Brian Matthew Kessler

13 November 1997

1. Steup is surely a friend of the idea that propositions are the bearers of truth. What are propositions and in what way are sentences just as abstract as propositions?

Propositions are the things that are expressed by sentences. In other words, the proposition remains the same (assuming the same proposition is accurately rendered) regardless of whether it is expressed in a mathematical formula, a sentence in English, a sentence in German, sign language, a pictorial diagram, or in some other medium. For example:

(A) 2 + 2 = 4

(B) The sum of two added to another two is equal to four.

© Zwei und zwei ist vier.(1)

(D) <insert hand signals for 2 + 2 = 4 here>(2)

(E) (..)+(..) = (....)

Though each of the above is expressed differently, they all represent and can be understood (theoretically, at least) to mean the same proposition.

Note that sentences and propositions are both abstractions of the actual supposed truth described. The sentence merely is a combination of words that represent some propositions, but there is no inherent link between the words and the properties they describe. For example, the words "two" and "four" have no inherent connection between either their sounds, their letter collections, or the form of their letters and the quantities they describe. They are only meaningful so far as we agree to communicate with a common English language -- similarly "dog", "cat", "work", "test", and any other word we are to chose out of either English or any other language will ultimately fair to be other than a more or less arbitrary symbol for the object or concept it represents.

The proposition itself is even an abstraction of the actual fact or lack thereof. As this is difficult to demonstrate with the proposition "2+2=4", let's consider something more tangible:

(F) Sam, the dog, is in the doghouse.

Let's assume that there is a real dog named Sam and there is a doghouse which can ordinarily be associated with the location of the dog named Sam. First, sentence (F) is an abstraction of the truth or falsehood of the sentence it represents; just like there is no inherent link between "two" or "four" and the quantities they represent, there is nothing inherent that the dog should be named Sam nor even called a dog. And though "doghouse" may be a fitting description of it's primary, current, and perhaps only function -- therefore well suited to the object it describes, it is ultimately as arbitrary as both the descriptions "dog" and "house". Thus, we can see that the sentence is an abstraction of the fact. But the proposition itself is also an abstraction. It can be conceived even if there is in reality neither "Sam, the dog", nor it's supposed doghouse. Or Sam, may be in a dog house without anyone (not even the dog) perceiving or conceiving of this fact (perhaps he blind dog that accidentally wondered into a shelter to get out of the rain and this shelter happened to be a doghouse), thus nobody ever formulates the proposition and the dog would still be in the doghouse. Thus the proposition can exist independent of the fact or the fact independent of the proposition.

Assuming that there are an infinite number of arithmetic truths, why does Steup think they cannot be "matched by an infinite number of corresponding sentence tokens?"

As numbers approach either infinity or infinitesimal, there is a diminished probability that anyone shall even think of the number to formulate sentences about that number. For example, take the number: 8,528,255,337,367,091,568,328,354,323,981,249,435,234,257,122,235.0245235213515798071351266154.

Most likely, this number has never been used by a human in any sentence previous to it, yet there are an infinite number of mathematical truths that can be related to what it is greater than, less than, equal to, divisible by, etc. If I simply state that this number is equal to itself, I have stated only one infinitesmal of all the sentences that would be needed to represent all the truths about that number. As there are an infinite number of numbers, the number of sentences that would be required to represent all mathematical truths would approach infinity squared. As only a limited number of sentences have ever been formulated in regards to mathematical truths, and those sentences in regard to only a very limited range of numbers, this task of representing all mathematical truths by sentences, no matter how hard and long we should work to rectify it, would ultimately result in failure because humans are naturally limited. We could only get one infinitesmal of the way there.

Let us assume however that some madman was willing to attempt this ludicrous task perhaps aided by a computer that can help to calculate these truths that would otherwise be beyond the scope of the human mind. Let us also say, for the sake of argument that time is no object and he has infinity to work out all these truths. As the computer prints out all these infinite truths on infinite pieces of paper, he is to work on formulating sentences based on these truths. As these numbers approach infinity, there is an increasingly deminished probability that the human mind could handle the value with meaning. Take for example the number offered above, the typical (non-mathematician) human would not be able to even label such a number in terms of the accepted English language (carry it a little further and even your best mathematicians couldn't label it without falling back on some perhaps archaic but accepted system; carry it much further and the labeling system would ultimately collapse into meaningless confusion if not in the creation, then at least to any reception of it). But let us assume that someone worked out that this number has a value of eight funfdecillion(3), five hundred twenty-eight vierdecillion, two hundred fifty-five dreidecillion, three hundred thirty-seven zwolftillion, three hundred sixty-seven elftillion, ninety-one decillion, five hundred sixty-eight nonillon, three hundred twenty-eight octillion, three hundred fifty-four septillion, three hundred twenty-three sectillion, nine hundred eighty-one quintillion, two hundred forty-nine quadrillion, four hundred thirty-five trillion, two hundred thirty-four billion, two hundred fifty-seven million, one hundred twenty-two thousand, two hundred thirty five and two hundred forty-five octillion, two hundred thirty-five sectillion, two hundred thirteen quintillion, five hundred fifteen quadrillion, seven hundred ninety-eight trillion, seventy-one billion, three hundred fifty-one million, two hundred sixty-six thousand, one hundred fifty four nonillionths and actually is willing to put such an absurd phrase into a sentence. Would any human actually be able to look at or listen to this sentence with an understanding? Could they either remember each digit to it's proper place and then then conceive of this number as a distinct value rather than simply "many and a small part more"? I find myself doubting the human ability to recognize distinct numbers as they approach mere millions or millionth. Discussion of such numbers bcomes an act of absurdity, not to mention increasing impracticality (possibly days to speak or miles to write) as numbers approach infinity or infinitesmal, therefore presenting a second reason sentences will never exist to express all mathematical truths.

Give original examples of propositions which are (a) necessarily true,

The following are necessarily true:

Whoever is deaf can not hear you.

If the sun shines it's light directly on me on a bright summer's day, I am not in the dark.

If there are five people in my car, my car has at least one person in my car.

If Joe has more money than Smith and Smith has more money than I, then Joe has more money than I.

(b) necessarily false

The following are necessarily false:

The blind man saw me coming from one mile away.

The empty box was full of mice.

Three pounds of salt weighs more than ten pounds of salt.

The cat was bigger than the dog, the dog was bigger than the elephant, and the elephant was bigger than the cat.

(c) contingently true, and

The following are contingently true:

There are over ten light bulbs in my bedroom.

One of my computers is used to runs free public bulletin board system.

My wife is in the shower as I type this sentence.

There are two plastic skulls in front of me.

(d) contingently false.

The following are contingently false:

I have ten years experience driving stick shift cars.

I am going to Siberia tommorow.

I lost a foot in the first world war.

I carry Webster's Unabridged Dictionary whereever I go.

What is the difference between logical and physical necessity? Give original examples of propositions that are logically but not physically possible.

Logical necessity is a matter what is rationally possible, as opposed to physical necessity being what is materially possible. The following examples are all logically possible, despite being physically impossible:

Jim spent last summer walking across the Atlantic Ocean.

John can leap over tall buildings in a single bound.

Tom can catch speeding bullets with his teeth.

Samantha heard a pin drop in the mosh pit of a GWAR concert.

2. For an analysis to be correct, the analysans must do what two things?

I. For an analysis to be correct the analysans must define how to apply the term such that all instances of the term's object will have the term applied to it. For example, an analysis of cats would not be correct if it excludes lions from the application of the term "cat".

II. For an analysis to be correct, the analysans must define how to apply the term such that all instances which are not the term's object will not have the term applied to it. For example, an analysis of cats would not be correct if it includes dogs in the application of the term "cat".

Below are two analyses of familiar (pun not intended) concepts. Explain what is wrong with sample analysis #2a and sample analysis #3a.

2a. For all x, x is a grandfather if and only if x has a child who has a child.

3a. For all x, x is a grandmother if and only if (i) x is female (ii) x has a child who has a daughter.

2a is primarily incorrect because x is not required to be male, thus 2a will include grandmothers as being grandfathers.

3a is primarily incorrect because condition (ii) require's that the child have a daughter, whereas the child could have a son and thus x will be made a grandmother.

Both 2a and 3a are also problematic in use of the term "has". First, "has" designates the present tense. It is possible that the grandfather or grandmother no longer has their child because some accident brought about an untimely death for their child, but not before that child could make them a grandparent. Thus, "x has" must be replaced in both 2a and 3a with "x had". The second problem with "has"/"had" is it does not necessitate a parental relationship between grandfather and child or child and child. "Has"/"Had" simply refers to possession. But could someone not possess a child as a slave, a servant, or even a stuffed decoration? Thus, replacing "has" with "had" is not adequate -- perhaps "spawned" should serve us better.

2a and 3a are also both problematic in the use of the term "child"(4) -- perhaps a consideration most niggly, but I find it awkward to state any of the following as being necessary to grandparenthood:

(A) a child has a child.

(B) a child had a child.

(C) a child spawned a child.

(A) and (B) I reject since they indicate mere possession, as explained above. As for (C), while it is true that sometimes parents are yet children (as defined by their local culture), in most cases parents are not children but adults. Therefore, I propose that for both 2a and 3a, each instance of the word child much be replaced with the phrase "first generational descendant" or some such equivalence. It is arguable that "first generational" need not be specified for if they have a second generational desecendant, it can be seen that they are grandparents by definition and if they have third generational desecendants they are great-grandparents which they could not become without having first become grandparents, and so one.

Thus corrected forms of 2a and 3a can be reflected by

2b. For all x, x is a grandfather if and only if (i) x is male (ii) x spawned a

first generational decendant who, in turn, spawned a first generational descendant unto itself.

3b. For all x, x is a grandmother if and only if (i) x is female (ii) x spawned a first generational decendant who, in turn, spawned a first generational descendant unto itself.

These may be otherwise stated as:

2c. For all x, x is a grandfather if and only if (i) x is male (ii) x spawned (possibly indirectly)(5) a second generational descendant.

3c. For all x, x is a grandmother if and only if (i) x is female (ii) x spawned (possibly indirectly)(6) a second generational descendant.

In the above examples someone who understood what it was to have a child and what it was to have a daughter would be able to understand what the analysis claims is involved in being a grandfather/mother. So a certain sort of intellectual progress is made; a person, through the analysis, could come to know what a new (to them) concept means. Steup then introduces his notion of a criteriological analysis. A criteriological analysis is designed to permit "reduction" by not requiring that the analysans mean the same as the analysandum. It would then be possible to give a criteriological analysis of a value concept such as "worth believing" and use only non-value laden terms. Analytic philosophers hoped that through careful reflection on our actual use of concepts and with the help of logical constructions they would be able to develop criteriological accounts or analyses of important philosophical concepts such as knowledge, justified belief, a priori justification, and even truth. The introduction of the notion of supervenience is designed to deal with difficulties in discovering criteriological analyses. Criteriological analyses are neat and simple biconditionals or if and only if statements; however, they are very hard to come by. Supervenience relations are much less neat but they still can effect the reduction of value laden concepts to non-(value-laden) or purelu descriptive concepts.

Explain what Steup has in mind by "epistemological pessimism" and then discuss whether or not you think you could describe in non-epistemic terms the conditions under which you are justified in believing things about the world of middle-sized objects that we all live and work in.

Epistemological pessimism is the view that although there are nonnormative properties (i.e., properties which exist prior to and without evaluation) on which epistemic justification supervenes (i.e., justification is built upon), we can't pin down what these properties are. This may be because either those properties are infinite in number or in degree of complexity.

There are many ways I justify my beliefs about the world around me. Some, I justify by perception, such as the belief that I am sitting on a grey swivel chair. Were I to try justifying this belief by memory without perception, my belief could prove incorrect, since often I forget whether I am sitting in the gray swivel chair or the black swivel chair, both of which tend to randomly travel around my bedroom. Were I to try to justify this belief by introspection without perception, I could come up with the known possibilities of what I am sitting on which would not only include the other chair I know to be in this room, but also the chance that someone perhaps moved a chair out of another room or even elsewhere which I then sat down upon without taking note of. Thus, neither memory nor introspection would prove an adequate foundation for justifying this belief since both can lead to other possibilities and neither to a definite affirmation of which seat I sit upon.

Others are more suitably justified by memory, such as the belief that my car is still sitting with a dying transmission in my home's driveway. There is no way I can perceive this without moving since several walls are between me and the object of this belief; my need for justifying this belief is not currently so great as to be worth the effort of such verification. And if I did go look, without memory to tell me what my car looks like and the condition it is in, the car I perceive may be a car other than my own and/or in a better condition. Thus I would need to verify ownership and condition of the car. Then I would need to remember how either may be verified... and so on... and without memory I should certainly forget the reason for my laborous verification processes. Introspection would allow me to realize the possibility that my car is in the driveway with it's dying transmission, but it will also tell me it is possible that George came to collect the car without my knowing or some thief could have wasted his time upon it. Or that it could even have been fixed without my knowledge and then returned to there or elsewhere around my house -- but all this introspection relies on my memory to indicate these possibilities.

Yet others I justify by introspection, such as the belief that killing my parents would not be a good thing. To justify this theory by perception is impossible without killing them first to observe the results; not liking the results, there would be no way to undo the act -- therefore this is an undesirable way of justifying the belief. As I have had no memory of doing such an act previously, it is likewise impossible to base just a justification on recollection of the past. It is much wiser to justify the believe by thinking about how much good they do for me by being alive, how much I love them as my parents, and how severely I might be punished by society and perhaps God for killing them, etc.

Although I can not currently think of other methods which I would use for justification, I am open to the possibility they exist and it may be expediant if not necessary to employ them in addition or even instead of those which we have discussed. It seems unlikely to me that we can reduce those three qualities to any single common denominator and in the event we add others to this list, they too shall prove likely as irreducable. This is because depending on the belief I wish to justify, my evidence may come from either within my mind or from without. It may be based on events in the past, the present, or the future. It may effect only myself, or by circumstance of accepting the belief, it may compel or even require me to affect others. As circumstances vary, the ways in which justification must be obtained and the level or degree to which it must be obtained will vary -- for this reason, I do not think it likely that we can make any simple criteriological analysis for justification. Whether infinite complexity is needed seems doubtful since only a limited number of sentient beings exist(7), most likely they shall only exist for a limited amount of time in a limited amount of space. Because of this, the quantity of their experience, however large it may be is similiarly imposed upon by an upper limit, even if an ultimately incalcuable one. As long as this limit can be assured to exist, then there must be a limited number of properties necessary for justification -- of course, that number may be large enough that it shall move outside of human managability. And if some of those sentient beings are not human, perhaps their methodology shall be too alien even for our true understanding. But as long as we shall limit the scope of justification to that done by the human population of Earth, I think it quite likely that those properties could be placed within a list of some reasonable size.

Conclude with a comment on the following remark: Ethical pessimism is unjustified since we are able to do the right thing and to get on in ethical matters without knowing any ultima facie ethical supervenience principles. So epistemological pessimism is equally unjustified.

The first problem to be had with this remark is a failure to define "the right thing". Wherefrom comes this "right"? Does it come from the individual actor? His peers, culture, or society? His perceived God? A real God possibly absent from his perception? Is it to be found in oral or written tradition? In precidents of past deeds? The perception of "right" can come from any of these sources, perhaps even more. Is it necessarily the same "to do right" as to perceive that one's act can be characterized as such? I may perceive that the right thing to do is drive to school three times a week to increase my level of education. Some may perceive this act to be wrong on the grounds that my car is polluting the environment and wasting the earth's resources. Others may object that my education is no more useful than an expensive hobby and the world would be better served if I were to simply quit school and find a job flipping burgers. Some may perceive that my education takes away from my soul's innocence and makes it more difficult for me to believe in the accepted God and therefore is poisonous to my soul and to the souls of anyone who should come in contact with me. Perhaps there is a god unperceivable to man that should define good and evil in ways beyond the comprehension of man (If a god is infinite in faculties, it is surely a matter of ego in hoping that humans with out limited mental faculties would be able to parallel his motivations or conclusions).

As outlined above, our ability "to do right" is by no means an obvious capability and it may be reasonable from an unknown God's perspective to conclude that a right act has yet to ever be done. We can even complicate the issue further by proposing that this God may find acts that are "right" simultaneously undesirable -- when God defines right and yet expects otherwise, what does "right" really mean(8)?

It may be impossible to know the ultimate source by which to define right and it is a matter of belief on which source to choose from, and for practicle reasons we are inclined to reject consideration of a god unintelligible to humanity. But even having choosen a source, one must then form at least in some instances, consciously or otherwise, belief on which duties come first or take precidence. Let us say I form a strong belief that killing everyone in our philosophy course shall prevent World War III from occuring within my lifetime. Believing that World War III would be a very bad thing, I may feel duty bound to kill everyone in the class. But at the same time, I believe that unjustified homocide is wrong and that a strong belief is not adequate justification without strong justification for the belief itself. I may also wish to consider how my life and the life of my family would be affected were I to be convicted of murder, especially if I could not justify the belief that prompted me to commit these murders. Would it be right to kill the class even though the belief may be completely delusional? Or would it be right, believing myself to have very accurate instincts(9) and believing in World War III millions more would die and be adversely effected than merely those who would be affected by the proposed homocides -- just those members of the class and their and my families? Should I seek compromise by only killing half the class and hoping it is enough to prevent The War? Depending on who's view you take and the importance you feel towards avoiding World War III, this situation lends itself to no easy answers -- and though the easiest answer may be to let everyone live and hope I my belief is wrong, there is no guarantee that this should ultimately prove right. Fortunately, I have no such belief as I would not wish to choose between the alternatives.

The other problem is with the statement "So, epistemological pessimism is equally unjustified." Just because pessimism may or may not be unjustified in one branch of philosophy which may have some parallels, I see no necessity that we can make blanket statements to allow or disallow pessimism in another branch of philosophy. Let us make an analogy in terms of mathematics. Let us refer to one branch of mathematics as "the branch of multiplication by five" and we can perceive a rule which states "the product of all decimal numbers multiplied by five will terminate in either five or zero". Would there be any wisdom in going to the parallel and relatively closely related "branch of multiplication by seven" and declaring a rule which states "the product of all decimal numbers multiplied by seven will terminate in either seven or zero"? No, it would not be wise; we would not get very far before proving the rule wrong: 7x2=14 (47, 40). Thus, whatever use one may make of analogies to ethics or other philosophical branchs, arguments one wants to make either for or against epistemological pessimism ultimately must be done within terms terms of epistemology itself.

1. Please excuse my German for being less elaborate than my English -- I haven't used the language in over ten years and I never knew it very well -- but regardless, the ineloquent German sentence still helps make my point as it represents the very same proposition. Return

2. My word processor can't generate the hand signals and I wouldn't know the ones to use anyway... but you can imagine the equation communicated by sign language here. Return

3. Don't take these large value labels as gospel... they are probably false... but they seem good enough to use for arguments sake). Return

4. Admittedly, to say "I am my parent's child" is a true statement in the sense that "child" can be used in place of "son" or "daughter". However, the word "child" carries a stigma of youth that may not be applicable in all instances. It is therefore best to avoid this loaded term even if the term is technically allowable. Return

5. Necessary to prevent incest as becoming a requirement to being a grandfather. Return

6. Necessary to prevent incest as becoming a requirement to being a grandmother. Return

7. Perhaps this belief is unjustified as there are no known limits to the universe. If the universe is infinite, it is possible that sentient beings should occur an infinite number of times within it and are therefore not actually limited in number... but trying to think upon such lines becomes an act of idle speculation since even if we stipulate these other beings we have no way to contact them or compare experiences. Return

8. This proposal is not as absurd as it may sound: in fact, it can be seen as a major issue within the Krishna religion's Baga-Gita (sp?). Within this scripture, Arjuna (sp?) is a great warrior who has been called upon to fight in a great war; he looks upon the enemy battlelines and sees both friends and family amongs them. The Godhead Krishna, a personal friend to Arjuna sees Arjuna's distress and confronts him upon it. He explains to Arjuna that it is not Arjuna's place in this life to live the life of the Good; Arjuna's path in this life is the path of the warrior: that is the path Arjuna is oblidged to follow, not the path of goodness; such is the dictate of Krishna who has been the one to define good. Return

9. A true example of making the wrong choice in similiar but less extreme circumstances occured about ten years ago while walking across my home town with a friend. Passing a lead pipe on the ground near where some construction was being done, I had an instinctive urge to take it with a believe I should need it to protect myself. This belief was ignored because I thought taking the pipe would be asking for trouble. Not fifteen minutes later the two of use were jumped by five local hoodlums who gave us both black eyes and received no serious harm in return. This is only one of many such incidents when instincts have accurately warned me without any other evidence of trouble that I should expect in the future. Thus, it may not be wise to simply dismiss prophetic intuitions when trying to judge the ethical qualities of performing or not performing an action. Return

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