Submitted by: Group 3B Karen Rizel Abella Kin Pearly Flores Kristine Lea Rabaja Crystal Gayle Nacua PHILO1 Th 1:00- 4:00 pm Bro. Jensen DG. Mañebog
SORITES Sorites is an abridged form of polysyllogism wherein the intermediate conclusions are left out. It is an argument which states the premises and a main conclusion but conceals conclusions in 1 between. There are two kinds of Sorites: Aristotelian sorites and Goclenian sorites.
A. Aristotelian Sorites Aristotelian sorites is an abridged polysyllogism in which the predicate of the preceding premise becomes the subject of the following. It has this form:
All A is B; All B is C; All C is D; All D is E; 2 ∴ All A is E. Example: All philosophers are wide readers; All wide readers are intelligent; All intelligent people are creative; All creative people are producers of good ideas; ∴ All philosophers are producers of good ideas.
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B. Goclenian Sorites Goclenian sorites is an abridged polysyllogism in which the subject of the preceding premise becomes the predicate of the following. It has this form:
All A is B; All C is A; All D is C; All E is D; ∴ All E is B.
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Example: One who will not sacrifice truth for power is a responsible person; One who is a paragon of honesty will not sacrifice truth for power; One who is worth emulating is a paragon of honesty; 1
Santiago, Alma Salvador Ph. D. LOGIC: The Art of Reasoning. 2002. P. 185. Ibid. 3 Ibid. 4 Santiago, Alma Salvador Ph. D. LOGIC: The Art of Reasoning. 2002. P. 186. 2
A model of decency is worth emulating;_______ 5 ∴ A model of decency is a responsible person. There is no essential difference between the Aristotelian sorites and Goclenian sorites except in the manner of the arrangement of the premises. To construct the Aristotelian sorites from Goclenian sorites and vice-versa, we start with the last premise and end with first. The 6 conclusion remains the same. Group 3B’s examples of Sorites Karen Rizel Abella’s example:
All animals are living things; All living things is reproductive; All reproductive things grow; Therefore, All animals grow. Kin Pearly Flores’ example:
All my daughters are slim. No child of mine is healthy who takes no exercise. All gluttons, who are children of mine, are fat. No sons of mine takes any exercise. Kristine Lea Rabaja’s example:
Every cat is a mammal, Every mammal is an animal, Every animal is God’s creation, Therefore every cat is God’s creation. Crystal Gayle Nacua’s example:
All persons fit to serve on a jury are sane persons. All sane persons are persons who can do Logic. All persons who can do Logic are intelligent. Therefore, all persons fit to serve on a jury are intelligent.
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Ibid. Ibid.
DILEMMA A dilemma (Greek: δί-λημμα "double proposition" ) is a problem offering two possibilities, neither of which is practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma" , neither horn being comfortable. This is sometimes more colorfully described as "Finding oneself impaled upon the horns of a dilemma", 7 referring to the sharp points of a bull's horns, equally uncomfortable (and dangerous). The dilemma is sometimes used as a rhetorical device, in the form "you must accept either A, or B"; here A and B would be propositions each leading to some further conclusion. Applied incorrectly, it constitutes a false dichotomy, a fallacy. Colloquially, we call a 'dilemma', any impossible choice. 'If I do this, I've had it; if I do that, I've had it — so I've had it anyway (and it is no use my doing this or that)'. This is indeed a case of dilemma, but in logic the expression is understood more broadly, to cover more positive situations. Thus, often, in action contexts, when we are faced with a choice of means to get to a goal, we might resolve the dilemma by using all available means, even at the cost of 8 redundancies, so as to ensure that the goal is attained one way or the other. Although dilemmatic argument may be derived from apodosis and syllogism, it has a certain autonomy of cogency and is commonly used in practise, so it deserves some analysis. Note well first that the disjunction used in dilemma is the 'and/or' type (not the 'or else' type), even if in practise this is not always made clear. The hypotheticals which constitute the major premise of a dilemma are called its 'horns'; they give an impression of presenting us with a predicament. The minor premise is a disjunction; it is said to 'take the dilemma by its horns'. The conclusion is said to 'resolve' the dilemma. a. Simple dilemma consists of a conjunction of subjunctives as major premise, a disjunctive as minor premise, and a (relative) categorical as conclusion. It normally involves 9 three theses. Tradition has identified two valid moods. (i)
The simple constructive dilemma.
If M, then P — and — if N, then P but M and/or N hence, P This is proved by reduction ad absurdum through two negative apodoses, as follows:
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http://en.wikipedia.org/wiki/Dilemma
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http://www.thelogician.net/2_future_logic/2_chapter_30.htm Ibid.
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If M, then P — and — if N, then P (original major premise) and not P (denial of conclusion) so, not M and not N (contrary of minor). Alternatively, we could regard the simple constructive dilemma as summarizing a number of positive apodoses, with reference to the matrix of alternative conjunctions underlying the minor premise: If M, then P — and — if N, then P but 'M (and not N)' or 'N (and not M)' whence, P whence, P
or 'M and N' whence, P and P
(common major) (alternative minors) (common conclusion).
This shows the essential continuity between the concepts of apodosis and dilemma, note. (ii)
The simple destructive dilemma.
If P, then M — and — if P, then N but not M and/or not N hence, not P This is proved by reduction ad absurdum through two apodoses, as follows: If P, then M — and — if P, then N (original major premise) and P (denial of conclusion) so, M and N (contrary of minor). In contrast, the following two arguments would be fallacious: If M, then P — and — if N, then P but not M and/or not N hence, not P
If P, then M — and — if P, then N but M and/or N hence, P
b. Complex dilemma consists of a conjunction of subjunctives as major premise, and disjunctives as minor premise and conclusion. Tradition has identified two valid moods. It 10 normally involves four theses, though two are occasionally merely mutual antitheses. (i)
The complex constructive dilemma.
If M, then P — and — if N, then Q but M and/or N hence, P and/or Q This can be proved by reductio ad absurdum, as in simple dilemma. Alternatively, we may analyze it through a sorites, as follows: 10
Ibid.
If not P, then not M (contrapose left horn) if not M, then N (from minor) if N, then Q (right horn) therefore, if not P, then Q (transform to conclusion). (ii)
The complex destructive dilemma.
If P, then M — and — if Q, then N but not M and/or not N hence, not P and/or not Q This can be proved by reductio ad absurdum, as in simple dilemma. Alternatively, we may analyze it through a sorites, as follows: If not not P, then P (axiomatic) if P, then M (left horn) if M, then not not M (axiomatic) if not not M, then not N, (from minor) if not N, then not Q (contrapose right horn) therefore, if not not P, then not Q (transform to conclusion). In contrast, the following two arguments would be fallacious: If M, then P — and — if N, then Q but not M and/or not N hence, not P and/or not Q
If P, then M — and — if Q, then N but M and/or N hence, P and/or Q
c. Concerning both the simple and complex valid moods, note that, formally speaking, we could use as minor premises the equivalent forms 'not M or else not N' and 'M or else N', respectively, in the valid constructive and destructive moods. But this would not reflect the true format of dilemma. The goal here is only to describe actual thought processes, not to accumulate useless formulas. However, in view of the similarity in appearance between these valid substitutes, and the minor premises of the invalid moods, it is well to be aware of the 11 possibility of confusion. A special case of complex constructive dilemma is worthy of note, because people sometimes argue in that way. Its form is: If M, then {P and nonQ} — and — if N, then {nonP and Q} but M and/or N hence, either P or Q. We may understand this argument as follows: contrapose the left horn to 'if not-{P and nonQ}, then nonM'; the minor premise means 'if nonM, then N'; these propositions, together with the right horn, form a sorites whose conclusion is 'if not-{P and nonQ}, then {nonP and Q}'. But 11
Ibid.
we know on formal grounds, for any two propositions, that 'if {P and nonQ}, then not-{nonP and Q}'. Therefore, 'either {P and nonQ} or {nonP and Q}' is true, which can in turn be rephrased as 'either P or Q'. Thus, what this argument achieves is the elimination of the remaining two formal alternatives, {P and Q} and {nonP and nonQ}; the combinations {P and nonQ} and {nonP and Q} become not merely incompatible, but also exhaustive. There is no destructive version of this argument, because its result would only be 'if {P and nonQ}, then not-{nonP and Q}', which is formally given anyway. There is also no equivalent argument in simple dilemma. But note that if we substitute nonM for N in the one above, we obtain something akin to it: if M, then {P and nonQ}, and if nonM, then {nonP and Q}; but either M or nonM; hence, either P or Q. This is not really simple dilemma because the antecedents are not identical; but there is a resemblance, in that only three theses are involved. Also, the minor premise here is redundant, since formally true, so the 12 conclusion may be viewed as an eduction from the compound major premise. Also note, simple and complex dilemmas may consist of more than two horns. The following are examples of multi-horned simple dilemma: Constructive: If B and/or C and/or D… is/are true, then A is true but B and/or C and/or D…etc. is/are true therefore A is true. Destructive: If A is true, then B and C and D …etc. are true but B and/or C and/or D…etc. is/are false therefore A is false'. Similarly with other sorts of arrays. This shows that we can view the horns of dilemmas as forming a single hypothetical proposition whose antecedent and/or consequent is/are conjunctive or disjunctive. It follows that simple and complex dilemma should not be viewed as essentially distinct forms of argument; rather, simple dilemma is a limiting case of complex dilemma, the process involved being essentially one of purging our knowledge of extraneous alternatives. The commonly employed form 'Whether P or Q, R' is normally understood as an abridged simple constructive dilemma, meaning 'If P, then R, and if Q, then R, but P and/or Q, hence R anyway'. However, we should be careful with it, because in some cases we intend it to dissociate R from P and Q, meaning 'If P not-then R, and if Q not-then R, but R'. Note well the difference. In the former case, the independence is an outcome of multiple dependence; in the latter case, the independence signals lack of connection.
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Ibid.
Dilemma, especially its ultimate, simple version, is a very significant form of reasoning, in that it is capable of yielding factual results from purely problematic theses (implicit in hypotheticals or disjunctives). Like the philosopher's stone of the alchemist, it turns lead into gold. Without this device, knowledge would ever be conjectural, a mass of logically related but unresolvable problems. Note however that the conclusion of a simple dilemma is still, logically, only factual in status. A thesis only acquires the status of logical necessity or impossibility, when it is implied or denied by all eventualities; this means, in dilemma, when the exhaustiveness of the alternatives in the premises is itself logically incontingent (rather than a function of the present context of knowledge). The significance of this will become more transparent as we proceed further, and 13 deal with paradoxical logic.
Group 3B’s examples of Dilemma Karen Rizel Abella’s example:
Either I finish my studies or I will travel around the world. If I finish my studies and not travel around the world, I will make my parents proud. If I travel around the world and not finish my studies, I will make my own dreams be fulfilled. Therefore, either I will make my parents proud or I will make my own dreams be fulfilled. Kin Pearly Flores’ example:
If we increase the price, sales will slump. If we decrease the quality, sales will slump. Either we increase the price or we decrease the quality. Therefore, sales will slump. Kristine Lea Rabaja’s example:
I must either jump or stay. If I jump, I shall die immediately from the fall. But, if I stay, I shall die immediately from the fire. Therefore, I shall die immediately.
Crystal Gayle Nacua’s example:
If I win this case, I shall not have to pay Euathlus. If I lose this case, I shall not have to pay Euathlus.
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Ibid.
I must either win or lose this case. Therefore, I do not have to pay Euathlus.
