identify what you can "possibly see or know" -- where does that knowledge come from? If it's not based on what you have experienced, then what is the source of that knowledge? And how fallible is that knowledge: is it possible for you to be in error about what you conclude you can possibly see?

So if I appeal to any empirical fact, it is far beyond anything I am aware of, to the point that I contest no empirical fact could be made use of in answering the question.

Uh huh. So you're saying that since LEM seems to be essential to your understanding the universe, then it must be a fact. But surely you don't think that the universe cares about your understanding. So there can be no rational debate, simply competing foundational declarations, unless someone grounds there position in existence and the fact that a consciousness can grasp the nature of existence.

I'm not convinced that ⊃ isn't necessary, or at least that some truth-functional logical operator isn't necessary to capture some portion of proper human reason.

Well, some operator would include negation or conjunction. I'm specifically rejecting ⊃ whose uses cover multiple cognitive functions and this is not a symbolization of a cognitive function.

And until the full method of concept-formation has been developed, from its root up to the formation of any valid concept whatsoever, I take it ⊃ and ∀ are decent starts.

As a decent start, I propose dropping ∃ ⊃ ∨, and reflecting on what useful thing of cognition they were intended to represent. Very simply, how should one formalize "all men are mortals"?

[Thomas M. Miovas Jr.]

Taking your man who learns the laws of logic--how did he make his observations in the first place, if not with logic to tell him how to go from his observations to his conclusions?

I think you have an implied idea that man's mind automatically conforms to reality -- i.e. that the human mind is logical by necessity. This isn't the case at all, there are no structures of the mind that compel him to think in terms of observations and facts; this is something he must learn to do, and he must learn to do it volitionally, of his own free will. The human mind can come up with all sorts of ideas and conclusions that fly in the face of reality; in fact, this is one of the major problems of mankind at its current state -- that many people do not know how to check their ideas against the facts of reality. How did the first logical person know how to do this? By observing that so long as his mind conforms to reality, he can get things done; and to the extent that his mind did not conform to reality, he couldn't get anything done.

I think you may be focusing too much on long chains of reasoning or logic and then wondering how the first logician came up with that, and the simple answer is that he did not come up with that; just as the first mathematician did not come up with vector calculus. The first men who understood reason to some degree lived on a very primitive level and barely had language. To know that to keep a fire going one must add wood to it was one of the more contextually complicated things he had to deal with; the first men lived in caves, they did not build the Empire State Building. So, at that very low level of conceptualization, he wasn't trying to figure out how to land a man on the moon, he was wondering how to keep the fire burning. It it is not that difficult to grasp that the wood changes into ash and more wood must be added to it. It was the observation that wood could catch fire that made it possible for him to conclude that so long as there was wood on the fire he could keep warm and cook his food. The logic to do that wasn't already there one day when man was born, it was something he had to figure out; and he didn't have the laws of logic there to guide him, the laws of logic had not yet been discovered. It is not as if he had the Objectivist epistemology and Atlas Shrugged well understood and then said, oh yeah, therefore if I put more wood on the fire I can keep warm.

In the early days, conclusions from observations were very short range; and gradually over time, he learned to apply what he learned to new situations that were contextually similar. And then many, many thousands if not millions of years later he was able to formulate the laws of logic in the way Aristotle was able to do it.

You are staying too much in the stratosphere, whereas if you got closer to ground level you would see that conclusions can be just baby steps requiring no formal knowledge of logic -- just observation and keeping your mind tied to reality.

[aleph_0]

One example involves looking at the formalizations of grammatical rules. We have a class of linguistic phenomena involving "identity-set" pairings that involves subsets of phonetic properties. Some of them involve "are identical" such as the pairs {p,b}, {t,d}, {k,g} -- the identity property in question is what's known as "place of articulation" -- so that two-segment sequences can be partitioned into the targeted pairs (sequences that undergo the rule) {{p,b}, {p,p}, {b,b}, {t,d}, {t,t}, {d,d}, {k,g}, {k,k},{g,g}} versus the excluded ones {{p,t}, {p,d}, {p,k}, {p,g}, {t,k}, {t,g}....}. So here we have the notion "for all of this set of properties, they are the same" which is crucial in the statement of the rule. Interestingly, human language phonological rules never operate in terms of "there exists some in this set of properties which are the same". The asymmetry between whether you find "all same" vs. "some same" doesn't make any formal sense. But as part of a cognitive theory that existential quantifiers are illegitimate qua cognitive tool, this is explicable.

The nature of the difference is obvious, I think, that universal quantification expresses a generalization and existential quantification does not. Apart from its function in symbolic systems, what do we need it for, when we have the specific instance -- "This cow is white; that cow is red"? Of course this conclusion could be shown to be wrong experimentally, if you could somehow cook up an experiment that shows that people are aware of or use a referent-neutered existential statement separate from their knowledge of any concrete instances.

I don't understand. This looks as though its an example of an application of universal quantification. I don't see (1) how the observations avoid assuming some already formalized laws of logic, like non-contradiction and identity, perhaps some form of modus ponens, and universal instantiation, and (2) how this could be seen as a proof rather than a description of a phenomenon.

Also, I'm not sure the phonological rules operate in terms of "are the same", unless that's meant in a loose way, in which case the relationship to universal quantification is likewise loose. Here, it would seem that they operate in terms of "are equivalent to", no?

I suppose some decades of studying and teaching about the nature of language, my knowledge of what "symbolic system" means, and specifically addressing the question of the difference between "language" and "symbolic system".

And on what, from this, do you base your judgment? Like I said, if the question is such a sensitive one, you need not answer it at all. I'm just trying to understand.

Invoke as in argue from, here? None. But I can't figure out how you can find the denial of the Law of the Excluded Middle to be "unfathomable", except on the assumption that because it is a fact that you know about reality, you cannot imagine denying reality... And how fallible is that knowledge: is it possible for you to be in error about what you conclude you can possibly see?... But surely you don't think that the universe cares about your understanding. So there can be no rational debate, simply competing foundational declarations, unless someone grounds there position in existence and the fact that a consciousness can grasp the nature of existence.

I find it unfathomable because it would require fathoming two mutually exclusive propositions to be true at the same time, and by mere meaning of the terms--without reference to any observation--it's flatly impossible. It's the nature of the axiom. I just know it. I can't even address whether it is fallible or how fallible it is, because I cannot even make sense of it being false. It's like asking how probable is it that the object outside my door is a round square. I cannot even begin to assign probability to it. The proposition is just nonsensical. I cannot even speak of whether the universe cares, because it is beyond me to even hypothesize about a contradiction.

Well, some operator would include negation or conjunction. I'm specifically rejecting ⊃ whose uses cover multiple cognitive functions and this is not a symbolization of a cognitive function.

But ⊃ is nothing more than ~(P & ~Q). We sometimes think it has an analogue to implication, and in fact it models some small portion of its behavior. Many logic classes, like the one I'm attending now, don't even take ⊃ for a genuine symbol in the language, but a mere abbreviation for a type of negated conjunction or a type of disjunction. This is precisely to keep students from thinking that it is, in fact, the standard English 'if... then...' W.V. Quine is quite harsh in his Methods of Logic to anybody who confuses material implication, biconditional, and the like for their standardly interpretted English equivalents. And some people, leaving an introductory symbolic logic class and never having more information on the philosophy of logic or conditionals, will still confuse ⊃ for → or >. But nobody with much training in logic, language, or conditionals, confuses one (or at least the first two) for the last, which is claimed to be a symbolization of a cognitive (or logical, or linguistic) function--and the precise meaning of which, there is no consensus. I mean, there isn't even consensus that ~ models English negation, that & models conjunction. It seems to me that v models disjunction, when disambiguated to excluded exclusive disjunction. Do you know of a professional philosopher who thinks that > is nothing more than ⊃? I don't seem to understand why you make such a point against ⊃. An analoge to all of this can be made for ∃, which abbreviates ~(∀x)~.

I think you have an implied idea that man's mind automatically conforms to reality -- i.e. that the human mind is logical by necessity. This isn't the case at all, there are no structures of the mind that compel him to think in terms of observations and facts; this is something he must learn to do, and he must learn to do it volitionally, of his own free will. The human mind can come up with all sorts of ideas and conclusions that fly in the face of reality; in fact, this is one of the major problems of mankind at its current state -- that many people do not know how to check their ideas against the facts of reality. How did the first logical person know how to do this? By observing that so long as his mind conforms to reality, he can get things done; and to the extent that his mind did not conform to reality, he couldn't get anything done.

I think you may be focusing too much on long chains of reasoning or logic and then wondering how the first logician came up with that, and the simple answer is that he did not come up with that; just as the first mathematician did not come up with vector calculus. The first men who understood reason to some degree lived on a very primitive level and barely had language. To know that to keep a fire going one must add wood to it was one of the more contextually complicated things he had to deal with; the first men lived in caves, they did not build the Empire State Building. So, at that very low level of conceptualization, he wasn't trying to figure out how to land a man on the moon, he was wondering how to keep the fire burning. It it is not that difficult to grasp that the wood changes into ash and more wood must be added to it. It was the observation that wood could catch fire that made it possible for him to conclude that so long as there was wood on the fire he could keep warm and cook his food. The logic to do that wasn't already there one day when man was born, it was something he had to figure out; and he didn't have the laws of logic there to guide him, the laws of logic had not yet been discovered. It is not as if he had the Objectivist epistemology and Atlas Shrugged well understood and then said, oh yeah, therefore if I put more wood on the fire I can keep warm.

In the early days, conclusions from observations were very short range; and gradually over time, he learned to apply what he learned to new situations that were contextually similar. And then many, many thousands if not millions of years later he was able to formulate the laws of logic in the way Aristotle was able to do it.

You are staying too much in the stratosphere, whereas if you got closer to ground level you would see that conclusions can be just baby steps requiring no formal knowledge of logic -- just observation and keeping your mind tied to reality.

I'm not focusing on long chains of deduction at all--I'm looking for an account of how anybody can observe anything without already having the laws of logic in his pocket. You cannot even get started if you don't already have the laws of logic. They are necessary to begin observing, or else you may observe a duck that is a water heater, and how do you get logic from that? The only reason you think I'm in the stratosphere is because I'm talking about the deductions that take place during and before observations, which are massive. That is to say, observation is in the stratosphere. It's extremely complicated and depends on the logic that must be in place for it to happen.

[DavidOdden]

I don't understand.

I see that. I'm trying to explain how research in cognitive science can address the question of valid logical concepts empirically. The point is that while formal universal quantification has a clear analog to cognitive objects, existential quantification does not: existential quantification predicts vast classes of unattested phenomena. This is explained in a cognitive-based theory of logic by the fact that universal quantification does correspond to something cognitively real, and existential quantification does not. The scientific burden is to explain why a huge class of conceivable operations is systematically unattested -- which is explained by restricting the class of logical primitives.

Also, I'm not sure the phonological rules operate in terms of "are the same", unless that's meant in a loose way, in which case the relationship to universal quantification is likewise loose.

It is a very precisely defined way, but it's also technical so I left out some details. It refers to the features which express physical properties of the articulation of sounds, such as voicing, nasality, various tongue configuration facts. (You can buy the pink book if you want details). These properties are organized into sets, and the rules compare values for all members of the set in the first and second segments. (And it "compares all", not "compares some").

And on what, from this, do you base your judgment? Like I said, if the question is such a sensitive one, you need not answer it at all. I'm just trying to understand.

It's not a sensitive question, I just don't understand what you are asking. It seems pretty straightforward to me. I know what "language" means, and what "symbolic system" means, and I'm just applying the literal meaning of the words. Examples of languages are French, English, German, Hebrew, Chinese etc. I don't actually think that "mathematics" is a specific symbolic system, it covers various specific mathematical symbolic systems like "algebra", "geometry", "number theory", "set theory" (and you can divide that up as you want, I'm making no claims about areas of math).

But ⊃ is nothing more than ~(P & ~Q).

A classical reason why it isn't even necessary. Same with the biconditional. What justifies a logical symbol? Why not simple reduce operators to stroke? When (if) you claim that there is some validity to a system of logical symbolization, what could justify proliferating symbols? If it is to satisfy cognitive demands, then ⊃ fails.

I don't seem to understand why you make such a point against ⊃.

The question is what it takes to justify a system of logical symbols. If you take the "symbolism without reference to reality" perspective -- the one I'm opposing -- then the only argument against ⊃ is simplicity (Occam's Razor), and that alone rules against ⊃. If you take the "symbolic logic reflects human cognition" standard, again it fails because ⊃ does not reflect human cognition. If you have some third alternative for justifying the inclusion of ⊃, please share. (If it's just to preserve a tradition and to keep the makers of the ⊃ symbol employed, you shouldn't share).

I'm not focusing on long chains of deduction at all--I'm looking for an account of how anybody can observe anything without already having the laws of logic in his pocket.

Specifically, you must be asking "how can man perceptually identify the identity of an entity, independent of the moment of perception" and "how can man abstract over similar entities and ignore perceptible differences". The emphasis here has to be on transduction from sensations to perception.

[Thomas M. Miovas Jr.]

I'm not focusing on long chains of deduction at all--I'm looking for an account of how anybody can observe anything without already having the laws of logic in his pocket. You cannot even get started if you don't already have the laws of logic. They are necessary to begin observing, or else you may observe a duck that is a water heater, and how do you get logic from that? The only reason you think I'm in the stratosphere is because I'm talking about the deductions that take place during and before observations, which are massive. That is to say, observation is in the stratosphere. It's extremely complicated and depends on the logic that must be in place for it to happen.

On the contrary, there are no laws of logic behind or at the base of perception. It is not the laws of logic that make it possible for you to see a duck and not a water heater. The senses automatically integrate their material so that we perceive objects and their attributes, but this is not done with a logical apparatus innate to the human mind; it's just a causal chain of events that take place in the biological structure of the senses and their integrating ability on the cellular level. In other words, it is not a law of logic that makes it possible for you to see THIS versus this.

This whole notion that laws of logic are behind perception comes from Kant, and he was wrong about that. There is no innate logic behind observation. And there is no way one is going to have a duck in front of oneself and see it as a water heater; not because logic prevents it, but because one observes what it is that is there in front of his eyes. In other words, one does not have to have the laws of logic in order to see THIS as one capitalized word; the capitalization makes it perceptually different from the other words in the sentence, and it wasn't logic that made that possible to see that difference.

Besides, you are talking about deduction and I am primarily talking about induction. Induction comes first or one will not have anything from which to deduce. So, in my example of the caveman trying to figure out how to stay warm, he first observed that burning wood created heat; he then noticed that so long as there was wood on the fire it would continue to create heat; and only then could he deduce that so long as he put wood on the fire he would have heat. But none of this happened in his mind because man has some sort of innate logic behind his observations.

Man was not born with logic already in his head; nor is any child today born with logic already in his head. Logic or being logical is something that must be learned; it is not innate to the human mind. And it is most certainly not innate to observations.

[aleph_0]

Without the Law of Identity, one can see both this and THIS, and simultaneously see neither this nor THIS. Without the Law of Identity, nothing makes sense.

[aleph_0]

I see that. I'm trying to explain how research in cognitive science can address the question of valid logical concepts empirically. The point is that while formal universal quantification has a clear analog to cognitive objects, existential quantification does not: existential quantification predicts vast classes of unattested phenomena. This is explained in a cognitive-based theory of logic by the fact that universal quantification does correspond to something cognitively real, and existential quantification does not. The scientific burden is to explain why a huge class of conceivable operations is systematically unattested -- which is explained by restricting the class of logical primitives.

I still don't understand. What does the analogy do here? What is deficient in the existential quantifier when, (1) it is nothing more than a schema of universal quantification and negation, and (2) its analog is in every existential statement, such as "There is a person," and "At least one thing exists,"? I don't understand how empiracle research can establish validity in the sense that any application of the sytnatic features preserves truth in its derivation where the derivations retain the same language of expressions as are in the theory.

That's obscure, so I'll say more. Take the example of Euclidean geometry given several posts before, or take the example of representing me by the letter 'a', and then take the letter 'b' to represent anything at all that you care to attribute existence. The language will then yield a = a, b = b, a = a & b = b, ∃(x)(x = x & x = a), and so on, and each derivation--when keeping the meaning of the language fixed--will always yield truth. Likewise, we can have an analog in Peano arithmetic. 0 is a privileged member of the domain of discourse, x' is a one-place relation, and 0 = 0, 0' = 0', ∃(x)(x = 0), ... I don't see the motivation for trimming down the notation, except perhaps economy. But not philosophical significance. Perhaps it would help if I knew the classes of unattested phenomena which this notation predicts, and an explanation of how it predicts them while its notational equivalent, ~∀~ does not.

It's not a sensitive question, I just don't understand what you are asking. It seems pretty straightforward to me. I know what "language" means, and what "symbolic system" means, and I'm just applying the literal meaning of the words. Examples of languages are French, English, German, Hebrew, Chinese etc. I don't actually think that "mathematics" is a specific symbolic system, it covers various specific mathematical symbolic systems like "algebra", "geometry", "number theory", "set theory" (and you can divide that up as you want, I'm making no claims about areas of math).

I see that mathematics is not the set of all languages, and that English is not the set of all languages, so I see that these are both subsets of the set of all languages, and each are subsets of the set of symbolic systems. What I don't understand is why mathematics is outside the set of languages and, moreover, why languages are distinct from the set of symbolic systems. Perhaps I insufficiently grasp English.

A classical reason why it isn't even necessary. Same with the biconditional. What justifies a logical symbol? Why not simple reduce operators to stroke? When (if) you claim that there is some validity to a system of logical symbolization, what could justify proliferating symbols? If it is to satisfy cognitive demands, then ⊃ fails... The question is what it takes to justify a system of logical symbols. If you take the "symbolism without reference to reality" perspective -- the one I'm opposing -- then the only argument against ⊃ is simplicity (Occam's Razor), and that alone rules against ⊃.

I don't think that it fails to satisfy all cognitive demands. For instance, ⊃ satisfies the following cognitive demand: Have a symbol such that, when it relates two atomic sentences (let's go with P and Q), knowledge of P allows one to derive knowledge of Q. This is something that is easy for introductory and advanced students of logic to understand, so its helpful merely in how to see a formula or derivation. The proliferation of symbols is not philosophically motivated, and the only two reasons I know of for not using nand is (1) there is no intuitive, obvious understanding of the operation, and (2) extra symbols increase speed of calculations at the cost of memorizing extra operations. Apparently philosophers thought the advent of nand was extremely significant, but today we largely recognize that it's meaningless. Occam's Razor doesn't rule out ⊃ any more than it rules out v or & or |, because you need at least one--besides which, Occam was shaving ontology, not symbols. If he cared so much about the bottle rather than the wine, he would campaign to just do away with every language in existence but one.

If you take the "symbolic logic reflects human cognition" standard, again it fails because ⊃ does not reflect human cognition.

Like I said, I think it reflects a very small portion of it--namely, the portion that deals with sets, math, and something similar to the English word 'when'. Or perhaps just those English expressions that go something like, "Consider all possible cases in which P. In all of these, Q."

Specifically, you must be asking "how can man perceptually identify the identity of an entity, independent of the moment of perception" and "how can man abstract over similar entities and ignore perceptible differences". The emphasis here has to be on transduction from sensations to perception.

I'm sorry. Again, I don't understand.

[Thomas M. Miovas Jr.]

Without the Law of Identity, one can see both this and THIS, and simultaneously see neither this nor THIS. Without the Law of Identity, nothing makes sense.

The law of identity is not behind or beneath perception; the law of identity is derived from perception via the observation of reality as given by the senses. We do not have philosophical structures in our brain leading it to giving us correct information as we look out at the world. The sense work because they are what they are, and the law of identity does not make them that way or make them work infallibly. The senses exist and act they way they do because they exist and are what they are, but it is not the law of identity that makes them conform to reality.

All of the axioms and all of the philosophical laws and all the physics laws are derived from observation of existence. They are abstractions developed according to the Objectivist epistemological principles of man's ability to form abstraction via measurement omission. These axioms and laws do not exist as something (a real force or a real substance or a god) in reality making things behave. That which we observe behaves and we formulate that observation into the laws of existence, including the law of identity and any laws of physics.

The laws of existence do not control our perception; our perception exists and from our observations we derive the laws of existence as abstractions.

[Hodge'sPodges]

David Odden wrote, "For the formal logician, propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method."

Wouldn't Frege endorse just this thesis?

I should think not; quite the contrary. I don't know how anyone would infer that Frege held that "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method." I am not a Frege expert, but even my modest knowledge of him allows me to recognize that the above quote is quite opposed to Frege's notions, aside from the matter of finding whatever it means to say that truth is a certain kind of method. What specific passages of Frege's do you have in mind? Though, I did see that later in your post you recognized that likely this is not anything of Frege's. Edited February 2, 2009 by Hodge'sPodges

[Hodge'sPodges]

It's like asking how probable is it that the object outside my door is a round square. I cannot even begin to assign probability to it.

The probability is 0. That is a triviality that follows from the fact that there is no object that is both square and round.

[Marc K.]

Suppose you have no laws of logic, and so you have no law of non-contradiction, and so you see a cat and at the same time it is a bicycle. Nothing is to stop the catcycle from being the dogskates that they are. Only non-contradiction, or something very like it, can keep away such absurdity.

Non-contradiction is a metaphysical law of the Universe so whether you know the rules of logic or not, you will never see a contradiction in nature.

So I contend that it's impossible for them to fail to preserve truth, and that naturally leads me to hold that they're necessary. I can't find a weakness in my own position.

I think the "round square" in the following quote from earlier in your post demonstrates that truth is not preserved.

It precedes it logically in the sense that one need not know anything about content that is put into the law to know that the law holds of everything. That is why we symbolize it with variables like A = A--you can fill in the 'A' with "cat" or "A cat", or "Jeff", or "Pegaus", or "round sqaure". In this way, you can have your law before any applications of it.

However you may just speak differently than me, which may also be the problem with the following quote:

That's not necessarily the claim being made here, though. [emphasis added]

The emphasized word can really derail a thread and it has, previously, when you and I had another discussion.

It sounds like you are saying: "that might be the claim I am making, but not necessarily". It sounds like you are trying to have it two ways, like you are leaving your options open so that you can escape being pinned down, so that you can change your argument, which implies argument for argument's sake. I find it extremely dishonest and disconcerting (if that is what you are doing). But, as I said, maybe you just have a different way of communicating than I do.

I'm not really going to engage you very much here, I've already had the pleasure. I just wanted you and your opponents to be aware of a problem I had while talking to you in the past.

[aleph_0]

I'll reply out of sequence, since I think Thomas and Marc make similar points.

The law of identity is not behind or beneath perception; the law of identity is derived from perception via the observation of reality as given by the senses.

...

The laws of existence do not control our perception...

Non-contradiction is a metaphysical law of the Universe so whether you know the rules of logic or not, you will never see a contradiction in nature.

I think, at this point, no more philosophical work is being done. I just do not understand how one can even talk about perception without the Law of Identity--in fact, I do not understand any conversation or consideration without the Law of Identity. I do not understand how such an observer every learns the Law of Identity without assuming it. For when he observes that a thing is itself, he necessarily has the thing, and nothing else, in mind. He comes to every observation already with the Law of Identity in hand. If the Law were a posteriori, then there is always the chance that he just hasn't seen the right things and that one day he may stumble upon a thing which is not itself. We rule this out as nonsense because it is de jur and not just de facto that we cannot even conceive of observation without identity.

But I'm sure the response this will receive is that the Law of Identity is inductively known, that reason is a process of integration, on and on. But that won't speak to my worry, which is about how induction takes place (It must take place in one way and not another, so I ask how we draw the line, and I answer: by means of the laws of logic. I have not identified an answer given by any Objectivist, though I'm willing to bet that many here think I have been given an answer [the very same answer] many times now. But I can't see how it successfully answers the question that I'm asking, even if it may perhaps answer some other question--I don't know.).

So I don't think further correspondence over the matter will be fruitful.

The emphasized word can really derail a thread and it has, previously, when you and I had another discussion.

It sounds like you are saying: "that might be the claim I am making, but not necessarily". It sounds like you are trying to have it two ways, like you are leaving your options open so that you can escape being pinned down, so that you can change your argument, which implies argument for argument's sake. I find it extremely dishonest and disconcerting (if that is what you are doing). But, as I said, maybe you just have a different way of communicating than I do.

You're right, at first I was ambivalent, not out of dishonesty but out of uncertainty. I have, from this conversation, found the idea of knowledge of logical necessity from the objective world less tenable. I still reserve judgment, but that should not be interpretted as dishonesty--in fact, it's more honest than just about every other philosopher tends to be, both in and outside of this forum. Most people engaged in a debate feel as if they must have an answer to everything, that they must be committed to perfect or nearly all-encompassing knowledge of every subject. I don't, and so I just express that which I can understand, that which seems right to me, my contributions to a discussion. And I try to understand other people's views.

I should think not; quite the contrary. I don't know how anyone would infer that Frege held that "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method." I am not a Frege expert, but even my modest knowledge of him allows me to recognize that the above quote is quite opposed to Frege's notions, aside from the matter of finding whatever it means to say that truth is a certain kind of method. What specific passages of Frege's do you have in mind? Though, I did see that later in your post you recognized that likely this is not anything of Frege's.

Well let us think about what Frege thought. He believed that there was a sense of a word, its referent, and its meaning. The sense of the word is what is shared between competent linguistic correspondents. The referent is that object to which the sense directs you. The meaning is how the word is used (Here, indexicals are the only particular I know how to parse uncontroversially. The sense of the word 'I' is the concept of the very person uttering the word [the concept of the speaker]. The referent of the word is different in different contexts. When I use it, it refers to me; when you use it, it refers to you. The meaning is the instruction manual that gets you to the (sense? concept?): When you hear this word, understand that what is meant is to refer to the person speaking.

Words are put together into sentences, which are the basic units of expressing facts. But sentences are the expressions, analogous to words. What do they express? Propositions, which are analogous to the sense of words. Sentences are the bearers of truth-values, but propositions--I suspect--are not. The referent of a sentence is its truth-value. But a sentence gets different truth-values based on the context in which it is uttered. In a way, all sentences are indexical. They refer to truth in that context. For example, "It's raining," or "Russia is a communist nation," are each sentences true at one time and false at another (Unless, perhaps, 'Russia' shares no extension with the USSR. In which case, we could use a sentence like 'Leningrad is in a communist nation.'). But the proposition is just what is shared between fellow speakers of the language, and this is the same both when its raining and when its not--when Russia is communist and it's not. We get the exact same proposition, or shared content of the expression, regardless of the context. Context merely supplies the truth-value.

So it seems Frege really did think that (1) propositions (not statements) are not about reality (if anything, they're about thoughts, or words, or the sense of words) because they stay fixed as reality changes, and (2) truth has nothing to do with a consciousness. Sentences, he held, are true or false regardless of whether there is anybody to express them or not. A proposition, in a given context, can be true or false without anybody to think it. Frege was a Platonist, so he believed that even though propositions are the shared content of expressions, they exist independent of the mind and that the mind comes to acquire some and not others.

As for the third claim, that some philosophers believe that truth has nothing to do with reality, I am not certain. I could at least initially understand this as something unfolding from the rationalists: logical truths are true with or without reality. Maybe. I don't know.

The probability is 0. That is a triviality that follows from the fact that there is no object that is both square and round.

This is one account, but I'm not sure I buy it. I probably ought to, but I don't yet understand how we can have meaningful sentences by way of meaningless terms.

[Hodge'sPodges]

Words are put together into sentences, which are the basic units of expressing facts. But sentences are the expressions, analogous to words. What do they express? Propositions, which are analogous to the sense of words. Sentences are the bearers of truth-values, but propositions--I suspect--are not. The referent of a sentence is its truth-value. But a sentence gets different truth-values based on the context in which it is uttered. In a way, all sentences are indexical. They refer to truth in that context. For example, "It's raining," or "Russia is a communist nation," are each sentences true at one time and false at another (Unless, perhaps, 'Russia' shares no extension with the USSR. In which case, we could use a sentence like 'Leningrad is in a communist nation.').

On that very last point, are you quite sure it is Frege's view about true at one time and not another?

But the proposition is just what is shared between fellow speakers of the language, and this is the same both when its raining and when its not--when Russia is communist and it's not. We get the exact same proposition, or shared content of the expression, regardless of the context. Context merely supplies the truth-value.

So it seems Frege really did think that (1) propositions (not statements) are not about reality (if anything, they're about thoughts, or words, or the sense of words) because they stay fixed as reality changes, and (2) truth has nothing to do with a consciousness.

Nothing you've said entails that Frege held that truth "has NOTHING TO DO WITH consciousness" [emphasis added] nor that Frege regarded truth as "a [certain kind of] method". Perhaps somewhere Frege wrote something that, in his views, entails such claims, but I'd like to know where. Nor have you supported that Frege held that, among the things propositions are about, reality is not one of them.

Sentences, he held, are true or false regardless of whether there is anybody to express them or not. A proposition, in a given context, can be true or false without anybody to think it. Frege was a Platonist, so he believed that even though propositions are the shared content of expressions, they exist independent of the mind and that the mind comes to acquire some and not others.

That does NOT entail that these things have "NOTHING to do with consciousness" [emphasis added] not that truth is "a [certain kind of] method". And if a method, then a method performed by whom or what?

As for the third claim, that some philosophers believe that truth has nothing to do with reality

The question was not whether some philosophers believe this or that, but rather whether formal logicians in general hold that "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method." Indeed, your own remarks lead to observing that, for example, Frege does not regard truth as "purely symbol transformation". Edited February 3, 2009 by Hodge'sPodges

[aleph_0]

On that very last point, are you quite sure it is Frege's view about true at one time and not another?

It's been a while since I read him, and I'm not quite sure how sure I am, and I'm not quite sure how sure is 'quite sure'. But I'm willing to state that it's true. Do you know of some of his writing that would contradict it?

Nothing you've said entails that Frege held that truth "has NOTHING TO DO WITH consciousness" [emphasis added] nor that Frege regarded truth as "a [certain kind of] method". Perhaps somewhere Frege wrote something that, in his views, entails such claims, but I'd like to know where. Nor have you supported that Frege held that, among the things propositions are about, reality is not one of them.

Sure, you could say that truth and consciousness are related in that one becomes conscious of truth--but I don't think that is when Odden had in mind. If I read him correctly, that kind of interpretation stretching is not very fruitful. It seems to me Odden was instead referring to a particular class of relationships between logic and consciousness, namely relationships in which one cannot understand truth without reference to consciousness.

It's a bit premature to be making such a charged statement as, "You have not supported such-and-such about your exegesis about Frege," isn't it? I would think a question would be more appropriate, something of the form, "From which of Frege’s passage(s) do you conclude this?" If I were doing a research project on him, I'd have been sure to include citations.

That does NOT entail that these things have "NOTHING to do with consciousness" [emphasis added] not that truth is "a [certain kind of] method". And if a method, then a method performed by whom or what?

I also find the excessive use of all-caps a bit unnecessary. Anyway, I'm not sure what you mean by (or, perhaps, why you impute to me) this thing about "method".

The question was not whether some philosophers believe this or that, but rather whether formal logicians in general hold that "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method." Indeed, your own remarks lead to observing that, for example, Frege does not regard truth as "purely symbol transformation".

I was under the impression that the question was about whether some philosophers believe this or that. Forgive me if I was mistaken. But if our question was, indeed, about formal logicians in general I'm not sure how one would go about answering either the affirmative or the negative answer. Should we poll formal logicians? Which logicians count as formal, which people count as logicians? Has anybody conducted any such poll? Would you care to go about it?

I simply thought that it was relevant to mention the relevant views of the creator of modern symbolic logic, who was a careful student of mathematics, logic, and philosophy, and who has influenced us to the point that we consider him the father of the modern analytic tradition (steeped in logic, language, and formalism as it is). I do not claim that Frege is representative, though I might suggest that he is indicative of views that some logicians may hold today. I know that modern logicians Hartry Field and Somebodyorother White have published Platonist-inspired mathematical theses with Fregean sympathies. There is a professional philosopher named, I think, Patrick Harvey, who has expressed to me just these kinds of Fregean beliefs. It seems fair to me that I suspect this Fregeanism is manifest in modern logic and philosophy to some small degree.

[aleph_0]

Oh, and I don't know if Frege believed that truth was purely symbol transformation. I also don't know why you impute to me this claim, as well. Perhaps that was ambiguous in my post, where I refer to "this thesis". In any case, I doubt that Frege believed truth was mere symbolic transformation, though it was such an entrenched belief of logicians and mathematicians before 1930 that Godel had a very difficult time explaining his celebrated proof because people could not seem to make the conceptual distinction required. See A World without Time by Palle Yourgrau for the history of this difficulty, among many other things. Today, as I believe I said elsewhere, almost no professional philosophers, mathematicians, or logicians make this mistake.

[Hodge'sPodges]

I said, "The probability is 0. That is a triviality that follows from the fact that there is no object that is both square and round."

This is one account, but I'm not sure I buy it. I probably ought to, but I don't yet understand how we can have meaningful sentences by way of meaningless terms.

To say that x is a round square is tantamount to a conjunction: x is round and x is square. Each predicate, 'round' and 'square' is meaningful, so the conjunction is meaningful, and, in this case, false, since there is no x such that x is round and x is square. I don't know what problem you find in this. Edited February 3, 2009 by Hodge'sPodges

[Hodge'sPodges]

Oh, and I don't know if Frege believed that truth was purely symbol transformation. I also don't know why you impute to me this claim, as well.

I'm not interested in sticking you with any particular claims. Rather David Odden made a claim that formal logicians hold a certain view (part of which was the bit about "symbol transformation") and I asked what formal logician holds such a view, then you offered Frege, though you also, reasonably, hedged your bet on that, as I mentioned. And my point with you is that it is not supported that Frege is a formal logician that holds the view Odden mentions.

truth was mere symbolic transformation, though it was such an entrenched belief of logicians and mathematicians before 1930

What logician or mathematician had such a view, let alone what support is there that such a view was common? Edited February 3, 2009 by Hodge'sPodges

[Hodge'sPodges]

Do you know of some of his writing that would contradict it?

One could start right at the first pages of Logical Investigations.

Sure, you could say that truth and consciousness are related in that one becomes conscious of truth--but I don't think that is when Odden had in mind.

One could find lots of relations. Whatever Odden had in mind, I don't know what formal logician's views can be fairly characterized as Odden did.

It's a bit premature to be making such a charged statement as, "You have not supported such-and-such about your exegesis about Frege," isn't it?

No, it's not. Support has not been given. But my saying that does not preclude that one might eventually provide such support.

I also find the excessive use of all-caps a bit unnecessary. Anyway, I'm not sure what you mean by (or, perhaps, why you impute to me) this thing about "method".

I don't go around shouting in all-caps. I just used all-caps as a text-only means of emphasis of certain words or phrases. As to 'method', it's the word used by Odden himself. I have no desire to stick you with agreeing with Odden, but when you argue that the views of a certain logician do (or may, or whatever) fit the description Odden gave, then this part about method is part of that description.

I was under the impression that the question was about whether some philosophers believe this or that.

It is about formal logicians, not just philosophers, and maybe it was meant by Odden to be only about some, or perhaps, as he left it unquantified, it supposed to be general in whatever sense. He or anyone may now sharpen to be more specific about that; that's fine with me. But in the meantime, I would have liked to know what formal logicians he has in mind. Who, specifically, are at least some of the people he's talking about? (Though, he may or may not wish to produce such an example, in which case it's fine with me to let the matter there rest.)

Should we poll formal logicians? Which logicians count as formal, which people count as logicians? Has anybody conducted any such poll? Would you care to go about it?

We don't have to quibble about what a "formal logician" is, and we don't need to poll. All that is needed for a start is for Odden to say who, specifically, he has in mind. (Previous disclaimer again.)

I simply thought that it was relevant to mention the relevant views of the creator of modern symbolic logic, who was a careful student of mathematics, logic, and philosophy, and who has influenced us to the point that we consider him the father of the modern analytic tradition (steeped in logic, language, and formalism as it is).

I don't mean to merely nitpick, but while Frege is one of the most important of his generation, he is not the only fountainhead of modern logic.

I do not claim that Frege is representative, though I might suggest that he is indicative of views that some logicians may hold today. I know that modern logicians Hartry Field and Somebodyorother White have published Platonist-inspired mathematical theses with Fregean sympathies. There is a professional philosopher named, I think, Patrick Harvey, who has expressed to me just these kinds of Fregean beliefs. It seems fair to me that I suspect this Fregeanism is manifest in modern logic and philosophy to some small degree.

Of course platonism, and realism of various kinds, and the influence of Fregean realism are very much at work in modern philosophy of logic and mathematics. But I don't recognize such views as Odden characterized them. Otherwise, it would help if he would just say who specifically he has in mind. (Previous disclaimer again.)

At this moment, I'm not too interested in hectoring Odden himself on that matter; as I've already asked him, he's not yet responded, so I'm content just to let it rest there with him specifically as he may elect to say more or not to say more at any later point. But you've continued the matter, and also as to the shape of the conversation among the three of us, so I can't properly address that without mentioning Odden's role too.

In closing, I have to say, this kind of getting bogged down in discussion about the conversation itself is not very interesting to me. My initial point is that I don't recognize the views of any particular formal logician in the characterization Odden made. And I've yet to see that characterization upheld. That is good enough for me to let the matter rest, unless we do find some specific writings of a formal logician that are accurately paraphrased as ""For the formal logician, propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method."

Edited February 3, 2009 by Hodge'sPodges

[aleph_0]

I said, "The probability is 0. That is a triviality that follows from the fact that there is no object that is both square and round."

To say that x is a round square is tantamount to a conjunction: x is round and x is square. Each predicate, 'round' and 'square' is meaningful, so the conjunction is meaningful, and, in this case, false, since there is no x such that x is round and x is square. I don't know what problem you find in this.

I'm not convinced that meaning is preserved through composition. I cannot understand the meaning of "∃x(Px & ~Px)". Many claim, and I am somewhat sympathetic, that this is just ungrammatical (even though a well-formed formula).

I'm not interested in sticking you with any particular claims. Rather David Odden made a claim that formal logicians hold a certain view (part of which was the bit about "symbol transformation") and I asked what formal logician holds such a view, then you offered Frege, though you also, reasonably, hedged your bet on that, as I mentioned. And my point with you is that it is not supported that Frege is a formal logician that holds the view Odden mentions.

What logician or mathematician had such a view, let alone what support is there that such a view was common?

I referred you to the book A World without Time. No names were named in the corpus of the text that I know of, though I remember the author telling me that Hilbert did not have the concepts perfectly distinct in his writing. He was obviously aware of some kind of relevant distinction, since he did list as the greatest priority in mathematics a proof of completeness. But so I am told, he did not have a perfectly clear understanding of the distinction between syntax and truth. You'd probably have to look at the book's references if you're interested, and glance at Hilbert's Der Grundlagen Der Elementaren Zahlentheorie (I don't know German, but it should be easy to find an English translation. From the German I do know, the title is something like The Foundations of Elementary ___-theory.).

Now your contest with Odden was many-faceted, as I pointed out. There were at least four different concepts being controverted, and I was proposing that Frege endorsed two, and I've supported those in the exegesis. So within that topic, I maintain that Frege was a formal logician who did hold the views (those two, out of at least four) Odden mentioned.

[DavidOdden]

At this moment, I'm not too interested in hectoring Odden himself on that matter; as I've already asked him, he's not yet responded, so I'm content just to let it rest there with him specifically as he may elect to say more or not to say more at any later point.

Kleene is an example of this syntactic view of logic. Now, I defy you to give me one example of a formal logician who claims that logical symbolism has a necessary connection with human consciousness or that formal deductions have a "metaphysically necessary" character.

[aleph_0]

One could start right at the first pages of Logical Investigations.

Before I start looking, do you have a passage in mind? In fact, to be clear, are you saying that the first pages (say, the first three) contradict this characterization?

One could find lots of relations. Whatever Odden had in mind, I don't know what formal logician's views can be fairly characterized as Odden did.

I gave a class of them, above.

No, it's not. Support has not been given. But my saying that does not preclude that one might eventually provide such support.

I don't go around shouting in all-caps. I just used all-caps as a text-only means of emphasis of certain words or phrases. As to 'method', it's the word used by Odden himself. I have no desire to stick you with agreeing with Odden, but when you argue that the views of a certain logician do (or may, or whatever) fit the description Odden gave, then this part about method is part of that description.

I said "excessive use of all-caps", as it did come off as an exasperated tone.

Now if I said that Descartes believed that the reason we can trust our senses is that god would not allow us to be fooled, it would be appropriate to cite that in an academic paper. I am not writing an academic paper. Yet your tone was accusatory, rather than inquisitive. If you would like a reference, your interest would be most respected if you asked for one. Just a suggestion--I'm not sure if politeness is a prerequisite for participating in conversation here.

In any case, from what I wrote about Frege, it should be clear that I was focusing on those two views and no other. In fact, I made a point to draw attention to just that fact near the end.

We don't have to quibble about what a "formal logician" is, and we don't need to poll. All that is needed for a start is for Odden to say who, specifically, he has in mind. (Previous disclaimer again.)

The point of my post was to vindicate for Odden at least that Frege might satisfy two of the claims (and who was a formal logician). Apparently, this is not what you were looking for. I'm actually not sure what you were looking for, since you don't want a poll and you don't want a particular individual. It seems you want evidence of the zeitgeist without reference to any individuals or groups.

Furthermore, Odden mentioned that he encounters this thinking every day professionally--and he is, indeed, a professor of linguistics. So if you're not going to quibble over who counts as a formal logician, then perhaps his students are.

I don't mean to merely nitpick, but while Frege is one of the most important of his generation, he is not the only fountainhead of modern logic.

He invented symbolic logic, which is the fountainhead of modern logic. So maybe he's not the fountainhead of modern logic, but he is the father of the fountainhead, which is pretty hot stuff. If anybody is to serve as an example of a modern formal logician, he's bound to be an apt candidate.