Dummett and the problem of abstract objects

Dummett’s views on the problem of abstract objects shifted significantly over the course of his philosophical career, and an examination of his views on this issue not only provides insight into his development; it also serves to elucidate his contribution and significance as a philosopher of language and mathematics. In the paper I attempt to demonstrate the way in which Dummett’s treatment of the problem of abstract objects is instructive for a consideration of his philosophy as a whole. Section 1 sketches the development of Dummett’s views on the problem from his attack on nominalism in the mid-1950’s to his advocacy of a tolerant reductionist position in Frege: Philosophy of Mathematics. Section 2 then examines the significance of Dummett’s views on abstract objects for his philosophical project more generally.

Synthesis, structure and spectral properties of dithiocarbamato bridged dirhenium(III,II) complexes: a combined experimental and theoretical study

Sodium salts of dimethyldithiocarbamate, diethyldithiocarbamate and pyrrolidinedithiocarbamate react with the multiply bonded paramagnetic dirhenium(III,II) complex Re₂(μ-O₂CCH₃)Cl₄(μ-dppm)₂, 1 (dppm = Ph₂PCH₂PPh₂) in refluxing ethanol to afford the paramagnetic substitution products of the type Re₂(η²-S,S)₂(μ-S,S)(μ-Cl)₂(μ-dppm), where S,S represents the dithiocarbamato ligands [S,S = S₂CNMe₂, 4(L_Me); S₂CNEt₂, 4(L_Et) and S₂CN(CH₂)₄, 4(L_Pyr)]. These are the first examples of dirhenium complexes that contain bridging dithiocarbamato ligand along with the dppm ligand. These complexes have very similar spectral (UV-Vis, IR, EPR) and electrochemical properties which are also reported. The identity of 4(L_Et) has been established by single-crystal X-ray structure determination (Re-Re distance 2.6385 (9) Å) and is shown to have edge-shared bioctahedral structure. The electronic structure and the absorption spectra of the complexes are scrutinized by the density functional theory (DFT) and time-dependent density functional theory (TD-DFT) analyses.

Acetylacetonato chelated ruthenium organometallics incorporating imine-phenol function: spectroscopic, structural, electrochemical and cytotoxicity studies

The heterogeneous phase reaction of Ru(η²-RL)(PPh₃)₂(CO)Cl, 1 with lithium acetylacetonate (Liacac) afforded the complexes of the type Ru(η¹-RL)(PPh₃)₂(CO)(acac), 2 in excellent yield where η²-RL is C₆H₂O-2-CHNHC₆H₄R(p)-3-Me-5 and η¹-RL is C₆H₂OH-2-CHNC₆H₄R(p)-3-Me-5 and R is H, Me, Cl. The chelation of acac is attended with the cleavage of Ru-O and Ru-Cl bonds and iminium-phenolato → imine-phenol prototropic shift. A sterically controlled change in rotational conformation is involved in the 1 → 2 conversion. The conversion is irreversible and the type 2 species are thermodynamically more stable than the carboxylate, nitrite and nitrate complexes of 1. The crystal structures of Ru(η¹-MeL)(PPh₃)₂(CO)(acac), 2(Me) and Ru(η¹-ClL)(PPh₃)₂(CO)(acac), 2(Cl) are reported. Spectral (UV-Vis, IR, ¹H NMR) and electrochemical data of the complexes are also reported. The electronic structure and the absorption spectra of the complexes are scrutinized by the density functional theory (DFT) and time-dependent density functional theory (TD-DFT) analyses. The complexes were also screened in vitro for their antiproliferative properties against the MCF-7 breast cancer cell lines by using the MTT assay. Flow cytometric analysis showed that the complexes arrested the cell cycle in the sub G0 phase.

Cleavage of Ru-C(aryl) bond of a four-membered ortho-metalated ruthenium(II) organometallics by mercaptopyrimidine and pyridine-2,6-dicarboxylate ligands: spectroscopic, structural and computational studies

The heterogeneous phase reaction of Ru(η2-RL)(PPh3)2(CO)Cl (1) with 2-mercaptopyrimidine(pymSH) and pyridine-2,6-dicarboxylate(dipic) ligands afforded the complexes of the type Ru(PPh3)(CO)(pymS)2 (2) and Ru(PPh3)2(CO)(dipic) (3) in excellent yield respectively. The chelation of pymS/dipic is attended with the cleavage of Ru-O, Ru-Cl and Ru-C(aryl) bonds and the RL ligand is no longer coordinated with the metal center in the products. The spectral (UV-Vis, IR, 1H NMR) and electrochemical data of the complexes are included. In dichloromethane solution both 2 and 3 display one quasi-reversible RuIII/RuII cyclic voltammetric response with E1/2 in the range 1.15-1.50 V vs Ag/AgCl. Structure determinations of 2 and the solvate 3·CH3CN have revealed distorted octahedral RuCN2S2P coordination sphere for 2 and RuCNO2P2 coordination sphere for 3·CH3CN. For 2 the pairs (P, N), (S, S) and (C, N) define the three trans directions whereas for 3·CH3CN those pairs are (P, P), (C, N) and (O, O). The electronic structures and the absorption spectra of 2 and 3 are also scrutinized by the density functional theory (DFT) and time-dependent density functional theory (TD-DFT) analysis.